#  @3blue1brown 3Blue1Brown 3Blue1Brown posts on YouTube about math, to the, what is, link the most. They currently have [---------] followers and [---] posts still getting attention that total [-------] engagements in the last [--] hours. ### Engagements: [-------] [#](/creator/youtube::UCYO_jab_esuFRV4b17AJtAw/interactions)  - [--] Week [---------] -3.80% - [--] Month [---------] +55% - [--] Months [----------] +23% - [--] Year [----------] +52% ### Mentions: [---] [#](/creator/youtube::UCYO_jab_esuFRV4b17AJtAw/posts_active)  - [--] Week [---] +17% - [--] Month [---] +15% - [--] Months [---] +19% - [--] Year [---] +31% ### Followers: [---------] [#](/creator/youtube::UCYO_jab_esuFRV4b17AJtAw/followers)  - [--] Week [---------] +0.25% - [--] Month [---------] +1% - [--] Months [---------] +7% - [--] Year [---------] +16% ### CreatorRank: [------] [#](/creator/youtube::UCYO_jab_esuFRV4b17AJtAw/influencer_rank)  ### Social Influence **Social category influence** [technology brands](/list/technology-brands) [finance](/list/finance) [social networks](/list/social-networks) [cryptocurrencies](/list/cryptocurrencies) #5861 [travel destinations](/list/travel-destinations) **Social topic influence** [math](/topic/math) #302, [to the](/topic/to-the), [what is](/topic/what-is) #638, [link](/topic/link) #4084, [pi](/topic/pi) #322, [tao](/topic/tao) #110, [how to](/topic/how-to), [intuition](/topic/intuition) #68, [puzzle](/topic/puzzle) #137, [light](/topic/light) #519 **Top accounts mentioned or mentioned by** [@ngvutuan2811](/creator/undefined) [@deepia](/creator/undefined) [@marshallbrunerrf](/creator/undefined) [@thuynganvu](/creator/undefined) [@teobucci](/creator/undefined) [@deye27](/creator/undefined) [@vcubingx](/creator/undefined) [@lazzyprogrammer](/creator/undefined) [@lfwarsen](/creator/undefined) [@wanderloots](/creator/undefined) [@bensyversen](/creator/undefined) [@welchlabs](/creator/undefined) [@cewkins](/creator/undefined) [@artoftheproblem](/creator/undefined) [@aleph0](/creator/undefined) [@hianji](/creator/undefined) [@korakot](/creator/undefined) [@spectralcollective](/creator/undefined) [@independentcode](/creator/undefined) [@dwarkeshpatel](/creator/undefined) **Top assets mentioned** [Bitcoin (BTC)](/topic/bitcoin) ### Top Social Posts Top posts by engagements in the last [--] hours "Taylor series Chapter [--] Essence of calculus Taylor polynomials are incredibly powerful for approximations and analysis. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/taylor-series#thanks Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/calculus Series like this one are funded largely by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Timestamps 0:00 -" [YouTube Link](https://youtube.com/watch?v=3d6DsjIBzJ4) 2017-05-07T14:06Z 8.1M followers, 5M engagements "The paradox of the derivative Chapter [--] Essence of calculus What is an "instantaneous rate of change" when change happens across time Help fund future projects: https://www.patreon.com/3blue1brown This video was supported in part by Art of Problem Solving: https://aops.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/derivatives#thanks Home page: https://www.3blue1brown.com/ Note to illustrate my point for the target audience of a new calculus student I discussed a hypothetical speedometer" [YouTube Link](https://youtube.com/watch?v=9vKqVkMQHKk) 2017-04-29T16:24Z 8.1M followers, 4.3M engagements "Who cares about topology (Old version) Theres now an updated version: https://youtu.be/IQqtsm-bBRU" [YouTube Link](https://youtube.com/watch?v=AmgkSdhK4K8) 2016-11-04T21:48Z 8.1M followers, 3.4M engagements "The Hairy Ball Theorem Unexpected applications and a beautiful proof. Looking for a new career Check out https://3b1b.co/talent Supporters get early access to new videos: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Credits: Senia Sheydvasser: Co-writing and sphere deformation animations made in Blender Paul Dancstep: Those lovely fluffy sphere animations made in Cinema4D Vince Rubinetti: Music Timestamps: 0:00 - To comb a hairy ball 1:24 - Applications 8:46 - The puzzle of one null point 12:12 - The proof" [YouTube Link](https://youtube.com/watch?v=BHdbsHFs2P0) 2026-01-31T14:57Z 8.1M followers, 2.2M engagements "Bayes theorem the geometry of changing beliefs Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks Home page: https://www.3blue1brown.com Here's an interactive version of the main diagram one viewer made: https://srulix.com/projects/bayesgroundstandalone=true The quick proof: https://youtu.be/U_85TaXbeIo Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/" [YouTube Link](https://youtube.com/watch?v=HZGCoVF3YvM) 2019-12-22T14:31Z 8.1M followers, 5.7M engagements "Dot products and duality Chapter [--] Essence of linear algebra Why the formula for dot products matches their geometric intuition. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations we can get a deeper feel for what's going on with the dot product and the connection between its numerical computation and its geometric interpretation. Full series:" [YouTube Link](https://youtube.com/watch?v=LyGKycYT2v0) 2016-08-24T19:20Z 8.1M followers, 3.2M engagements "The hardest problem on the hardest test A difficult Putnam question with an elegant solution. This video was sponsored by Brilliant: https://brilliant.org/3b1b Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/putnam-thanks Home page: https://www.3blue1brown.com/ Solution to the puzzle mentioned at the end: https://brilliant.org/3b1bindicator/ These videos exist thanks to Patreon: https://www.patreon.com/3blue1brown A different write-up of this solution:" [YouTube Link](https://youtube.com/watch?v=OkmNXy7er84) 2017-12-08T15:04Z 8.1M followers, 16.8M engagements "Tips to be a better problem solver Last live lecture Ep. [--] Lockdown live math Tips on problem-solving with examples from geometry trig and probability. Past episodes with integrated quizzes: https://itempool.com/c/3b1b Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Huge huge thanks to Ben Eater: https://www.youtube.com/user/eaterbc And Cam Christensen creator of ItemPool: https://itempool.com/ Notes by Ngn V:" [YouTube Link](https://youtube.com/watch?v=QvuQH4_05LI) 2020-05-22T20:14Z 8.1M followers, 1.4M engagements "Terence Tao on the cosmic distance ladder The Cosmic Distance Ladder: How we learned distances in the heavens. Next part: https://youtu.be/hFMaT9oRbs4 Patreon supporters see early views of new videos: https://www.patreon.com/3blue1brown Artwork by Kurt Bruns Thanks to Paul Dancstep for several animations such as the powers of [--] zoom out and the simulations of shadows on the moon. Terry has kindly cataloged many of the added nuances including a few corrections in this post:" [YouTube Link](https://youtube.com/watch?v=YdOXS_9_P4U) 2025-02-08T13:35Z 8.1M followers, 4.4M engagements "But what is a neural network Deep learning chapter [--] What are the neurons why are there layers and what is the math underlying it Help fund future projects: https://www.patreon.com/3blue1brown Written/interactive form of this series: https://www.3blue1brown.com/topics/neural-networks Additional funding for this project was provided by Amplify Partners For those who want to learn more I highly recommend the book by Michael Nielsen that introduces neural networks and deep learning: https://goo.gl/Zmczdy There are two neat things about this book. First it's available for free so consider joining" [YouTube Link](https://youtube.com/watch?v=aircAruvnKk) 2017-10-05T15:11Z 8.1M followers, 22.8M engagements "Simulating an epidemic Experiments with toy SIR models Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/sir-thanks Home page: https://www.3blue1brown.com Awesome fan-made interactives: https://prajwalsouza.github.io/Experiments/Epidemic-Simulation.html https://learningsim.itch.io/pandemic-spread-simulation Simulations by Harry Stevens at the Washington Post: https://www.washingtonpost.com/graphics/2020/world/corona-simulator/ Simulations by Kevin Simler" [YouTube Link](https://youtube.com/watch?v=gxAaO2rsdIs) 2020-03-27T19:47Z 8.1M followers, 5.4M engagements "Implicit differentiation what's going on here Chapter [--] Essence of calculus Implicit differentiation can feel strange but thought of the right way it makes a lot of sense. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/implicit-differentiation#thanks Home page: https://www.3blue1brown.com Series like this one are funded largely by the community through Patreon where supporters get early access as the series is being produced." [YouTube Link](https://youtube.com/watch?v=qb40J4N1fa4) 2017-05-03T15:38Z 8.1M followers, 2.3M engagements "Integration and the fundamental theorem of calculus Chapter [--] Essence of calculus Intuition for integrals and why they are inverses of derivatives. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/integration#thanks Check out the Art of Problem Solving: https://aops.com/3blue1brown Timestamps: 0:00 - Car example 8:20 - Areas under graphs 11:18 - Fundamental theorem of calculus 16:20 - Recap 17:45 - Negative area 18:55 - Outro Thanks to these" [YouTube Link](https://youtube.com/watch?v=rfG8ce4nNh0) 2017-05-05T15:05Z 8.1M followers, 2.9M engagements "But what is the Riemann zeta function Visualizing analytic continuation Unraveling the enigmatic function behind the Riemann hypothesis Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/zeta-thanks Home page: https://www.3blue1brown.com/ Posters/shirts for this visualization at http://3b1b.co/store Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function Check out some of Vince's other work here:" [YouTube Link](https://youtube.com/watch?v=sD0NjbwqlYw) 2016-12-09T17:50Z 8.1M followers, 5.2M engagements "The other way to visualize derivatives Chapter [--] Essence of calculus A visual for derivatives that generalizes more nicely to topics beyond calculus. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/alt-calc-thanks And by Brilliant: https://brilliant.org/3b1b Home page: https://www.3blue1brown.com Essence of calculus series: http://3b1b.co/calculus Really nice applet made based on this video by Reddit user Larconneur: https://www.geogebra.org/m/rftwacsy Music by" [YouTube Link](https://youtube.com/watch?v=CfW845LNObM) 2018-05-19T14:09Z 8.1M followers, 3.8M engagements "The determinant Chapter [--] Essence of linear algebra The determinant measures how much volumes change during a transformation. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Vietnamese:" [YouTube Link](https://youtube.com/watch?v=Ip3X9LOh2dk) 2016-08-10T22:31Z 8.1M followers, 4.7M engagements "What was Euclid really doing Guest video by Ben Syversen What role were ruler and compass constructions really serving Check out Ben's channel: @bensyversen Interview with the author of this video: https://youtu.be/VohYM99j8e0 Supporters get early views of new videos: https://3b1b.co/support Written produced edited and animated by Ben Syversen Additional editing: Jack Saxon 3d Blender model: Jan-Hendrik Mller Additional Blender help: Thibaut Modrzyk (@Deepia) Illustrations: Alex Zepherin/DonDada Studio Camera: Giacomo Belletti Drums: Jeremy Gustin Additional music from Epidemic Sound Special" [YouTube Link](https://youtube.com/watch?v=M-MgQC6z3VU) 2025-09-18T14:13Z 8.1M followers, 689.7K engagements "Derivative formulas through geometry Chapter [--] Essence of calculus Some common derivative formulas explained with geometric intuition. This video was sponsored by Brilliant: https://brilliant.org/3b1b Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/lessons/derivatives-power-rule#thanks Time stamps: 0:00 Intro 1:38 f(x) = x2 4:41 f(x) = x3 6:54 f(x) = xn "Power Rule" 10:07 f(x) = 1/x 12:36 Sine 16:56 Outro Great video by Think Twice showing this geometric view of the" [YouTube Link](https://youtube.com/watch?v=S0_qX4VJhMQ) 2017-04-30T15:24Z 8.1M followers, 3.5M engagements "Abstract vector spaces Chapter [--] Essence of linear algebra This is really the reason linear algebra is so powerful. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Russian: e-p-h ------------------ 3blue1brown is" [YouTube Link](https://youtube.com/watch?v=TgKwz5Ikpc8) 2016-09-24T19:29Z 8.1M followers, 1.7M engagements "Visualizing the chain rule and product rule Chapter [--] Essence of calculus A visual explanation of what the chain rule and product rule are and why they are true. Help fund future projects: https://www.patreon.com/3blue1brown This video was sponsored by Brilliant: https://brilliant.org/3b1b An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/chain-rule-and-product-rule#thanks Home page: https://www.3blue1brown.com Series like this one are funded largely by the community through Patreon where supporters get early" [YouTube Link](https://youtube.com/watch?v=YG15m2VwSjA) 2017-05-01T15:19Z 8.1M followers, 2.2M engagements "Why is in the normal distribution (beyond integral tricks) Where's the circle And how does it relate to where e(-x2) comes fromHelp fund future projects: https://www.patreon.com/3blue1brown Special thanks to these supporters: https://www.3blue1brown.com/lessons/gaussian-integral#thanks An equally valuable form of support is to simply share the videos. The artwork in this video is by Kurt Bruns who used Midjourney as part of the process for some pieces. I wrote more about the specifics of that process and my thoughts around it here: https://www.patreon.com/posts/thoughts-on-ai-83881719 Here" [YouTube Link](https://youtube.com/watch?v=cy8r7WSuT1I) 2023-04-02T15:30Z 8.1M followers, 2.2M engagements "Cross products Chapter [--] Essence of linear algebra This covers the main geometric intuition behind the 2d and 3d cross products. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ *Note in all the computations here I list the coordinates of the vectors as columns of a matrix but many textbooks put them in the rows of a matrix instead. It makes no difference for the result since the determinant is unchanged after a transpose but given how I've framed most of this" [YouTube Link](https://youtube.com/watch?v=eu6i7WJeinw) 2016-09-01T03:54Z 8.1M followers, 2.3M engagements "Terence Tao continuing historys cleverest cosmological measurements How we know the distances to the planets stars and faraway galaxies. Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support FAQ with added details and corrections: https://terrytao.wordpress.com/2025/02/13/cosmic-distance-ladder-video-with-grant-sanderson-3blue1brown-commentary-and-corrections/ An equally valuable form of support is to simply share the videos. Terry and his collaborator Tanya have an Instagram about the cosmic distance ladder:" [YouTube Link](https://youtube.com/watch?v=hFMaT9oRbs4) 2025-02-23T14:54Z 8.1M followers, 1.4M engagements "But how do AI images and videos actually work Guest video by Welch Labs Diffusion models CLIP and the math of turning text into images Welch Labs Book: https://www.welchlabs.com/resources/imaginary-numbers-book Sections 0:00 - Intro 3:37 - CLIP 6:25 - Shared Embedding Space 8:16 - Diffusion Models & DDPM 11:44 - Learning Vector Fields 22:00 - DDIM 25:25 - Dall E [--] 26:37 - Conditioning 30:02 - Guidance 33:39 - Negative Prompts 34:27 - Outro 35:32 - About guest videos Special Thanks to: Jonathan Ho - Jonathan is the Author of the DDPM paper and the Classifier Free Guidance Paper." [YouTube Link](https://youtube.com/watch?v=iv-5mZ_9CPY) 2025-07-25T12:14Z 8.1M followers, 1.6M engagements "But what is a Laplace Transform Visualizing the most important tool for differential equations. Previous chapter: https://youtu.be/-j8PzkZ70Lg Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Pi creature car artwork by Kurt Bruns Engine animation borrowed with permission from this (excellent) blog: https://ciechanow.ski/internal-combustion-engine/ Timestamps: 0:00 - Understanding the engine 1:16 - Key background ideas 5:41 - Definition" [YouTube Link](https://youtube.com/watch?v=j0wJBEZdwLs) 2025-10-12T11:19Z 8.1M followers, 1.3M engagements "How AI connects text and images From this guest video by @WelchLabs on how diffusion models work: https://youtu.be/iv-5mZ_9CPY Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=j5h9dBtWZXM) 2025-08-21T18:24Z 8.1M followers, 99.5K engagements "Linear combinations span and basis vectors Chapter [--] Essence of linear algebra The fundamental concepts of span linear combinations linear dependence and bases. Help fund future projects: https://www.patreon.com/3blue1brown Thanks to Elo Marie Viennot and Ambros Gleixner from HTW Berlin (www.htw-berlin.de) for contributing German translations and dubbing. Thanks to these viewers for their contributions to translations Arabic: @Cewkins Hazem Hebrew: Omer Tuchfeld Spanish: Juan Carlos Largo Vietnamese: @ngvutuan2811 ------------------ 3blue1brown is a channel about animating math in all senses" [YouTube Link](https://youtube.com/watch?v=k7RM-ot2NWY) 2016-08-06T23:49Z 8.1M followers, 7M engagements "Limits L'Hpital's rule and epsilon delta definitions Chapter [--] Essence of calculus Formal derivatives the epsilon-delta definition and why L'Hpital's rule works. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/limits#thanks Home page: https://www.3blue1brown.com Timestamps 0:00 - Intro 1:17 - Formal definition of derivatives 4:52 - Epsilon delta definition 9:53 - L'Hpital's rule 17:17 - Outro Thanks to these viewers for their contributions to" [YouTube Link](https://youtube.com/watch?v=kfF40MiS7zA) 2017-05-04T15:05Z 8.1M followers, 2.5M engagements "Measuring the earth with Terence Tao From this video: https://youtu.be/YdOXS_9_P4U Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=uT4-WVa-YfU) 2025-02-08T13:35Z 8.1M followers, 597.8K engagements "e(i) in [----] minutes using dynamics DE5 Euler's formula about e to the i pi explained with velocities to positions. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://www.3blue1brown.com Not familiar with the calculus referenced in this video Try taking a look at this one: https://youtu.be/m2MIpDrF7Es Another perspective on this formula from Mathologer: https://youtu.be/-dhHrg-KbJ0 Another perspective from this channel: https://youtu.be/mvmuCPvRoWQ And yet another" [YouTube Link](https://youtube.com/watch?v=v0YEaeIClKY) 2019-07-07T14:08Z 8.1M followers, 3.4M engagements "Newtons fractal (which Newton knew nothing about) Who knew root-finding could be so complicated Next part: https://youtu.be/LqbZpur38nw Special thanks to the following supporters: https://3b1b.co/lessons/newtons-fractal#thanks An equally valuable form of support is to simply share the videos. Thanks to these viewers for their contributions to translations German: Luatic Hebrew: Omer Tuchfeld Portuguese: luiz12apn ------------------ Interactive for this video: https://www.3blue1brown.com/lessons/newtons-fractal On fractal dimension: https://youtu.be/gB9n2gHsHN4 Mathologer on the cubic formula:" [YouTube Link](https://youtube.com/watch?v=-RdOwhmqP5s) 2021-10-12T18:57Z 8.1M followers, 3.2M engagements "What does area have to do with slope Chapter [--] Essence of calculus One view on why integrals and derivatives are inverses. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/area-and-slope#thanks Full series: http://3b1b.co/calculus Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Vietnamese: ngvutuan2811 ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you" [YouTube Link](https://youtube.com/watch?v=FnJqaIESC2s) 2017-05-06T13:53Z 8.1M followers, 1.7M engagements "Change of basis Chapter [--] Essence of linear algebra How do you translate back and forth between coordinate systems that use different basis vectors Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Vietnamese: @ngvutuan2811" [YouTube Link](https://youtube.com/watch?v=P2LTAUO1TdA) 2016-09-11T17:56Z 8.1M followers, 2.4M engagements "Vectors Chapter [--] Essence of linear algebra Beginning the linear algebra series with the basics. Help fund future projects: https://www.patreon.com/3blue1brown Music: https://vincerubinetti.bandcamp.com/track/grants-etude Thanks to Elo Marie Viennot and Ambros Gleixner from HTW Berlin (www.htw-berlin.de) for contributing German translations and dubbing. Thanks also to these viewers for their contributions to the subtitles Arabic: @Cewkins Hazem Bengali: Md Rasheduzzaman Czech: @Chnapak Greek: Nikolaos Tsagkas Hebrew: Omer Tuchfeld Italian: mattiacolucci Spanish: Juan Carlos Largo Thai: own" [YouTube Link](https://youtube.com/watch?v=fNk_zzaMoSs) 2016-08-06T00:05Z 8.1M followers, 11.4M engagements "Transformers the tech behind LLMs Deep Learning Chapter [--] Breaking down how Large Language Models work visualizing how data flows through. Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support --- Here are a few other relevant resources Build a GPT from scratch by Andrej Karpathy https://youtu.be/kCc8FmEb1nY If you want a conceptual understanding of language models from the ground up @vcubingx just started a short series of videos on the topic: https://youtu.be/1il-s4mgNdIsi=XaVxj6bsdy3VkgEX If you're interested in the herculean task of" [YouTube Link](https://youtube.com/watch?v=wjZofJX0v4M) 2024-04-01T19:13Z 8.1M followers, 9.4M engagements "Euler's Formula and Graph Duality A description of planar graph duality and how it can be applied in a particularly elegant proof of Euler's Characteristic Formula. Music: Wyoming [---] by Time For Three Thanks to these viewers for their contributions to translations Marathi: realcalal" [YouTube Link](https://youtube.com/watch?v=-9OUyo8NFZg) 2015-06-21T06:05Z 8.1M followers, 527.4K engagements "The Physics of Euler's Formula Laplace Transform Prelude The simple harmonic oscillator and the fundamental role of complex exponents for ODEs. Next chapter on the Laplace Transform video: https://youtu.be/j0wJBEZdwLs Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Timestamps: 0:00 - Intro 1:51 - Euler's formula explained dynamically 9:27 - The harmonic oscillator 21:08 - General linear equations 22:47 - Motivating the Laplace Transform" [YouTube Link](https://youtube.com/watch?v=-j8PzkZ70Lg) 2025-10-05T13:53Z 8.1M followers, 881.4K engagements "The AI that solved IMO Geometry Problems Guest video by @Aleph0 How AlphaGeometry combines logic and intuition. Check out Aleph0s channel: https://youtube.com/@Aleph0 Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. Home page: https://www.3blue1brown.com Special thanks to Trieu Trinh for fact-checking the script. Blog post on an open-sourced geometry solver: https://harmonic.fun/news#blog-post-geometry AlphaGeometry announcement:" [YouTube Link](https://youtube.com/watch?v=4NlrfOl0l8U) 2025-08-17T13:02Z 8.1M followers, 408.1K engagements "Why colliding blocks compute pi The physics behind one of the most surprising occurrences of pi Next video on Grover's Algorithm: https://youtu.be/RQWpF2Gb-gU Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Next video on Grover's Algorithm: https://youtu.be/RQWpF2Gb-gU The original paper by Gregory Galperin: https://www.maths.tcd.ie/lebed/Galperin.%20Playing%20pool%20with%20pi.pdf Adam Brown's paper on the analogy with Grover's Algorithm: https://arxiv.org/pdf/1912.02207" [YouTube Link](https://youtube.com/watch?v=6dTyOl1fmDo) 2025-03-13T15:36Z 8.1M followers, 5.2M engagements "Why do prime numbers make these spirals Dirichlets theorem and pi approximations A curious pattern approximations for pi and prime distributions. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/spiral-thanks Based on this Math Stack Exchange post: https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers/885894 Want to learn more about rational approximations See this Mathologer video. https://youtu.be/CaasbfdJdJg" [YouTube Link](https://youtube.com/watch?v=EK32jo7i5LQ) 2019-10-08T17:02Z 8.1M followers, 7.5M engagements "Gradient descent how neural networks learn Deep Learning Chapter [--] Cost functions and training for neural networks. Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these supporters: http://3b1b.co/nn2-thanks Written/interactive form of this series: https://www.3blue1brown.com/topics/neural-networks This video was supported by Amplify Partners. For any early-stage ML startup founders Amplify Partners would love to hear from you via 3blue1brown@amplifypartners.com To learn more I highly recommend the book by Michael Nielsen" [YouTube Link](https://youtube.com/watch?v=IHZwWFHWa-w) 2017-10-16T16:48Z 8.1M followers, 8.9M engagements "Can you even imagine [----] Originally written as a supplement to an explanation of the cryptography behind Bitcoin: https://youtu.be/bBC-nXj3Ng4 (An active link is on the bottom of the video player) Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=X4jpqCu-wlA) 2023-12-16T00:00Z 8.1M followers, 2.3M engagements "Why the ancient Greeks rejected heliocentrism From this video on the cosmic distance ladder: https://youtu.be/YdOXS_9_P4U Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=YP1mMXRCnaI) 2025-02-27T15:00Z 8.1M followers, 1.4M engagements "What is Euler's formula actually saying Ep. [--] Lockdown live math What does it mean to compute epi i Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258220129327800320 https://twitter.com/ThuyNganVu/status/1258220541686628353 Not on the "homework" to show that exp(x + y) = exp(x) * exp(y). This gets a little more intricate if you start asking seriously about whether the series really" [YouTube Link](https://youtube.com/watch?v=ZxYOEwM6Wbk) 2020-04-28T19:58Z 8.1M followers, 1.7M engagements "Why is pi here And why is it squared A geometric answer to the Basel problem A most beautiful proof of the Basel problem using light. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/basel-thanks This video was sponsored by Brilliant: https://brilliant.org/3b1b Brilliant's principles list that I referenced: https://brilliant.org/principles/ Get early access and more through Patreon: https://www.patreon.com/3blue1brown The content here was based on a paper" [YouTube Link](https://youtube.com/watch?v=d-o3eB9sfls) 2018-03-02T16:23Z 8.1M followers, 7.2M engagements "Fractals are typically not self-similar An explanation of fractal dimension. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/fractals-thanks And by Affirm: https://www.affirm.com/careers Home page: https://www.3blue1brown.com/ One technical note: It's possible to have fractals with an integer dimension. The example to have in mind is some *very* rough curve which just so happens to achieve roughness level exactly [--]. Slightly rough might be around" [YouTube Link](https://youtube.com/watch?v=gB9n2gHsHN4) 2017-01-27T17:29Z 8.1M followers, 4.5M engagements "But what is a partial differential equation DE2 The heat equation as an introductory PDE. Strogatz's new book: https://amzn.to/3bcnyw0 Special thanks to these supporters: http://3b1b.co/de2thanks An equally valuable form of support is to simply share some of the videos. Timestamps: 0:00 - Introduction 3:29 - Partial derivatives 6:52 - Building the heat equation 13:18 - ODEs vs PDEs 14:29 - The laplacian 16:04 - Book recommendation Typo corrections: - 1:33 - it should be Black-Scholes - 16:21 - it should read "scratch an itch". If anyone asks I purposefully leave at least one typo in each" [YouTube Link](https://youtube.com/watch?v=ly4S0oi3Yz8) 2019-04-21T16:53Z 8.1M followers, 3.1M engagements "Group theory abstraction and the 196883-dimensional monster An introduction to group theory (Minor error corrections below) Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/monster-thanks Timestamps: 0:00 - The size of the monster 0:50 - What is a group 7:06 - What is an abstract group 13:27 - Classifying groups 18:31 - About the monster Errors: *Typo on the "hard problem" at 14:11 it should be a/(b+c) + b/(a+c) + c/(a+b) = [--] *Typo-turned-speako: The" [YouTube Link](https://youtube.com/watch?v=mH0oCDa74tE) 2020-08-19T14:01Z 8.1M followers, 3.7M engagements "Three-dimensional linear transformations Chapter [--] Essence of linear algebra What do 3d linear transformations look like Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------" [YouTube Link](https://youtube.com/watch?v=rHLEWRxRGiM) 2016-08-09T22:01Z 8.1M followers, 2.5M engagements "Solving Wordle using information theory An excuse to teach a lesson on information theory and entropy. These lessons are funded by viewers: https://www.patreon.com/3blue1brown Special thanks to these supporters: https://3b1b.co/lessons/wordle#thanks An equally valuable form of support is to simply share the videos. Contents: 0:00 - What is Wordle 2:43 - Initial ideas 8:04 - Information theory basics 18:15 - Incorporating word frequencies 27:49 - Final performance Original wordle site: https://www.powerlanguage.co.uk/wordle/ Music by Vincent Rubinetti. https://www.vincentrubinetti.com/ Shannon" [YouTube Link](https://youtube.com/watch?v=v68zYyaEmEA) 2022-02-06T13:28Z 8.1M followers, 11.8M engagements "The medical test paradox (well "paradox") A link to the full video about Bayesian thinking is at the bottom of the screen. Or for reference: https://youtu.be/lG4VkPoG3ko Long-to-short editing by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=xIMlJUwB1m8) 2024-01-15T07:00Z 8.1M followers, 11.5M engagements "What makes the natural log "natural" Ep. [--] Lockdown live math All about ln(x). Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1259288683489849344 Errors: At minute [--] the sum should be written with a "." to indicate going to infinity. At minute [--] the exponent should have 1/(2s2) instead of 1/s2 for s to represent standard deviation. At minute [--] an equal sign was mistakenly used in" [YouTube Link](https://youtube.com/watch?v=4PDoT7jtxmw) 2020-05-08T20:22Z 8.1M followers, 1.7M engagements "Complex number fundamentals Ep. [--] Lockdown live math Intro to the geometry complex numbers. Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258219199769440257 Errors: - On the first sketch of a complex plane there is a "2i" written instead of "-2i". - At the end in writing the angle sum identity the last term should be sin(beta) instead of sin(alpha). - During Q9 the terms in" [YouTube Link](https://youtube.com/watch?v=5PcpBw5Hbwo) 2020-04-24T20:31Z 8.1M followers, 2.1M engagements "How might LLMs store facts Deep Learning Chapter [--] Unpacking the multilayer perceptrons in a transformer and how they may store facts Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. AI Alignment forum post from the Deepmind researchers referenced at the video's start: https://www.alignmentforum.org/posts/iGuwZTHWb6DFY3sKB/fact-finding-attempting-to-reverse-engineer-factual-recall Anthropic posts about superposition referenced near the end:" [YouTube Link](https://youtube.com/watch?v=9-Jl0dxWQs8) 2024-08-31T12:11Z 8.1M followers, 1.9M engagements "The Brachistochrone with Steven Strogatz Steven Strogatz and I talk about a famous historical math problem a clever solution and a modern twist. ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to stay posted about new videos subscribe and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more a good place to start is this playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDPHP40bzkb0TKLRPwQGAoC- Various social media stuffs:" [YouTube Link](https://youtube.com/watch?v=Cld0p3a43fU) 2016-04-01T20:27Z 8.1M followers, 1.4M engagements "Where my explanation of Grovers algorithm failed Addressing viewer questions from the last video: https://youtu.be/RQWpF2Gb-gU These lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. The subtitles on this video were done using AI and are likely imperfect but they are open for community corrections at https://criblate.com/ Timestamps: 0:00 - The confusion 1:25 - Example: Sudokus 7:58 - Linearity 14:19 - Is this useful ------------------ These animations are largely made using a custom Python library manim. See the FAQ" [YouTube Link](https://youtube.com/watch?v=Dlsa9EBKDGI) 2025-05-04T11:45Z 8.1M followers, 632.4K engagements "But why is a sphere's surface area four times its shadow The formula is no mere coincidence. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/sphere-thanks Discussion on Reddit: https://www.reddit.com/r/3Blue1Brown/comments/a2gqo0/but_why_is_a_spheres_surface_area_four_times_its/ The first proof goes back to Greek times due to Archimedes who was charmed by the fact that a sphere has 2/3 the volume of a cylinder encompassing it and 2/3 the surface area as" [YouTube Link](https://youtube.com/watch?v=GNcFjFmqEc8) 2018-12-02T20:08Z 8.1M followers, 8.8M engagements "Convolutions Why X+Y in probability is a beautiful mess Adding random variables with connections to the central limit theorem. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. 0:00 - Intro quiz 2:24 - Discrete case diagonal slices 6:49 - Discrete case flip-and-slide 8:41 - The discrete formula 10:58 - Continuous case flip-and-slide 15:53 - Example with uniform distributions 18:42 - Central limit theorem 20:50 - Continuous case diagonal slices 25:26 - Returning to the intro quiz Thanks to these viewers for their" [YouTube Link](https://youtube.com/watch?v=IaSGqQa5O-M) 2023-06-27T15:08Z 8.1M followers, 965.3K engagements "How (and why) to raise e to the power of a matrix DE6 General exponentials love Schrdinger and more. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/mat-exp-thanks Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ The Romeo-Juliet example is based on this essay by Steven Strogatz: http://www.stevenstrogatz.com/essays/loves-me-loves-me-not-do-the-math The book shown at the start is Vladimir Arnold's" [YouTube Link](https://youtube.com/watch?v=O85OWBJ2ayo) 2021-04-01T15:50Z 8.1M followers, 3.5M engagements "But what is quantum computing (Grover's Algorithm) Qubits state vectors and Grover's algorithm for search. Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. The subtitles on this video were done using AI and are likely imperfect but they are open for community corrections at https://criblate.com/ Adam Brown's paper on the connection between Grover's Algorithm and block collisions: https://arxiv.org/pdf/1912.02207 If you want to learn the relevant underlying quantum mechanics here a" [YouTube Link](https://youtube.com/watch?v=RQWpF2Gb-gU) 2025-04-30T12:32Z 8.1M followers, 3.2M engagements "Fractal charm: Space filling curves A montage of space-filling curves meant as a supplement to the Hilbert curve video. https://youtu.be/3s7h2MHQtxc These animations are largely made using a custom python library manim. See the FAQ comments here: https://www.3blue1brown.com/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ You can find code for specific videos and projects here: https://github.com/3b1b/videos/ Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld" [YouTube Link](https://youtube.com/watch?v=RU0wScIj36o) 2016-01-17T01:43Z 8.1M followers, 2.1M engagements "Solving the heat equation DE3 Boundary conditions and set up for how Fourier series are useful. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/de3thanks Home page: https://www.3blue1brown.com More about the heat equation with a derivation in terms of slope corresponding to heat flow from MIT OCW: https://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006/lecture-notes/heateqni.pdf If you want to learn more about" [YouTube Link](https://youtube.com/watch?v=ToIXSwZ1pJU) 2019-06-16T16:31Z 8.1M followers, 1.6M engagements "Matrix multiplication as composition Chapter [--] Essence of linear algebra Multiplying two matrices represents applying one transformation after another. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer" [YouTube Link](https://youtube.com/watch?v=XkY2DOUCWMU) 2016-08-08T22:20Z 8.1M followers, 4.1M engagements "Why probability of [--] does not mean impossible Probabilities of probabilities part [--] An introduction to probability density functions Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/thanks Curious about measure theory This does require some background in real analysis but if you want to dig in here is a textbook by the always-great Terence Tao. https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf Also for the real analysis buffs" [YouTube Link](https://youtube.com/watch?v=ZA4JkHKZM50) 2020-04-12T15:41Z 8.1M followers, 3.4M engagements "How wiggling charges give rise to light Explaining the barber pole effect from the last video: https://youtu.be/QCX62YJCmGk Next video on the index of refraction: https://youtu.be/KTzGBJPuJwM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. This Feynman lecture describes this particular approach in more detail: https://www.feynmanlectures.caltech.edu/I_28.html Timestamps: 0:00 - Recap 0:44 - The radiation law 6:10 - Simulating the radiation law 11:11 - Why the diagonal stripes 16:31 - Why does it twist Thanks to" [YouTube Link](https://youtube.com/watch?v=aXRTczANuIs) 2023-09-01T13:39Z 8.1M followers, 1.8M engagements "But how does bitcoin actually work The math behind cryptocurrencies. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/btc-thanks This video was also funded with help from Protocol Labs: https://protocol.ai/join/ Some people have asked if this channel accepts contributions in cryptocurrency form. As a matter of fact it does: http://3b1b.co/crypto ENS: 3b1b.eth [----] video: https://youtu.be/S9JGmA5_unY Music by Vincent Rubinetti:" [YouTube Link](https://youtube.com/watch?v=bBC-nXj3Ng4) 2017-07-07T16:51Z 8.1M followers, 18.2M engagements "How pi was almost [--------]. In some of his notes Euler used to represent [----]. So why did we adopt [----]. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com The idea for this video as well as the live shots came from Ben Hambrecht with the writing and animating done by Grant Sanderson. Special thanks to: - University Library Basel for letting us rummage through their historical collection - Martin Mattmller from the Bernoulli-Euler center for helpful discussion -" [YouTube Link](https://youtube.com/watch?v=bcPTiiiYDs8) 2018-03-14T13:05Z 8.1M followers, 1.8M engagements "Visualizing the 4d numbers Quaternions How to think about this 4d number system in our 3d space. Part 2: https://youtu.be/zjMuIxRvygQ Interactive version of these visuals: https://eater.net/quaternions Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/quaternion-thanks Quanta article on quaternions: https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/ The math of Alice in Wonderland:" [YouTube Link](https://youtube.com/watch?v=d4EgbgTm0Bg) 2018-09-06T14:59Z 8.1M followers, 5.4M engagements "Cramer's rule explained geometrically Chapter [--] Essence of linear algebra This rule seems random to many students but it has a beautiful reason for being true. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ---- If you want to contribute translated subtitles or to help review those that have already been made by others and need approval you can click the gear icon in the video" [YouTube Link](https://youtube.com/watch?v=jBsC34PxzoM) 2019-03-17T04:35Z 8.1M followers, 1.5M engagements "Essence of linear algebra preview Home page: https://www.3blue1brown.com/ This introduces the "Essence of linear algebra" series aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear algebra course. Error corrections: - At one point I mistakenly allude to calculators using the Taylor expansion of sine for its computations when in reality most use CORDIC (or something like it). - Around [--] seconds in there is a typo in how the determinant is written which should be ad - bc Full series: http://3b1b.co/eola Future series like this are funded by the" [YouTube Link](https://youtube.com/watch?v=kjBOesZCoqc) 2016-08-05T01:01Z 8.1M followers, 2.7M engagements "What's so special about Euler's number e Chapter [--] Essence of calculus What is e And why are exponentials proportional to their own derivatives Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/eulers-number#thanks Home page: https://www.3blue1brown.com Timestamps 0:00 - Motivating example 3:57 - Deriving the key proportionality property 7:36 - What is e 8:48 - Natural logs 11:23 - Writing ect is a choice Corrections: 9:40 - I meant to say "*the" [YouTube Link](https://youtube.com/watch?v=m2MIpDrF7Es) 2017-05-02T15:09Z 8.1M followers, 5M engagements "This puzzle is trickier than it seems From this full video: https://youtu.be/piJkuavhV50 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=nAT-MCsJeik) 2024-11-19T19:06Z 8.1M followers, 1.4M engagements "Divergence and curl: The language of Maxwell's equations fluid flow and more Visualizing two core operations in calculus. (Small error correction below) Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/divcurl-thanks My work on this topic at Khan Academy: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives Timestamps 0:00 - Vector fields 2:15 - What is divergence 4:31 - What is curl 5:47 - Maxwell's equations 7:36 - Dynamic" [YouTube Link](https://youtube.com/watch?v=rB83DpBJQsE) 2018-06-21T18:34Z 8.1M followers, 5.1M engagements "The ladybug clock puzzle This is the first in a set of monthly puzzles curated by Peter Winkler. This one was originally suggested by Richard Stanley. You can sign up to hear his description of the answer at http://momath.org/mindbenders Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=t3jZ2xGOvYg) 2026-01-16T14:16Z 8.1M followers, 702.4K engagements "Backpropagation calculus Deep Learning Chapter [--] Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/nn3-thanks Written/interactive form of this series: https://www.3blue1brown.com/topics/neural-networks This one is a bit more symbol-heavy and that's actually the point. The goal here is to represent in somewhat more formal terms the intuition for how backpropagation works in part [--] of the series hopefully providing some connection between that video and other texts/code" [YouTube Link](https://youtube.com/watch?v=tIeHLnjs5U8) 2017-11-03T14:08Z 8.1M followers, 3.7M engagements "Inverse matrices column space and null space Chapter [--] Essence of linear algebra How to think about linear systems of equations geometrically. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld" [YouTube Link](https://youtube.com/watch?v=uQhTuRlWMxw) 2016-08-15T22:00Z 8.1M followers, 3.6M engagements "The impossible chessboard puzzle An information puzzle with an interesting twist Solution on Stand-up Maths: https://youtu.be/as7Gkm7Y7h4 Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/chess-thanks Home page: https://www.3blue1brown.com Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ 0:00 Introduction 3:58 Visualizing the two-square case 5:46 Visualizing the three-square case 12:19 Proof that" [YouTube Link](https://youtube.com/watch?v=wTJI_WuZSwE) 2020-07-05T18:50Z 8.1M followers, 2.2M engagements "The meaning within the Mandelbrot set The full video dives deeper into the field of math studying this called holomorphic dynamics: https://youtu.be/LqbZpur38nw Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=y9BK--OxZpY) 2024-11-24T17:00Z 8.1M followers, 936.1K engagements "Error correction is incredible A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/X8jsijhllIA Editing from long-form to short by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=yZMw2rOKYwE) 2023-12-10T00:00Z 8.1M followers, 5.5M engagements "But what is the Central Limit Theorem A visual introduction to probability's most important theorem Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these lovely supporters: https://www.3blue1brown.com/lessons/clt#thanks An equally valuable form of support is to simply share the videos. Galton board shown in the video: https://amzn.to/3ZJK8nY Thanks to these viewers for their contributions to translations Hebrew: David Bar-On Omer Tuchfeld Hindi: Tapender1 Italian: anna-lombardo ----------------- Timestamps 0:00 - Introduction 1:53 - A simplified Galton Board" [YouTube Link](https://youtube.com/watch?v=zeJD6dqJ5lo) 2023-03-14T18:36Z 8.1M followers, 4.4M engagements "Ellipses have multiple definitions how are these the same A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/pQa_tWZmlGs The full video this comes from proves why slicing a cone gives the same shape as the two-thumbtacks-and-string construction which is beautiful. Editing from long-form to short by Dawid Koodziej" [YouTube Link](https://youtube.com/watch?v=-3jPW_TGATI) 2024-01-19T19:00Z 8M followers, 63.4K engagements "A challenging puzzle about subset sums A link to the full video answering this is at the bottom of the screen. Or for reference: https://youtu.be/bOXCLR3Wric Thanks to these viewers for their contributions to translations French: GiveMeChocolate Hindi: rajeshwar-pandey Spanish: Yago Iglesias" [YouTube Link](https://youtube.com/watch?v=-ikRg-OfFHc) 2024-01-22T06:00Z 7.8M followers, 1M engagements "Binary Hanoi and Sierpinski part [--] Binary counting can solve the towers of Hanoi puzzle and if this isn't surprising enough it can lead to a method for finding a curve that fills Sierpinski's triangle (which I get to in part 2). Thanks to Desmos for their help in supporting this video. They're hiring and anyone interested should check out https://www.desmos.com/careers Thanks to all Patreon supporters as well you can support and get early access to future "Essence of" series here: https://www.patreon.com/3blue1brown I also want to give a special shoutout to the following patrons: CrypticSwarm" [YouTube Link](https://youtube.com/watch?v=2SUvWfNJSsM) 2016-11-25T17:30Z 7.9M followers, 768.2K engagements "What is a group A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/mH0oCDa74tE That video introduces group theory and the monster group. Editing from long-form to short by Dawid Koodziej" [YouTube Link](https://youtube.com/watch?v=3KbiJ-z0j44) 2023-12-27T19:00Z 8M followers, 156.3K engagements "Simulating the electric field and a moving charge A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/aXRTczANuIs" [YouTube Link](https://youtube.com/watch?v=81QNyDnYtg0) 2024-01-26T06:00Z 8M followers, 1.3M engagements "tum khud Hi socho chhod dungi to apna aur apne bete ka kharcha #trending #viralvideo #subscribe tum khud Hi socho chhod dungi to apna aur apne bete ka kharcha #trending #viralvideo #subscribe" [YouTube Link](https://youtube.com/watch?v=9sTtAFArYe0) 2025-12-17T17:11Z 100K followers, 281.6K engagements "Why does light slowing imply a bend (Beyond the tank/car analogy) A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/Cz4Q4QOuoo8 That video answers various viewer questions about the index of refraction. Editing from long-form to short by Dawid Koodziej" [YouTube Link](https://youtube.com/watch?v=DWnb2UUlqd0) 2024-01-11T00:00Z 7.9M followers, 1.4M engagements "How are holograms possible 3d scenes on 2d film and a diffraction lesson along the way. Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. Hologram credits: The Microscope is by Walter Spierings [----] Donations Hologram by Cherry Optical Holography Lucy in a Tin Hat is by Patrick Keown Boyd [----] The Star Wars-themed Direct-Write Digital Holograms were produced by Zebra Imaging. The 'Shakespeare' embossed animated integral hologram was made by Applied Holographics. Walter Spierings who" [YouTube Link](https://youtube.com/watch?v=EmKQsSDlaa4) 2024-10-05T15:31Z 8.1M followers, 6.1M engagements "Order from chaos A link to the full video on the Central Limit Theorem is at the bottom of the screen. Or for reference: https://youtu.be/zeJD6dqJ5lo Thanks to Dawid Koodziej from long-to-short editing" [YouTube Link](https://youtube.com/watch?v=GOSezO0CHss) 2023-12-15T00:00Z 7.9M followers, 14.1M engagements "The simpler quadratic formula Ep. [--] Lockdown live math Another view on the quadratic formula. Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258217451323416577 Po Shen Loh on quadratics: https://www.youtube.com/watchv=ZBalWWHYFQc Welch Labs on imaginary numbers: https://www.youtube.com/playlistlist=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF Mistakes (there will always be mistakes): At minute" [YouTube Link](https://youtube.com/watch?v=MHXO86wKeDY) 2020-04-17T20:04Z 8M followers, 1.5M engagements "How They Fool Ya (live) Math parody of Hallelujah Happy Tau Day Here's something a bit out of the ordinary for you. Thanks to Matt Parker @standupmaths for the invite. More about the event: https://festivalofthespokennerd.com/show/an-evening-of-unnecessary-detail/ Thanks to Tim Blais @acapellascience for helpful thoughts on the song including the key phrase "How they fool ya" Video about the circle pattern https://youtu.be/YtkIWDE36qU Video about those integrals https://youtu.be/851U557j6HE Video about the primes in base [--] https://youtu.be/jhObLT1Lrfo Timestamps: 0:00 - Intro 1:20 - Song" [YouTube Link](https://youtube.com/watch?v=NOCsdhzo6Jg) 2023-06-28T19:17Z 7.8M followers, 1.2M engagements "I'm still astounded this is true A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/6dTyOl1fmDo Sliding blocks on a frictionless plane counter their collisions and. Thanks to Dawid Koodziej for editing together this short" [YouTube Link](https://youtube.com/watch?v=P11ykXwx4-k) 2023-12-07T01:11Z 8M followers, 66M engagements "All possible pythagorean triples visualized To understand all pythagorean triples like (3 [--] 5) (5 [--] 13) etc. look to complex numbers. This video was sponsored by Remix: https://www.remix.com/jobs Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/triples-thanks Home page: https://www.3blue1brown.com/ Regarding the brief reference to Fermat's Last Theorem what should be emphasized is that it refers to *positive* integers. You can of course have things like" [YouTube Link](https://youtube.com/watch?v=QJYmyhnaaek) 2017-05-26T17:58Z 7.8M followers, 4.1M engagements "Q&A with Grant Sanderson (3blue1brown) To commemorate crossing [---] subscribers. FAQ from home page: https://www.3blue1brown.com/faq Subreddit: https://www.reddit.com/r/3blue1brown AMC problem shown on screen: https://artofproblemsolving.com/wiki/index.phptitle=2002_AMC_12A_Problems/Problem_22 Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to stay posted on new videos subscribe:" [YouTube Link](https://youtube.com/watch?v=Qe6o9j4IjTo) 2018-08-24T16:34Z 7.9M followers, 860.3K engagements "The quick proof of Bayes' theorem Including some added words on independence. Main video: https://youtu.be/HZGCoVF3YvM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks ------------------ These animations are largely made using manim a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out I feel compelled to warn you that it's not the most well-documented tool and it has many other quirks you might" [YouTube Link](https://youtube.com/watch?v=U_85TaXbeIo) 2019-12-22T14:45Z 8M followers, 561.5K engagements "Don't let it fool you A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/YtkIWDE36qU Thanks to Dawid Koodziej for editing together this short" [YouTube Link](https://youtube.com/watch?v=VFbyGEZLMZw) 2023-12-07T01:11Z 8M followers, 18M engagements "Why this puzzle is impossible Featuring quite a few science/math YouTubers Vihart response: https://youtu.be/CruQylWSfoU Brought to you by you: http://3b1b.co/mug-thanks And by Brilliant: https://brilliant.org/3b1b Timestamps: 0:00 - Featured guests 4:30 - Why it's "impossible" 12:20 - Surfaces with holes 16:27 - Your challenge 17:35 - Sponsorship and end Thanks to all the following channels for participating. Standup Maths https://www.youtube.com/user/standupmaths Wendover Productions https://www.youtube.com/user/Wendoverproductions Welch Labs: https://www.youtube.com/user/Taylorns34" [YouTube Link](https://youtube.com/watch?v=VvCytJvd4H0) 2017-12-23T16:43Z 7.9M followers, 3.3M engagements "For anyone who might not know how links in shorts work YouTube disabled links in descriptions and comments but we can add links to videos on the shorts player itself. For reference the one at the bottom of this screen is https://youtu.be/KTzGBJPuJwM" [YouTube Link](https://youtube.com/watch?v=W1gW1dHRsOw) 2023-12-21T00:15Z 7.9M followers, 268.6K engagements "Hologram preview Full video: https://youtu.be/EmKQsSDlaa4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=W3-kpRz-e1Q) 2024-10-11T14:00Z 8.1M followers, 67.1K engagements "What "Follow Your Dreams" Misses Harvey Mudd Commencement Speech [----] I had the pleasure of being invited to give Harvey Mudd's commencement speech this year. Reposted here with permission from the University Timestamps: 0:00 - End of Harriet Nembhard's introduction 0:45 - The clich 2:28 - The shifting goal 5:57 - Action precedes motivation 7:02 - Timing 10:47 - Know your influence 12:05 - Anticipate change ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. If you're reading the bottom of a video description I'm guessing you're more interested" [YouTube Link](https://youtube.com/watch?v=W3I3kAg2J7w) 2024-05-18T14:50Z 8M followers, 1.5M engagements "The most absurd product I've made Because why not make a pi creature neck pillow Available at 3b1b.co/store" [YouTube Link](https://youtube.com/watch?v=Y0Aqc174FMM) 2025-11-24T16:30Z 8M followers, 143K engagements "Hamming codes part 2: The one-line implementation A cleaner perspective on Hamming error correction codes Part 1: https://youtu.be/X8jsijhllIA Watch Ben Eater's video: https://youtu.be/h0jloehRKas Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/hamming-thanks You can read Hamming's own perspective on his discovery of these codes in chapter [--] of "The Art of Doing Science and Engineering". https://amzn.to/3lwcnmh Heavily related is the chessboard puzzle" [YouTube Link](https://youtube.com/watch?v=b3NxrZOu_CE) 2020-09-04T15:36Z 7.9M followers, 962.3K engagements "Binary Hanoi and Sierpinski part [--] After seeing how binary counting can solve the towers of Hanoi puzzle in the last video here we see how ternary counting solve a constrained version of the puzzle and how this gives a way to walk through a Sierpinski triangle graph structure. Thanks to Desmos for their help in supporting this video. They're hiring and anyone interested should check out https://www.desmos.com/careers Thanks to all Patreon supporters as well you can support and get early access to future "Essence of" series here: https://www.patreon.com/3blue1brown I also want to give a" [YouTube Link](https://youtube.com/watch?v=bdMfjfT0lKk) 2016-11-25T17:30Z 7.9M followers, 330.5K engagements "A pretty reason why Gaussian + Gaussian = Gaussian A visual trick to compute the sum of two normally distributed variables. 3b1b mailing list: https://3blue1brown.substack.com/ Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these supporters: https://www.3blue1brown.com/lessons/gaussian-convolution#thanks For the technically curious who want to go deeper here's a proof of the central limit theorem using Moment generating functions: https://www.cs.toronto.edu/yuvalf/CLT.pdf And here's a nice discussion of methods using entropy:" [YouTube Link](https://youtube.com/watch?v=d_qvLDhkg00) 2023-07-11T15:53Z 7.9M followers, 937.1K engagements "The power tower puzzle Ep. [--] Lockdown live math A fun puzzle stemming from repeated exponentiation. Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Notes by Ngn V: https://twitter.com/ThuyNganVu/status/1261014161464516608s=20 Play along on Desmos: https://www.desmos.com/calculator/nul32eaaa9 Related videos. Calculus series: https://www.youtube.com/playlistlist=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr In particular look at: https://youtu.be/CfW845LNObM Numberphile on" [YouTube Link](https://youtube.com/watch?v=elQVZLLiod4) 2020-05-12T19:59Z 7.8M followers, 935.4K engagements "The medical test paradox and redesigning Bayes' rule About Likelihood Ratios also sometimes called Bayes Factors*. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/bayes-factor-thanks Home page: https://www.3blue1brown.com The book by my friend Matt Cook about paradoxes mentioned at the end: https://amzn.to/3aBrEzg On the topic I can't help also mentioning another paradox book I'm rather fond of by Bunch: https://amzn.to/3mBDSKE Another video on Bayes'" [YouTube Link](https://youtube.com/watch?v=lG4VkPoG3ko) 2020-12-22T17:42Z 8M followers, 1.4M engagements "Q&A #2 + Net Neutrality Nuance Questions: http://3b1b.co/questions Answers: https://youtu.be/1nxF19qDBQ0 Full net neutrality video: https://youtu.be/hKD-lBrZ_Gg Ben Eater's channel: https://www.youtube.com/user/eaterbc First Q&A Answers: https://youtu.be/8r5WKpK9-m8 CGPGrey's (excellent) video on Net Neutrality: https://youtu.be/wtt2aSV8wdw ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to stay posted on new videos subscribe and click the bell to receive notifications (if you're into that). If" [YouTube Link](https://youtube.com/watch?v=liL66CApESk) 2017-12-14T15:57Z 7.9M followers, 153.5K engagements "A beautiful international math olympiad problem The link to the full video is at the bottom of the screen. For reference here it is: https://youtu.be/M64HUIJFTZM" [YouTube Link](https://youtube.com/watch?v=teYL0Er4c3g) 2024-01-03T07:00Z 8.1M followers, 2.7M engagements "Using topology for discrete problems The Borsuk-Ulam theorem and stolen necklaces Solving a discrete math puzzle using topology I was originally inspired to cover this thanks to a Quora post by Alon Amit Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/borsuk-thanks Home page: https://www.3blue1brown.com Want more fair division math fun Check out this Mathologer video https://youtu.be/7s-YM-kcKME (Seriously Mathologer is great) These videos are supported" [YouTube Link](https://youtube.com/watch?v=yuVqxCSsE7c) 2018-11-18T14:09Z 8.1M followers, 974.7K engagements "How to count to [----] on two hands Typically when we think of counting on two hands we count up to [--] but fingers can contain much more information than that This video shows how to think about counting in binary" [YouTube Link](https://youtube.com/watch?v=1SMmc9gQmHQ) 2015-09-18T21:53Z 8.1M followers, 461.4K engagements "This tests your understanding of light The barber pole effect The barber pole effect of shining polarized light into sugar water. Next video: https://youtu.be/aXRTczANuIs Steve Mould's video on the topic: https://youtu.be/975r9a7FMqc Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. Thanks to Quinn Brodsky for setting up the demo and to the MIT Physics Instructional Resources Lab for their help and materials especially Josh Wolfe and Caleb Bonyun. Thanks to these viewers for their contributions to translations" [YouTube Link](https://youtube.com/watch?v=QCX62YJCmGk) 2023-09-01T13:13Z 8.1M followers, 1.4M engagements "Linear transformations and matrices Chapter [--] Essence of linear algebra Quite possibly the most important idea for understanding linear algebra. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld" [YouTube Link](https://youtube.com/watch?v=kYB8IZa5AuE) 2016-08-07T21:39Z 8.1M followers, 6.7M engagements "Researchers thought this was a bug (Borwein integrals) A pattern of integrals that all equal pi.until they don't. Next video on convolutions: https://youtu.be/KuXjwB4LzSA John Baez has a really fun article about this: https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/ Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these patrons: https://3b1b.co/lessons/borwein#thanks An equally valuable form of support is to simply share the videos. Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Hindi:" [YouTube Link](https://youtube.com/watch?v=851U557j6HE) 2022-11-04T15:54Z 8.1M followers, 4.6M engagements "Binomial distributions Probabilities of probabilities part [--] Part 2: https://youtu.be/ZA4JkHKZM50 Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/beta1-thanks John Cook post: https://www.johndcook.com/blog/2011/09/27/bayesian-amazon/ ------------------ These animations are largely made using manim a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out I feel compelled to warn you that it's not the most" [YouTube Link](https://youtube.com/watch?v=8idr1WZ1A7Q) 2020-03-15T18:28Z 8.1M followers, 2.6M engagements "e to the pi i a nontraditional take (old version) Wait There's an improved version: https://youtu.be/mvmuCPvRoWQ Also for the calculus-savvy you'll prefer this one: https://youtu.be/v0YEaeIClKY Home page: https://www.3blue1brown.com/ The enigmatic equation epi i = [---] is usually explained using Taylor's formula during a calculus class. This video offers a different perspective which involves thinking about numbers as actions and about ex as something which turns one action into another. For more information on viewing exponential functions in this new light check out this article:" [YouTube Link](https://youtube.com/watch?v=F_0yfvm0UoU) 2015-03-05T06:15Z 8.1M followers, 2.8M engagements "How to derive a formula for A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/NaL_Cb42WyY That video explores how this question leads to a quandary on prime numbers and how a pattern in primes allows for a clean final answer. Editing from long-form to short by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=R1e7aHBKLnM) 2023-12-25T19:00Z 8.1M followers, 1.1M engagements "Why 5/3 is a fundamental constant for turbulence Some mathematical order amidst the chaos of turbulence. Vortex rings with Physics Girl: https://youtu.be/N7d_RWyOv20 Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/turbulence-thanks Home page: https://www.3blue1brown.com Thanks to Dan Walsh for many great ideas and thanks to Mike Hansen for many helpful conversations. Error correction: I meant to describe Kolmogorov as a 20th-century mathematician not" [YouTube Link](https://youtube.com/watch?v=_UoTTq651dE) 2018-11-07T20:20Z 8.1M followers, 807.8K engagements "Olympiad level counting (Generating functions) A lesson on generating functions and clever uses of complex numbers for counting Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. Special thanks: https://3b1b.co/lessons/subsets-puzzle#thanks Artwork by Kurt Burns Music by Vince Rubinetti Nice writeup and video giving solutions to the exercises at the end by Benjamin Hackl https://benjamin-hackl.at/blog/2022/06/generating-functions-3b1b.html https://youtu.be/9SzwfM-S9sk [---] Combinatorial problems by Titu Andreescu" [YouTube Link](https://youtube.com/watch?v=bOXCLR3Wric) 2022-05-23T15:55Z 8.1M followers, 2.3M engagements "What makes a great math explanation SoME2 results Winners and honorable mentions for the SoME2 contest Playlist of all entries: https://www.youtube.com/playlistlist=PLnQX-jgAF5pTZXPiD8ciEARRylD9brJXU Help fund future projects: https://www.patreon.com/3blue1brown Post with links to all entries: https://www.3blue1brown.com/blog/some2 **Winners** Clear Crystal Conundrums A Multifaceted Intro to Group Theory https://explanaria.github.io/crystalgroups/ The Lore of Calculus https://youtu.be/5M2RWtD4EzI How Realistic CGI Works (And How To Do It Way Faster) https://www.youtube.com/watchv=gsZiJeaMO48" [YouTube Link](https://youtube.com/watch?v=cDofhN-RJqg) 2022-10-01T19:23Z 8.1M followers, 800.4K engagements "The limit of limiting arguments A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/VYQVlVoWoPY That video gives multiple examples of lying with visual proofs Editing from the original video into this short by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=tjIOqIr80ns) 2023-12-23T00:00Z 8.1M followers, 2.1M engagements "Seeing with sound A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/3s7h2MHQtxc Editing from the original video into this short by Dawid Koodziej" [YouTube Link](https://youtube.com/watch?v=1tLvj_HSjPk) 2023-12-08T00:00Z 5.9M followers, 652.6K engagements "The barber pole effect A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/QCX62YJCmGk Filming by Quinn Brodsky Editing from long-form to short by Dawid Koodziej" [YouTube Link](https://youtube.com/watch?v=31xm81m0iYs) 2023-12-09T00:00Z 7.6M followers, 511K engagements "Summer of Math Exposition #4 Teachers I'd love to hear from you Make a math explainer get feedback and receive prizes: https://some.3b1b.co Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. ------------------ These animations are largely made using a custom Python library manim. See the FAQ comments here: https://3b1b.co/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ All code for specific videos is visible here: https://github.com/3b1b/videos/" [YouTube Link](https://youtube.com/watch?v=3foYyPDp0Ho) 2025-05-05T15:00Z 7.3M followers, 88.4K engagements "A simple image convolution A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/KuXjwB4LzSA That video introduces convolutions as used in image processing probability and signal processing. Editing from long-form to short by Dawid Koodziej" [YouTube Link](https://youtube.com/watch?v=4xWpQe3G9qI) 2023-12-12T00:00Z 7.2M followers, 1.1M engagements "25 Math explainers you may enjoy SoME3 results Playlist of all entries: https://www.youtube.com/playlistlist=PLnQX-jgAF5pQS2GUFCsatSyZkSH7e8UM8 All non-video entries: https://some.3b1b.co/non-videos Thank you to Jane Street both for funding the event and providing eager and able guest judges to the final stages of the process. Organization and logistics were handled by James Schloss aka @LeiosLabs Web development by Frdric Crozatier 0:00 - The event 1:34 - Pixel Art Anti-aliasing 2:26 - The Enola Gay 3:40 - Pitch shifter 4:14 - Cayley Graphs 4:51 - Longest Increasing Subsequence 5:49 - Matrix" [YouTube Link](https://youtube.com/watch?v=6a1fLEToyvU) 2023-10-07T14:28Z [--] followers, 537K engagements "The dynamics of e(i) A fuller version of this explanation also including the reason we care about complex exponents in the first place: https://youtu.be/-j8PzkZ70Lg" [YouTube Link](https://youtube.com/watch?v=8Qi_a9rGNtk) 2025-10-11T21:28Z 7.8M followers, 68.3K engagements "Q&A with Grant windy walk edition Thank you for [---] subscribers. Store: http://3b1b.co/store Links to things discussed below The Bit Player https://thebitplayer.com/ The Idea Factory https://amzn.to/325PY6W The Information A History A Theory A Flood https://amzn.to/2QhfUtR You can read about Lorenz in "Chaos" also by James Gleick https://amzn.to/3tcXtVF Anthropocene reviewed https://www.wnycstudios.org/podcasts/anthropocene-reviewed Hardcore history https://www.dancarlin.com/ The Numberphile podcast https://www.numberphile.com/podcast Recent Quanta article on the eigenvector discovery" [YouTube Link](https://youtube.com/watch?v=Agbh95KyWxY) 2019-11-23T01:00Z 6.6M followers, 455.1K engagements "The space of musical note pairs Full video: https://youtu.be/IQqtsm-bBRU" [YouTube Link](https://youtube.com/watch?v=BCgqR4yh6fo) 2025-01-08T21:11Z 6.9M followers, 769.4K engagements "The DP-3T algorithm for contact tracing (with Nicky Case) This is a video adaptation of a post by my friend Nicky Case: https://ncase.me/contact-tracing/ New post by Nicky on COVID-19: https://ncase.me/covid-19/ Consider supporting their work: https://www.patreon.com/ncase/ Supporters of this video: https://3b1b.co/ctracing-thanks DP-3T Whitepaper: https://github.com/DP-3T/documents/blob/master/DP3T%20White%20Paper.pdf Full repo: https://github.com/DP-3T Where did the number 60% come from https://science.sciencemag.org/content/early/2020/04/09/science.abb6936 The specific figure is Figure 3" [YouTube Link](https://youtube.com/watch?v=D__UaR5MQao) 2020-05-14T15:00Z 7.8M followers, 386.5K engagements "Snell's law proof using springs This is a supplement to the Brachistochrone video proving Snell's law with a clever little argument by Mark Levi" [YouTube Link](https://youtube.com/watch?v=Iq1a_KJTWJ8) 2016-04-01T20:27Z 7.5M followers, 218.1K engagements "The chessboard and coins puzzle Video with the solution: https://youtu.be/as7Gkm7Y7h4 3b1b on a meta-puzzle: https://youtu.be/wTJI_WuZSwE (These description links aren't active in the shorts player but you can follow the link on the bottom of the video screen itself) This comes from a collaboration I did with Stand-up Maths where on his channel we covered the solution and here on 3blue1brown we analyze a meta-puzzle. Editing from long-form to short by Dawid Koodziej This comes from a collaboration I did with Stand-up Maths where on his channel we covered the solution and here on 3blue1brown" [YouTube Link](https://youtube.com/watch?v=NQFIU5Exjuo) 2023-12-10T00:00Z 7.1M followers, 4.3M engagements "When being beautifully wrong leads to discovery Full video: https://youtu.be/YdOXS_9_P4U Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=TZAC0WFemvE) 2025-02-28T15:00Z 8.1M followers, 2.5M engagements "A cute probability fact (part 1) max(rand() rand()) has the same effect as sqrt(rand()) The next short explains why: https://youtube.com/shorts/sNWDjbaT208 See Matt Parker's video for more: https://youtu.be/ga9Qk38FaHM" [YouTube Link](https://youtube.com/watch?v=UJfTBQRY2Cs) 2024-09-10T15:42Z 6.6M followers, 343.8K engagements "Other math channels you'd enjoy Think Twice: https://www.youtube.com/channel/UC9yt3wz-6j19RwD5m5f6HSg LeiosOS: https://www.youtube.com/user/LeiosOS Welch Labs: https://www.youtube.com/user/Taylorns34 Infinity plus one: https://infinityplusonemath.wordpress.com/ Check out the ones on relativity https://infinityplusonemath.wordpress.com/2017/03/11/a-mathematical-intro-to-special-relativity/ Music by Enoch Kim https://soundcloud.com/themusemaker ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to" [YouTube Link](https://youtube.com/watch?v=VcgJro0sTiM) 2018-06-27T16:29Z [--] followers, 240.1K engagements "Winding numbers and domain coloring An algorithm for numerically solving certain 2d equations. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/winding-thanks Writing and animations by Sridhar Ramesh with editing and narration by Grant Sanderson. Even though we described how winding numbers can be used to solve 2d equations at a high level it's worth pointing out that there are a few details missing for if you wanted to actually implement this. For" [YouTube Link](https://youtube.com/watch?v=b7FxPsqfkOY) 2018-03-24T14:42Z 7.2M followers, 978.8K engagements "How colliding blocks act like a beam of light.to compute pi. The third and final part of the block collision sequence. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/clacks-thanks Home page: https://www.3blue1brown.com Error correction: I wrote the answer as floor(pi/theta) when really it should be ceiling(pi/theta) - [--] t account for values of theta perfectly dividing pi. For example the case of equal masses gives an angle of pi/4 and [--] total clacks." [YouTube Link](https://youtube.com/watch?v=brU5yLm9DZM) 2019-02-03T16:23Z 7.2M followers, 1.4M engagements "Music And Measure Theory A connection between a classical puzzle about rational numbers and what makes music harmonious. Thanks to these viewers for their contributions to translations German: Josh Russian: e-p-h" [YouTube Link](https://youtube.com/watch?v=cyW5z-M2yzw) 2015-10-04T02:14Z 7.8M followers, 1.7M engagements "Why do colliding blocks compute pi Even prettier solution: https://youtu.be/brU5yLm9DZM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/clacks-thanks Home page: https://www.3blue1brown.com Many of you shared solutions attempts and simulations with me this last week. I loved it You all are the best. Here are just two of my favorites. By a channel STEM cell: https://youtu.be/ils7GZqp_iE By Doga Kurkcuoglu:" [YouTube Link](https://youtube.com/watch?v=jsYwFizhncE) 2019-01-20T16:40Z 7.1M followers, 7.3M engagements "A cute probability fact (part 3) Why max(rand() rand()) is the same as sqrt(rand()) See Matt Parker's video for more: https://youtu.be/ga9Qk38FaHM" [YouTube Link](https://youtube.com/watch?v=lpzUZDefha0) 2024-09-10T15:42Z 6.6M followers, 222.4K engagements "Make math videos Summer of Math Exposition announcement Announcement for the [----] Summer of Math Exposition Details: https://3b1b.co/SoME1 Podcast/New channel: https://www.youtube.com/GrantSanderson Things referenced through the video James Schloss: https://www.youtube.com/user/LeiosOS Free will theorem: https://www.ams.org/notices/200902/rtx090200226p.pdf Kolmogorov complexity and primes: https://people.cs.uchicago.edu/fortnow/papers/kaikoura.pdf Tadashi Tokieda talk: https://youtu.be/tQQ3oiB32GI Boarbarktree: https://www.youtube.com/channel/UCFeIEAkqvS4fJMTwUtF4OFw Mathologer:" [YouTube Link](https://youtube.com/watch?v=ojjzXyQCzso) 2021-07-16T18:39Z 7.2M followers, 764.4K engagements "Infinite Lighthouses and A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/d-o3eB9sfls" [YouTube Link](https://youtube.com/watch?v=p9i3cYMQtBY) 2023-12-21T00:00Z 7.1M followers, 2.2M engagements "A cute probability fact (part 2) How do think about max(rand() rand()) The next short finishes the explanation: https://youtube.com/shorts/lpzUZDefha0" [YouTube Link](https://youtube.com/watch?v=sNWDjbaT208) 2024-09-10T15:42Z 6.6M followers, 105.1K engagements "Pure Fourier series animation montage Because why not Learn the math behind this: https://youtu.be/r6sGWTCMz2k If you're curious about the number of vectors used for each animation: - Eighth note: [---] - Sigma: [---] - Britain: [---] - Fourier drawing: [---] - Nail and Gear: [---] - Treble clef: [---] - Hilbert curve: [---] (relatively small given the detail which is why it looks puzzley) - Seattle: [---] These animations are made using manim a scrappy open source python library: https://github.com/3b1b/manim If you want to check it out I feel compelled to warn you that it's not the most well-documented" [YouTube Link](https://youtube.com/watch?v=-qgreAUpPwM) 2019-07-03T04:05Z 8.1M followers, 702.9K engagements "The twirling tiles puzzle Full video: https://youtu.be/piJkuavhV50 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=0W243LGSJFU) 2024-11-13T18:01Z 8.1M followers, 257.7K engagements "Higher order derivatives Chapter [--] Essence of calculus A very quick primer on the second derivative third derivative etc. Next chapter: https://youtu.be/3d6DsjIBzJ4 Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Italian: hi-anji Vietnamese: ngvutuan2811 ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to stay posted about new videos subscribe and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see" [YouTube Link](https://youtube.com/watch?v=BLkz5LGWihw) 2017-05-07T14:05Z 8.1M followers, 888.2K engagements "Zooming out by powers of [--] From this video: https://youtu.be/YdOXS_9_P4U Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=C8baNzpnZ7o) 2025-03-26T18:37Z 8.1M followers, 2.8M engagements "Answering viewer questions about refraction Why bending how can light go "faster" than light and more Lessons are primarily funded directly by viewers who get early access to new videos: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Much of the last video as well as this one is based on the following Feynman Lecture: https://www.feynmanlectures.caltech.edu/I_31.html Looking Glass Universe videos on the refractive index: https://youtu.be/uo3ds0FVpXssi=Q12Rgz9vN1JMo_di Timestamps: 0:00 - Why slowing implies bending 3:36 - Recap for how slowing" [YouTube Link](https://youtube.com/watch?v=Cz4Q4QOuoo8) 2023-12-03T11:35Z 8.1M followers, 1.1M engagements "2021 Summer of Math Exposition results Take a look at the full playlist (really): https://www.youtube.com/watchv=fJWnA4j0_ho&list=PLnQX-jgAF5pTkwtUuVpqS5tuWmJ-6ZM-Z Blog post with more details: https://3b1b.co/some1-results Thanks as always to the supporters of this channel for helping to make this whole project possible: http://3b1b.co/thanks ------------------ Typo at 2:00 it should read "Burkard Polster" Videos and posts mentioned in this video. That weird light at the bottom of a mug ENVELOPES https://youtu.be/fJWnA4j0_ho Hiding Images in Plain Sight: The Physics Of Magic Windows" [YouTube Link](https://youtube.com/watch?v=F3Qixy-r_rQ) 2021-10-23T20:25Z 8.1M followers, 833.7K engagements "Newtons Fractal is beautiful Full video: https://youtu.be/-RdOwhmqP5s" [YouTube Link](https://youtube.com/watch?v=LOulCFdVOGY) 2024-11-16T16:53Z 8.1M followers, 216.3K engagements "A quick trick for computing eigenvalues Chapter [--] Essence of linear algebra How to write the eigenvalues of a 2x2 matrix just by looking at it. Need a refresher on eigenvalues https://youtu.be/PFDu9oVAE-g Thanks to Tim for the jingle: https://www.youtube.com/acapellascience Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. Special thanks to these supporters: https://3b1b.co/quick-eigen-thanks Lockdown math lecture talking about the mean product formula: https://youtu.be/MHXO86wKeDY Timestamps: 0:00 - Background" [YouTube Link](https://youtube.com/watch?v=e50Bj7jn9IQ) 2021-05-07T21:39Z 8.1M followers, 1.3M engagements "Fourier series A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/r6sGWTCMz2k That video tells the story of how this concept was originally invented to solve the heat equation. Thanks to Dawid Koodziej for editing together this short Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=nXIHYB0Gp70) 2023-12-08T00:00Z 8.1M followers, 2.4M engagements "Triangle of Power Alternate notation for powers logs and roots. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. (This is the corrected version of the one I put out a month or so ago in which my animation for all the inverse operations was incorrect) Here's a sketch from the math redditer Cosmologicon showing how this might be usual with practical space considerations: http://i.imgur.com/hAeJokq.jpg This original comes from an answer to a math exchange post by Alex Jordan which you can find here:" [YouTube Link](https://youtube.com/watch?v=sULa9Lc4pck) 2016-06-26T05:51Z 8.1M followers, 835.7K engagements "Euler's Formula Poem A poem about why e to the pi i equals [---] based on this video: http://youtu.be/F_0yfvm0UoU Full text of the poem here: http://3blue1brown.com/poems/epii Music: "Sundays" by Time for Three http://www.tf3.com/" [YouTube Link](https://youtube.com/watch?v=zLzLxVeqdQg) 2015-03-05T06:15Z 8.1M followers, 184.4K engagements "The barber pole optical mystery Series exploring optics: https://www.youtube.com/watchv=QCX62YJCmGk&list=PLZHQObOWTQDMKqfyUvG2kTlYt-QQ2x-ui Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=0TdBP9m4R74) 2025-01-06T15:37Z 8.1M followers, 949.3K engagements "Thinking through double slits Extracted from this video about holograms: https://youtu.be/EmKQsSDlaa4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=DgMhayP2NPU) 2024-12-26T16:48Z 8.1M followers, 630K engagements "Exponential growth and epidemics A primer on exponential and logistic growth Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/covid-thanks Home page: https://www.3blue1brown.com Excellent visualization of this kind of growth from Minutephysics and Aatish Bhatia: https://www.youtube.com/watchv=54XLXg4fYsc Data source: https://www.worldometers.info/coronavirus/coronavirus-cases/#case-tot-outchina Some have (quite rightfully) commented on how you shouldn't" [YouTube Link](https://youtube.com/watch?v=Kas0tIxDvrg) 2020-03-08T16:58Z 8.1M followers, 6.2M engagements "Temperature in LLMs This comes from a full video breaking down how LLMs work. The link is on the bottom of the screen (in the shorts feed at least) or here for reference: https://youtu.be/wjZofJX0v4M Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=XsLK3tPy9SI) 2024-04-28T15:22Z 8.1M followers, 366K engagements "Incomplete open cubes Full video: https://youtu.be/_BrFKp-U8GI Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=1lZpowy21Gc) 2025-09-07T12:25Z 8.1M followers, 219.3K engagements "Hilbert's Curve: Is infinite math useful Space-filling curves and the connection between infinite and finite math. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com Supplement with more space-filling curve fun: https://youtu.be/RU0wScIj36o For more information on sight-via sound this paper involving rewiring a ferret's retinas to its auditory cortex is particularly thought-provoking: http://phy.ucsf.edu/houde/coleman/sur2.pdf Alternatively here is the NYT summary:" [YouTube Link](https://youtube.com/watch?v=3s7h2MHQtxc) 2017-07-21T15:33Z 8.1M followers, 2.4M engagements "The Wallis product for pi proved geometrically A geometric proof of a famous Wallis product for pi. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/wallis-thanks If you want to dive into the relevant ideas required to make this proof more rigorous the relevant search term is "dominated convergence". https://en.wikipedia.org/wiki/Dominated_convergence_theorem Here's a good blog post on the topic: https://www.math3ma.com/blog/dominated-convergence-theorem" [YouTube Link](https://youtube.com/watch?v=8GPy_UMV-08) 2018-04-20T18:59Z 8.1M followers, 912.3K engagements "How Earth's size was computed by Eratosthenes From this video: https://youtu.be/YdOXS_9_P4U Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=9s0srZneJ38) 2025-02-12T15:00Z 8.1M followers, 288.1K engagements "Definition of a "bit" in information theory A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/v68zYyaEmEA That video describes using information theory to write a bot that plays Wordle Editing from long-form to short by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=BTryyW7gqg4) 2024-01-02T00:00Z 8.1M followers, 237.4K engagements "Cross products in the light of linear transformations Chapter [--] Essence of linear algebra Why the formula for cross products matches the geometric intuition. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ For anyone who wants to understand the cross-product more deeply this video shows how it relates to a certain linear transformation via duality. This perspective gives a very elegant explanation of why the traditional computation of a dot product corresponds to" [YouTube Link](https://youtube.com/watch?v=BaM7OCEm3G0) 2016-09-01T03:54Z 8.1M followers, 1.5M engagements "Holograms are wild (full video linked above) Full video: https://youtu.be/EmKQsSDlaa4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=DnjATyPuFFk) 2024-10-05T15:35Z 8.1M followers, 2.1M engagements "Sphere surface area proof sketch Full video: https://youtu.be/GNcFjFmqEc8" [YouTube Link](https://youtube.com/watch?v=EPDZTLavmcg) 2024-11-17T16:00Z 8.1M followers, 1.6M engagements "Why Laplace transforms are so useful Studying the forced harmonic oscillator by taking a Laplace transform and studying its poles. Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Chapter on the Laplace Transform: https://youtu.be/j0wJBEZdwLs Chapter on the S-plane and Simple Harmonic Motion: https://youtu.be/-j8PzkZ70Lg Timestamps: 0:00 - Opening puzzle 1:06 - Key properties of a Laplace Transform 3:29 - Qualitative analysis with Laplace" [YouTube Link](https://youtube.com/watch?v=FE-hM1kRK4Y) 2025-11-05T13:09Z 8.1M followers, 633.8K engagements "How word vectors encode meaning This comes from a full video dissecting how LLMs work. In the shorts player you can click the link at the bottom of the screen or for reference: https://youtu.be/wjZofJX0v4M" [YouTube Link](https://youtube.com/watch?v=FJtFZwbvkI4) 2024-04-11T16:23Z 8.1M followers, 3.4M engagements "How prisms work (full video linked above) A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/KTzGBJPuJwM There I wanted to dig deeper to understand light slows down and why this would depend on the color. Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=GSIuXqgPsnY) 2023-12-07T01:31Z 8.1M followers, 8.4M engagements "The most unexpected answer to a counting puzzle Solution: https://youtu.be/6dTyOl1fmDo Light-based solution: https://youtu.be/brU5yLm9DZM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/clacks-thanks New to this channel It's all about teaching math visually. Take a look and see if there's anything you'd like to learn. NY Times blog post about this problem: https://wordplay.blogs.nytimes.com/2014/03/10/pi/ The original paper by Gregory Galperin:" [YouTube Link](https://youtube.com/watch?v=HEfHFsfGXjs) 2019-01-13T16:12Z 8.1M followers, 14.5M engagements "Imaginary interest rates Ep. [--] Lockdown live math Compound interest e and how it relates to circles. Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Great Mathologer video: https://youtu.be/-dhHrg-KbJ0 Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258221677990703105 https://twitter.com/ThuyNganVu/status/1258222002889875457 My other videos on imaginary exponents: https://youtu.be/v0YEaeIClKY https://youtu.be/mvmuCPvRoWQ Mistakes:" [YouTube Link](https://youtube.com/watch?v=IAEASE5GjdI) 2020-05-01T20:11Z 8.1M followers, 948.2K engagements "This open problem taught me what topology is The inscribed square/rectangle problem solved using Mbius strips and Klein bottles. Playlist with more neat proofs: https://www.youtube.com/playlistlist=PLZHQObOWTQDPSKntUcMArGheySM4gL7wS Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. This argument was originally by Herbert Vaughan appearing for examples in this issue of the Topology Proceedings. https://topology.nipissingu.ca/tp/reprints/v06/tp06107.pdf The on-screen argument for" [YouTube Link](https://youtube.com/watch?v=IQqtsm-bBRU) 2024-12-24T17:50Z 8.1M followers, 2.1M engagements "Backpropagation intuitively Deep Learning Chapter [--] What's actually happening to a neural network as it learns Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/nn3-thanks Written/interactive form of this series: https://www.3blue1brown.com/topics/neural-networks And by CrowdFlower: http://3b1b.co/crowdflower Home page: https://www.3blue1brown.com/ The following video is sort of an appendix to this one. The main goal with the follow-on video is to show the" [YouTube Link](https://youtube.com/watch?v=Ilg3gGewQ5U) 2017-11-03T14:03Z 8.1M followers, 5.9M engagements "The Triangle Of Power The referenced stack exchange post by usename 2'5 9'2 http://math.stackexchange.com/questions/30046/alternative-notation-for-exponents-logs-and-roots" [YouTube Link](https://youtube.com/watch?v=JNVZK4ofW-Y) 2024-11-15T15:58Z 8.1M followers, 569.6K engagements "The topology of two-note chords Based on a construction in this video: https://youtu.be/IQqtsm-bBRU Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=K-pGGb0f3tc) 2025-01-30T15:00Z 8.1M followers, 1.3M engagements "LLMs are next-word predictors Full video: https://youtu.be/wjZofJX0v4M Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=KHEtJUlpqcg) 2024-11-04T15:24Z 8.1M followers, 209.3K engagements "But why would light "slow down" Visualizing Feynman's lecture on the refractive index How the index of refraction arises and why it depends on color (as seen with a prism) Quotebook Notebooks: https://3b1b.co/store These lessons are primarily funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. This video is largely based on the following Feynmann lecture https://www.feynmanlectures.caltech.edu/I_31.html Looking Glass Universe videos on the index of refraction: https://youtu.be/uo3ds0FVpXs The explanation for why the phase of a" [YouTube Link](https://youtube.com/watch?v=KTzGBJPuJwM) 2023-11-30T18:42Z 8.1M followers, 2.7M engagements "But what is a convolution Discrete convolutions from probability to image processing and FFTs. Video on the continuous case: https://youtu.be/IaSGqQa5O-M Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these supporters: https://3b1b.co/lessons/convolutions#thanks An equally valuable form of support is to simply share the videos. Other videos I referenced Live lecture on image convolutions for the MIT Julia lab https://youtu.be/8rrHTtUzyZA Lecture on Discrete Fourier Transforms https://youtu.be/g8RkArhtCc4 Reducible video on FFTs https://youtu.be/h7apO7q16V0" [YouTube Link](https://youtube.com/watch?v=KuXjwB4LzSA) 2022-11-18T16:00Z 8.1M followers, 3.6M engagements "Large Language Models explained briefly A light intro to LLMs chatbots pretraining and transformers. Dig deeper here: https://www.youtube.com/playlistlist=PLZHQObOWTQDNU6R1_67000Dx_ZCJB-3pi Technical details as a talk: https://youtu.be/KJtZARuO3JY This was made for an exhibit at the Computer History Museum: https://computerhistory.org/ Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support No secret end-screen vlog for this one the end-screen real estate was all full ------------------ These animations are largely made using a custom Python library" [YouTube Link](https://youtube.com/watch?v=LPZh9BOjkQs) 2024-11-20T15:07Z 8.1M followers, 5.4M engagements "Beyond the Mandelbrot set an intro to holomorphic dynamics An intro to holomorphic dynamics the study of iterated complex functions. Video on Newton's fractal: https://youtu.be/-RdOwhmqP5s Special thanks to these supporters: https://3b1b.co/lessons/holomorphic-dynamics#thanks Extra special thanks to Sergey Shemyakov of Aix-Marseille University for helpful conversations and for introducing me to this phenomenon. Introduction to Fatou sets and Julia sets including a discussion of Montel's theorem and its consequences: http://www.math.stonybrook.edu/scott/Papers/India/Fatou-Julia.pdf Numberphile" [YouTube Link](https://youtube.com/watch?v=LqbZpur38nw) 2021-10-16T12:39Z 8.1M followers, 1.8M engagements "The inscribed square problem Full video: https://youtu.be/IQqtsm-bBRU Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=LuVUnd0C07U) 2024-12-24T18:46Z 8.1M followers, 4.6M engagements "The unexpectedly hard windmill question (2011 IMO Q2) The famous (infamous) "windmill" problem on the [----] IMO Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/windmillthanks Home page: https://www.3blue1brown.com The author of this problem was Geoff Smith. You can find the full list of problems considered for the IMO that year together with their solutions here: https://www.imo-official.org/problems/IMO2011SL.pdf You can find data for past IMO results" [YouTube Link](https://youtube.com/watch?v=M64HUIJFTZM) 2019-08-04T17:03Z 8.1M followers, 5.7M engagements "Measuring the speed of light using Jupiter's moons From this video with Terry Tao: https://youtu.be/hFMaT9oRbs4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=M6LUPYsjods) 2025-04-07T15:57Z 8.1M followers, 2.4M engagements "The more general uncertainty principle regarding Fourier transforms The meaning of the uncertainty principle in the context of Fourier transforms Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/uncertainty-thanks For more on quantum mechanical wave functions I highly recommend this video by udiprod: https://youtu.be/p7bzE1E5PMY Minute physics on special relativity: https://youtu.be/1rLWVZVWfdY Main video on the Fourier transform" [YouTube Link](https://youtube.com/watch?v=MBnnXbOM5S4) 2018-02-25T00:25Z 8.1M followers, 2.3M engagements "Some light quantum mechanics (with minutephysics) The math of superposition and quantum states. Minutephysics channel: https://www.youtube.com/user/minutephysics Help fund future projects: https://www.patreon.com/3blue1brown This video was sponsored by Brilliant: https://brilliant.org/3b1b An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/light-quantum-thanks Huge thanks to my friend Evan Miyazono both for encouraging me to do this project and for helping me understand many things along the way. This is a simple" [YouTube Link](https://youtube.com/watch?v=MzRCDLre1b4) 2017-09-13T14:06Z 8.1M followers, 2.2M engagements "Pi hiding in prime regularities A story of pi primes complex numbers and how number theory braids them together. Mathologer on why 4k + 1primes break down as sums of squares: https://youtu.be/DjI1NICfjOk Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/leibniz-thanks Home page: https://www.3blue1brown.com/ For those of you curious about the finer details here's a writeup from the viewer Daniel Flores justifying the final approximation:" [YouTube Link](https://youtube.com/watch?v=NaL_Cb42WyY) 2017-05-19T15:41Z 8.1M followers, 2.8M engagements "Eigenvectors and eigenvalues Chapter [--] Essence of linear algebra A visual understanding of eigenvectors eigenvalues and the usefulness of an eigenbasis. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com Full series: https://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support A solution to the puzzle at the end:" [YouTube Link](https://youtube.com/watch?v=PFDu9oVAE-g) 2016-09-15T18:22Z 8.1M followers, 6M engagements "A bizarre probability fact I learned this from Matt Parker who then made a full video: https://youtu.be/ga9Qk38FaHM" [YouTube Link](https://youtube.com/watch?v=Pny70rNPJLk) 2024-11-12T23:09Z 8.1M followers, 1.8M engagements "How secure is [---] bit security How hard is it to find a 256-bit hash just by guessing and checking Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Several people have commented about how [----] would be the maximum number of attempts not the average. This depends on the thing being attempted. If it's guessing a private key you are correct but for something like guessing which input to a hash function gives the desired output (as in bitcoin mining for example) which" [YouTube Link](https://youtube.com/watch?v=S9JGmA5_unY) 2017-07-08T14:19Z 8.1M followers, 3.7M engagements "These integrals all equal until. A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/851U557j6HE These are known as Borwein integrals Editing from long-form to short by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=VS9yOhwtVDY) 2023-12-11T00:00Z 8.1M followers, 829.4K engagements "How to lie using visual proofs Three false proofs and what lessons they teach. New notebooks: https://store.dftba.com/collections/3blue1brown/products/mathematical-quotebook-notebook Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. Here's a nice short video on the false pi = [--] proof https://www.youtube.com/watchv=6Qnfd5dRyf4 Time stamps: 0:00 - Fake sphere proof 1:39 - Fake pi = [--] proof 5:16 - Fake proof that all triangles are isosceles 9:54 - Sphere "proof" explanation 15:09 - pi = [--] "proof" explanation 16:57 -" [YouTube Link](https://youtube.com/watch?v=VYQVlVoWoPY) 2022-07-03T15:03Z 8.1M followers, 4.2M engagements "The essence of calculus What might it feel like to invent calculus Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/lessons/essence-of-calculus#thanks In this first video of the series we see how unraveling the nuances of a simple geometry question can lead to integrals derivatives and the fundamental theorem of calculus. Thanks to these viewers for their contributions to translations Dutch: @LFWarsen Lauri Warsen Hebrew: Imri Omer Tuchfeld Hindi: Vinayak Hungarian:" [YouTube Link](https://youtube.com/watch?v=WUvTyaaNkzM) 2017-04-28T15:58Z 8.1M followers, 11.2M engagements "But what are Hamming codes The origin of error correction A discovery-oriented introduction to error correction codes. Part 2: https://youtu.be/b3NxrZOu_CE Ben Eater:'s take: https://youtu.be/h0jloehRKas Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/hamming-thanks Heavily related is the chessboard puzzle I did with Matt Parker: https://youtu.be/as7Gkm7Y7h4 You can read Hamming's own perspective on his discovery of these codes in chapter [--] of "The Art" [YouTube Link](https://youtube.com/watch?v=X8jsijhllIA) 2020-09-04T15:32Z 8.1M followers, 3M engagements "What does it feel like to invent math An exploration of infinite sums from convergent to divergent including a brief introduction to the 2-adic metric all themed on that cycle between discovery and invention in math. Home page: https://www.3blue1brown.com/ Music: Legions (Reverie) by Zoe Keating Thanks to these viewers for their contributions to translations Italian: Marco Fantozzi Thai: @korakot own doggoVV ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to stay posted about new videos" [YouTube Link](https://youtube.com/watch?v=XFDM1ip5HdU) 2015-08-14T01:20Z 8.1M followers, 4.6M engagements "Testing your intuition for quantum computing Full video: https://youtu.be/RQWpF2Gb-gU Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=XX8mjBXBqz8) 2025-04-30T12:32Z 8.1M followers, 1.3M engagements "This pattern breaks but for a good reason Moser's circle problem An apparent pattern that breaks and the reason behind it. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. This is a remake of one of the earliest videos on the channel. It's such a wonderful problem and the audio/pacing in earlier videos was really suboptimal so I wanted to freshen it up a little here. Timestamps 0:00 - The pattern 2:20 - Counting chords 4:03 - Counting intersection points 6:20 - Euler's characteristic formula 11:30 - Connection" [YouTube Link](https://youtube.com/watch?v=YtkIWDE36qU) 2023-07-02T04:41Z 8.1M followers, 2.9M engagements "Exploration & Epiphany Guest video by Paul Dancstep Sol LeWitt's "Incomplete Open Cubes" and rediscovering Burnside's lemma in group theory An interview with the author of this video: https://youtu.be/JEeM2ABUMoo Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. Home page: https://www.3blue1brown.com Thanks to the Wadsworth Atheneum for granting permission to use LeWitt's notebooks. Talks by Paul you can find online: What is Category Theory: https://youtu.be/eXBwU9ieLL0 How to Predict" [YouTube Link](https://youtube.com/watch?v=_BrFKp-U8GI) 2025-09-07T12:25Z 8.1M followers, 472.1K engagements "How to measure nearby galaxies From this video: https://youtu.be/hFMaT9oRbs4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=aQwEJKWATlE) 2025-04-20T19:36Z 8.1M followers, 180.8K engagements "Measuring the distance to Venus without radar From this video with Terry Tao: https://youtu.be/hFMaT9oRbs4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=aw-8BhCilj0) 2025-04-08T13:45Z 8.1M followers, 428.4K engagements "The dynamics of e(i) A fuller version of this explanation also including the reason we care about complex exponents in the first place: https://youtu.be/-j8PzkZ70Lg Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue" [YouTube Link](https://youtube.com/watch?v=bnjKwiUg-kw) 2025-10-12T12:40Z 8.1M followers, 1.1M engagements "Logarithm Fundamentals Ep. [--] Lockdown live math Back to the basics with logarithms. Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Triangle of power: https://youtu.be/sULa9Lc4pck Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258222677573001219 Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ The live question setup with stats on-screen is powered by Itempool." [YouTube Link](https://youtube.com/watch?v=cEvgcoyZvB4) 2020-05-05T20:36Z 8.1M followers, 1.2M engagements Limited data mode. Full metrics available with subscription: lunarcrush.com/pricing
@3blue1brown 3Blue1Brown
3Blue1Brown posts on YouTube about math, to the, what is, link the most. They currently have [---------] followers and [---] posts still getting attention that total [-------] engagements in the last [--] hours.
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Social Influence
Social category influence technology brands finance social networks cryptocurrencies #5861 travel destinations
Social topic influence math #302, to the, what is #638, link #4084, pi #322, tao #110, how to, intuition #68, puzzle #137, light #519
Top accounts mentioned or mentioned by @ngvutuan2811 @deepia @marshallbrunerrf @thuynganvu @teobucci @deye27 @vcubingx @lazzyprogrammer @lfwarsen @wanderloots @bensyversen @welchlabs @cewkins @artoftheproblem @aleph0 @hianji @korakot @spectralcollective @independentcode @dwarkeshpatel
Top assets mentioned Bitcoin (BTC)
Top Social Posts
Top posts by engagements in the last [--] hours
"Taylor series Chapter [--] Essence of calculus Taylor polynomials are incredibly powerful for approximations and analysis. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/taylor-series#thanks Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/calculus Series like this one are funded largely by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Timestamps 0:00 -"
YouTube Link 2017-05-07T14:06Z 8.1M followers, 5M engagements
"The paradox of the derivative Chapter [--] Essence of calculus What is an "instantaneous rate of change" when change happens across time Help fund future projects: https://www.patreon.com/3blue1brown This video was supported in part by Art of Problem Solving: https://aops.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/derivatives#thanks Home page: https://www.3blue1brown.com/ Note to illustrate my point for the target audience of a new calculus student I discussed a hypothetical speedometer"
YouTube Link 2017-04-29T16:24Z 8.1M followers, 4.3M engagements
"Who cares about topology (Old version) Theres now an updated version: https://youtu.be/IQqtsm-bBRU"
YouTube Link 2016-11-04T21:48Z 8.1M followers, 3.4M engagements
"The Hairy Ball Theorem Unexpected applications and a beautiful proof. Looking for a new career Check out https://3b1b.co/talent Supporters get early access to new videos: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Credits: Senia Sheydvasser: Co-writing and sphere deformation animations made in Blender Paul Dancstep: Those lovely fluffy sphere animations made in Cinema4D Vince Rubinetti: Music Timestamps: 0:00 - To comb a hairy ball 1:24 - Applications 8:46 - The puzzle of one null point 12:12 - The proof"
YouTube Link 2026-01-31T14:57Z 8.1M followers, 2.2M engagements
"Bayes theorem the geometry of changing beliefs Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks Home page: https://www.3blue1brown.com Here's an interactive version of the main diagram one viewer made: https://srulix.com/projects/bayesgroundstandalone=true The quick proof: https://youtu.be/U_85TaXbeIo Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/"
YouTube Link 2019-12-22T14:31Z 8.1M followers, 5.7M engagements
"Dot products and duality Chapter [--] Essence of linear algebra Why the formula for dot products matches their geometric intuition. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations we can get a deeper feel for what's going on with the dot product and the connection between its numerical computation and its geometric interpretation. Full series:"
YouTube Link 2016-08-24T19:20Z 8.1M followers, 3.2M engagements
"The hardest problem on the hardest test A difficult Putnam question with an elegant solution. This video was sponsored by Brilliant: https://brilliant.org/3b1b Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/putnam-thanks Home page: https://www.3blue1brown.com/ Solution to the puzzle mentioned at the end: https://brilliant.org/3b1bindicator/ These videos exist thanks to Patreon: https://www.patreon.com/3blue1brown A different write-up of this solution:"
YouTube Link 2017-12-08T15:04Z 8.1M followers, 16.8M engagements
"Tips to be a better problem solver Last live lecture Ep. [--] Lockdown live math Tips on problem-solving with examples from geometry trig and probability. Past episodes with integrated quizzes: https://itempool.com/c/3b1b Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Huge huge thanks to Ben Eater: https://www.youtube.com/user/eaterbc And Cam Christensen creator of ItemPool: https://itempool.com/ Notes by Ngn V:"
YouTube Link 2020-05-22T20:14Z 8.1M followers, 1.4M engagements
"Terence Tao on the cosmic distance ladder The Cosmic Distance Ladder: How we learned distances in the heavens. Next part: https://youtu.be/hFMaT9oRbs4 Patreon supporters see early views of new videos: https://www.patreon.com/3blue1brown Artwork by Kurt Bruns Thanks to Paul Dancstep for several animations such as the powers of [--] zoom out and the simulations of shadows on the moon. Terry has kindly cataloged many of the added nuances including a few corrections in this post:"
YouTube Link 2025-02-08T13:35Z 8.1M followers, 4.4M engagements
"But what is a neural network Deep learning chapter [--] What are the neurons why are there layers and what is the math underlying it Help fund future projects: https://www.patreon.com/3blue1brown Written/interactive form of this series: https://www.3blue1brown.com/topics/neural-networks Additional funding for this project was provided by Amplify Partners For those who want to learn more I highly recommend the book by Michael Nielsen that introduces neural networks and deep learning: https://goo.gl/Zmczdy There are two neat things about this book. First it's available for free so consider joining"
YouTube Link 2017-10-05T15:11Z 8.1M followers, 22.8M engagements
"Simulating an epidemic Experiments with toy SIR models Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/sir-thanks Home page: https://www.3blue1brown.com Awesome fan-made interactives: https://prajwalsouza.github.io/Experiments/Epidemic-Simulation.html https://learningsim.itch.io/pandemic-spread-simulation Simulations by Harry Stevens at the Washington Post: https://www.washingtonpost.com/graphics/2020/world/corona-simulator/ Simulations by Kevin Simler"
YouTube Link 2020-03-27T19:47Z 8.1M followers, 5.4M engagements
"Implicit differentiation what's going on here Chapter [--] Essence of calculus Implicit differentiation can feel strange but thought of the right way it makes a lot of sense. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/implicit-differentiation#thanks Home page: https://www.3blue1brown.com Series like this one are funded largely by the community through Patreon where supporters get early access as the series is being produced."
YouTube Link 2017-05-03T15:38Z 8.1M followers, 2.3M engagements
"Integration and the fundamental theorem of calculus Chapter [--] Essence of calculus Intuition for integrals and why they are inverses of derivatives. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/integration#thanks Check out the Art of Problem Solving: https://aops.com/3blue1brown Timestamps: 0:00 - Car example 8:20 - Areas under graphs 11:18 - Fundamental theorem of calculus 16:20 - Recap 17:45 - Negative area 18:55 - Outro Thanks to these"
YouTube Link 2017-05-05T15:05Z 8.1M followers, 2.9M engagements
"But what is the Riemann zeta function Visualizing analytic continuation Unraveling the enigmatic function behind the Riemann hypothesis Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/zeta-thanks Home page: https://www.3blue1brown.com/ Posters/shirts for this visualization at http://3b1b.co/store Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function Check out some of Vince's other work here:"
YouTube Link 2016-12-09T17:50Z 8.1M followers, 5.2M engagements
"The other way to visualize derivatives Chapter [--] Essence of calculus A visual for derivatives that generalizes more nicely to topics beyond calculus. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/alt-calc-thanks And by Brilliant: https://brilliant.org/3b1b Home page: https://www.3blue1brown.com Essence of calculus series: http://3b1b.co/calculus Really nice applet made based on this video by Reddit user Larconneur: https://www.geogebra.org/m/rftwacsy Music by"
YouTube Link 2018-05-19T14:09Z 8.1M followers, 3.8M engagements
"The determinant Chapter [--] Essence of linear algebra The determinant measures how much volumes change during a transformation. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Vietnamese:"
YouTube Link 2016-08-10T22:31Z 8.1M followers, 4.7M engagements
"What was Euclid really doing Guest video by Ben Syversen What role were ruler and compass constructions really serving Check out Ben's channel: @bensyversen Interview with the author of this video: https://youtu.be/VohYM99j8e0 Supporters get early views of new videos: https://3b1b.co/support Written produced edited and animated by Ben Syversen Additional editing: Jack Saxon 3d Blender model: Jan-Hendrik Mller Additional Blender help: Thibaut Modrzyk (@Deepia) Illustrations: Alex Zepherin/DonDada Studio Camera: Giacomo Belletti Drums: Jeremy Gustin Additional music from Epidemic Sound Special"
YouTube Link 2025-09-18T14:13Z 8.1M followers, 689.7K engagements
"Derivative formulas through geometry Chapter [--] Essence of calculus Some common derivative formulas explained with geometric intuition. This video was sponsored by Brilliant: https://brilliant.org/3b1b Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/lessons/derivatives-power-rule#thanks Time stamps: 0:00 Intro 1:38 f(x) = x2 4:41 f(x) = x3 6:54 f(x) = xn "Power Rule" 10:07 f(x) = 1/x 12:36 Sine 16:56 Outro Great video by Think Twice showing this geometric view of the"
YouTube Link 2017-04-30T15:24Z 8.1M followers, 3.5M engagements
"Abstract vector spaces Chapter [--] Essence of linear algebra This is really the reason linear algebra is so powerful. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Russian: e-p-h ------------------ 3blue1brown is"
YouTube Link 2016-09-24T19:29Z 8.1M followers, 1.7M engagements
"Visualizing the chain rule and product rule Chapter [--] Essence of calculus A visual explanation of what the chain rule and product rule are and why they are true. Help fund future projects: https://www.patreon.com/3blue1brown This video was sponsored by Brilliant: https://brilliant.org/3b1b An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/chain-rule-and-product-rule#thanks Home page: https://www.3blue1brown.com Series like this one are funded largely by the community through Patreon where supporters get early"
YouTube Link 2017-05-01T15:19Z 8.1M followers, 2.2M engagements
"Why is in the normal distribution (beyond integral tricks) Where's the circle And how does it relate to where e(-x2) comes fromHelp fund future projects: https://www.patreon.com/3blue1brown Special thanks to these supporters: https://www.3blue1brown.com/lessons/gaussian-integral#thanks An equally valuable form of support is to simply share the videos. The artwork in this video is by Kurt Bruns who used Midjourney as part of the process for some pieces. I wrote more about the specifics of that process and my thoughts around it here: https://www.patreon.com/posts/thoughts-on-ai-83881719 Here"
YouTube Link 2023-04-02T15:30Z 8.1M followers, 2.2M engagements
"Cross products Chapter [--] Essence of linear algebra This covers the main geometric intuition behind the 2d and 3d cross products. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ *Note in all the computations here I list the coordinates of the vectors as columns of a matrix but many textbooks put them in the rows of a matrix instead. It makes no difference for the result since the determinant is unchanged after a transpose but given how I've framed most of this"
YouTube Link 2016-09-01T03:54Z 8.1M followers, 2.3M engagements
"Terence Tao continuing historys cleverest cosmological measurements How we know the distances to the planets stars and faraway galaxies. Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support FAQ with added details and corrections: https://terrytao.wordpress.com/2025/02/13/cosmic-distance-ladder-video-with-grant-sanderson-3blue1brown-commentary-and-corrections/ An equally valuable form of support is to simply share the videos. Terry and his collaborator Tanya have an Instagram about the cosmic distance ladder:"
YouTube Link 2025-02-23T14:54Z 8.1M followers, 1.4M engagements
"But how do AI images and videos actually work Guest video by Welch Labs Diffusion models CLIP and the math of turning text into images Welch Labs Book: https://www.welchlabs.com/resources/imaginary-numbers-book Sections 0:00 - Intro 3:37 - CLIP 6:25 - Shared Embedding Space 8:16 - Diffusion Models & DDPM 11:44 - Learning Vector Fields 22:00 - DDIM 25:25 - Dall E [--] 26:37 - Conditioning 30:02 - Guidance 33:39 - Negative Prompts 34:27 - Outro 35:32 - About guest videos Special Thanks to: Jonathan Ho - Jonathan is the Author of the DDPM paper and the Classifier Free Guidance Paper."
YouTube Link 2025-07-25T12:14Z 8.1M followers, 1.6M engagements
"But what is a Laplace Transform Visualizing the most important tool for differential equations. Previous chapter: https://youtu.be/-j8PzkZ70Lg Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Pi creature car artwork by Kurt Bruns Engine animation borrowed with permission from this (excellent) blog: https://ciechanow.ski/internal-combustion-engine/ Timestamps: 0:00 - Understanding the engine 1:16 - Key background ideas 5:41 - Definition"
YouTube Link 2025-10-12T11:19Z 8.1M followers, 1.3M engagements
"How AI connects text and images From this guest video by @WelchLabs on how diffusion models work: https://youtu.be/iv-5mZ_9CPY Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-08-21T18:24Z 8.1M followers, 99.5K engagements
"Linear combinations span and basis vectors Chapter [--] Essence of linear algebra The fundamental concepts of span linear combinations linear dependence and bases. Help fund future projects: https://www.patreon.com/3blue1brown Thanks to Elo Marie Viennot and Ambros Gleixner from HTW Berlin (www.htw-berlin.de) for contributing German translations and dubbing. Thanks to these viewers for their contributions to translations Arabic: @Cewkins Hazem Hebrew: Omer Tuchfeld Spanish: Juan Carlos Largo Vietnamese: @ngvutuan2811 ------------------ 3blue1brown is a channel about animating math in all senses"
YouTube Link 2016-08-06T23:49Z 8.1M followers, 7M engagements
"Limits L'Hpital's rule and epsilon delta definitions Chapter [--] Essence of calculus Formal derivatives the epsilon-delta definition and why L'Hpital's rule works. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/limits#thanks Home page: https://www.3blue1brown.com Timestamps 0:00 - Intro 1:17 - Formal definition of derivatives 4:52 - Epsilon delta definition 9:53 - L'Hpital's rule 17:17 - Outro Thanks to these viewers for their contributions to"
YouTube Link 2017-05-04T15:05Z 8.1M followers, 2.5M engagements
"Measuring the earth with Terence Tao From this video: https://youtu.be/YdOXS_9_P4U Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-02-08T13:35Z 8.1M followers, 597.8K engagements
"e(i) in [----] minutes using dynamics DE5 Euler's formula about e to the i pi explained with velocities to positions. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://www.3blue1brown.com Not familiar with the calculus referenced in this video Try taking a look at this one: https://youtu.be/m2MIpDrF7Es Another perspective on this formula from Mathologer: https://youtu.be/-dhHrg-KbJ0 Another perspective from this channel: https://youtu.be/mvmuCPvRoWQ And yet another"
YouTube Link 2019-07-07T14:08Z 8.1M followers, 3.4M engagements
"Newtons fractal (which Newton knew nothing about) Who knew root-finding could be so complicated Next part: https://youtu.be/LqbZpur38nw Special thanks to the following supporters: https://3b1b.co/lessons/newtons-fractal#thanks An equally valuable form of support is to simply share the videos. Thanks to these viewers for their contributions to translations German: Luatic Hebrew: Omer Tuchfeld Portuguese: luiz12apn ------------------ Interactive for this video: https://www.3blue1brown.com/lessons/newtons-fractal On fractal dimension: https://youtu.be/gB9n2gHsHN4 Mathologer on the cubic formula:"
YouTube Link 2021-10-12T18:57Z 8.1M followers, 3.2M engagements
"What does area have to do with slope Chapter [--] Essence of calculus One view on why integrals and derivatives are inverses. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/area-and-slope#thanks Full series: http://3b1b.co/calculus Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Vietnamese: ngvutuan2811 ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you"
YouTube Link 2017-05-06T13:53Z 8.1M followers, 1.7M engagements
"Change of basis Chapter [--] Essence of linear algebra How do you translate back and forth between coordinate systems that use different basis vectors Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Vietnamese: @ngvutuan2811"
YouTube Link 2016-09-11T17:56Z 8.1M followers, 2.4M engagements
"Vectors Chapter [--] Essence of linear algebra Beginning the linear algebra series with the basics. Help fund future projects: https://www.patreon.com/3blue1brown Music: https://vincerubinetti.bandcamp.com/track/grants-etude Thanks to Elo Marie Viennot and Ambros Gleixner from HTW Berlin (www.htw-berlin.de) for contributing German translations and dubbing. Thanks also to these viewers for their contributions to the subtitles Arabic: @Cewkins Hazem Bengali: Md Rasheduzzaman Czech: @Chnapak Greek: Nikolaos Tsagkas Hebrew: Omer Tuchfeld Italian: mattiacolucci Spanish: Juan Carlos Largo Thai: own"
YouTube Link 2016-08-06T00:05Z 8.1M followers, 11.4M engagements
"Transformers the tech behind LLMs Deep Learning Chapter [--] Breaking down how Large Language Models work visualizing how data flows through. Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support --- Here are a few other relevant resources Build a GPT from scratch by Andrej Karpathy https://youtu.be/kCc8FmEb1nY If you want a conceptual understanding of language models from the ground up @vcubingx just started a short series of videos on the topic: https://youtu.be/1il-s4mgNdIsi=XaVxj6bsdy3VkgEX If you're interested in the herculean task of"
YouTube Link 2024-04-01T19:13Z 8.1M followers, 9.4M engagements
"Euler's Formula and Graph Duality A description of planar graph duality and how it can be applied in a particularly elegant proof of Euler's Characteristic Formula. Music: Wyoming [---] by Time For Three Thanks to these viewers for their contributions to translations Marathi: realcalal"
YouTube Link 2015-06-21T06:05Z 8.1M followers, 527.4K engagements
"The Physics of Euler's Formula Laplace Transform Prelude The simple harmonic oscillator and the fundamental role of complex exponents for ODEs. Next chapter on the Laplace Transform video: https://youtu.be/j0wJBEZdwLs Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Timestamps: 0:00 - Intro 1:51 - Euler's formula explained dynamically 9:27 - The harmonic oscillator 21:08 - General linear equations 22:47 - Motivating the Laplace Transform"
YouTube Link 2025-10-05T13:53Z 8.1M followers, 881.4K engagements
"The AI that solved IMO Geometry Problems Guest video by @Aleph0 How AlphaGeometry combines logic and intuition. Check out Aleph0s channel: https://youtube.com/@Aleph0 Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. Home page: https://www.3blue1brown.com Special thanks to Trieu Trinh for fact-checking the script. Blog post on an open-sourced geometry solver: https://harmonic.fun/news#blog-post-geometry AlphaGeometry announcement:"
YouTube Link 2025-08-17T13:02Z 8.1M followers, 408.1K engagements
"Why colliding blocks compute pi The physics behind one of the most surprising occurrences of pi Next video on Grover's Algorithm: https://youtu.be/RQWpF2Gb-gU Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Next video on Grover's Algorithm: https://youtu.be/RQWpF2Gb-gU The original paper by Gregory Galperin: https://www.maths.tcd.ie/lebed/Galperin.%20Playing%20pool%20with%20pi.pdf Adam Brown's paper on the analogy with Grover's Algorithm: https://arxiv.org/pdf/1912.02207"
YouTube Link 2025-03-13T15:36Z 8.1M followers, 5.2M engagements
"Why do prime numbers make these spirals Dirichlets theorem and pi approximations A curious pattern approximations for pi and prime distributions. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/spiral-thanks Based on this Math Stack Exchange post: https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers/885894 Want to learn more about rational approximations See this Mathologer video. https://youtu.be/CaasbfdJdJg"
YouTube Link 2019-10-08T17:02Z 8.1M followers, 7.5M engagements
"Gradient descent how neural networks learn Deep Learning Chapter [--] Cost functions and training for neural networks. Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these supporters: http://3b1b.co/nn2-thanks Written/interactive form of this series: https://www.3blue1brown.com/topics/neural-networks This video was supported by Amplify Partners. For any early-stage ML startup founders Amplify Partners would love to hear from you via 3blue1brown@amplifypartners.com To learn more I highly recommend the book by Michael Nielsen"
YouTube Link 2017-10-16T16:48Z 8.1M followers, 8.9M engagements
"Can you even imagine [----] Originally written as a supplement to an explanation of the cryptography behind Bitcoin: https://youtu.be/bBC-nXj3Ng4 (An active link is on the bottom of the video player) Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2023-12-16T00:00Z 8.1M followers, 2.3M engagements
"Why the ancient Greeks rejected heliocentrism From this video on the cosmic distance ladder: https://youtu.be/YdOXS_9_P4U Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-02-27T15:00Z 8.1M followers, 1.4M engagements
"What is Euler's formula actually saying Ep. [--] Lockdown live math What does it mean to compute epi i Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258220129327800320 https://twitter.com/ThuyNganVu/status/1258220541686628353 Not on the "homework" to show that exp(x + y) = exp(x) * exp(y). This gets a little more intricate if you start asking seriously about whether the series really"
YouTube Link 2020-04-28T19:58Z 8.1M followers, 1.7M engagements
"Why is pi here And why is it squared A geometric answer to the Basel problem A most beautiful proof of the Basel problem using light. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/basel-thanks This video was sponsored by Brilliant: https://brilliant.org/3b1b Brilliant's principles list that I referenced: https://brilliant.org/principles/ Get early access and more through Patreon: https://www.patreon.com/3blue1brown The content here was based on a paper"
YouTube Link 2018-03-02T16:23Z 8.1M followers, 7.2M engagements
"Fractals are typically not self-similar An explanation of fractal dimension. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/fractals-thanks And by Affirm: https://www.affirm.com/careers Home page: https://www.3blue1brown.com/ One technical note: It's possible to have fractals with an integer dimension. The example to have in mind is some very rough curve which just so happens to achieve roughness level exactly [--]. Slightly rough might be around"
YouTube Link 2017-01-27T17:29Z 8.1M followers, 4.5M engagements
"But what is a partial differential equation DE2 The heat equation as an introductory PDE. Strogatz's new book: https://amzn.to/3bcnyw0 Special thanks to these supporters: http://3b1b.co/de2thanks An equally valuable form of support is to simply share some of the videos. Timestamps: 0:00 - Introduction 3:29 - Partial derivatives 6:52 - Building the heat equation 13:18 - ODEs vs PDEs 14:29 - The laplacian 16:04 - Book recommendation Typo corrections: - 1:33 - it should be Black-Scholes - 16:21 - it should read "scratch an itch". If anyone asks I purposefully leave at least one typo in each"
YouTube Link 2019-04-21T16:53Z 8.1M followers, 3.1M engagements
"Group theory abstraction and the 196883-dimensional monster An introduction to group theory (Minor error corrections below) Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/monster-thanks Timestamps: 0:00 - The size of the monster 0:50 - What is a group 7:06 - What is an abstract group 13:27 - Classifying groups 18:31 - About the monster Errors: *Typo on the "hard problem" at 14:11 it should be a/(b+c) + b/(a+c) + c/(a+b) = [--] *Typo-turned-speako: The"
YouTube Link 2020-08-19T14:01Z 8.1M followers, 3.7M engagements
"Three-dimensional linear transformations Chapter [--] Essence of linear algebra What do 3d linear transformations look like Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------"
YouTube Link 2016-08-09T22:01Z 8.1M followers, 2.5M engagements
"Solving Wordle using information theory An excuse to teach a lesson on information theory and entropy. These lessons are funded by viewers: https://www.patreon.com/3blue1brown Special thanks to these supporters: https://3b1b.co/lessons/wordle#thanks An equally valuable form of support is to simply share the videos. Contents: 0:00 - What is Wordle 2:43 - Initial ideas 8:04 - Information theory basics 18:15 - Incorporating word frequencies 27:49 - Final performance Original wordle site: https://www.powerlanguage.co.uk/wordle/ Music by Vincent Rubinetti. https://www.vincentrubinetti.com/ Shannon"
YouTube Link 2022-02-06T13:28Z 8.1M followers, 11.8M engagements
"The medical test paradox (well "paradox") A link to the full video about Bayesian thinking is at the bottom of the screen. Or for reference: https://youtu.be/lG4VkPoG3ko Long-to-short editing by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-01-15T07:00Z 8.1M followers, 11.5M engagements
"What makes the natural log "natural" Ep. [--] Lockdown live math All about ln(x). Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1259288683489849344 Errors: At minute [--] the sum should be written with a "." to indicate going to infinity. At minute [--] the exponent should have 1/(2s2) instead of 1/s2 for s to represent standard deviation. At minute [--] an equal sign was mistakenly used in"
YouTube Link 2020-05-08T20:22Z 8.1M followers, 1.7M engagements
"Complex number fundamentals Ep. [--] Lockdown live math Intro to the geometry complex numbers. Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258219199769440257 Errors: - On the first sketch of a complex plane there is a "2i" written instead of "-2i". - At the end in writing the angle sum identity the last term should be sin(beta) instead of sin(alpha). - During Q9 the terms in"
YouTube Link 2020-04-24T20:31Z 8.1M followers, 2.1M engagements
"How might LLMs store facts Deep Learning Chapter [--] Unpacking the multilayer perceptrons in a transformer and how they may store facts Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. AI Alignment forum post from the Deepmind researchers referenced at the video's start: https://www.alignmentforum.org/posts/iGuwZTHWb6DFY3sKB/fact-finding-attempting-to-reverse-engineer-factual-recall Anthropic posts about superposition referenced near the end:"
YouTube Link 2024-08-31T12:11Z 8.1M followers, 1.9M engagements
"The Brachistochrone with Steven Strogatz Steven Strogatz and I talk about a famous historical math problem a clever solution and a modern twist. ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to stay posted about new videos subscribe and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more a good place to start is this playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDPHP40bzkb0TKLRPwQGAoC- Various social media stuffs:"
YouTube Link 2016-04-01T20:27Z 8.1M followers, 1.4M engagements
"Where my explanation of Grovers algorithm failed Addressing viewer questions from the last video: https://youtu.be/RQWpF2Gb-gU These lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. The subtitles on this video were done using AI and are likely imperfect but they are open for community corrections at https://criblate.com/ Timestamps: 0:00 - The confusion 1:25 - Example: Sudokus 7:58 - Linearity 14:19 - Is this useful ------------------ These animations are largely made using a custom Python library manim. See the FAQ"
YouTube Link 2025-05-04T11:45Z 8.1M followers, 632.4K engagements
"But why is a sphere's surface area four times its shadow The formula is no mere coincidence. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/sphere-thanks Discussion on Reddit: https://www.reddit.com/r/3Blue1Brown/comments/a2gqo0/but_why_is_a_spheres_surface_area_four_times_its/ The first proof goes back to Greek times due to Archimedes who was charmed by the fact that a sphere has 2/3 the volume of a cylinder encompassing it and 2/3 the surface area as"
YouTube Link 2018-12-02T20:08Z 8.1M followers, 8.8M engagements
"Convolutions Why X+Y in probability is a beautiful mess Adding random variables with connections to the central limit theorem. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. 0:00 - Intro quiz 2:24 - Discrete case diagonal slices 6:49 - Discrete case flip-and-slide 8:41 - The discrete formula 10:58 - Continuous case flip-and-slide 15:53 - Example with uniform distributions 18:42 - Central limit theorem 20:50 - Continuous case diagonal slices 25:26 - Returning to the intro quiz Thanks to these viewers for their"
YouTube Link 2023-06-27T15:08Z 8.1M followers, 965.3K engagements
"How (and why) to raise e to the power of a matrix DE6 General exponentials love Schrdinger and more. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/mat-exp-thanks Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ The Romeo-Juliet example is based on this essay by Steven Strogatz: http://www.stevenstrogatz.com/essays/loves-me-loves-me-not-do-the-math The book shown at the start is Vladimir Arnold's"
YouTube Link 2021-04-01T15:50Z 8.1M followers, 3.5M engagements
"But what is quantum computing (Grover's Algorithm) Qubits state vectors and Grover's algorithm for search. Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. The subtitles on this video were done using AI and are likely imperfect but they are open for community corrections at https://criblate.com/ Adam Brown's paper on the connection between Grover's Algorithm and block collisions: https://arxiv.org/pdf/1912.02207 If you want to learn the relevant underlying quantum mechanics here a"
YouTube Link 2025-04-30T12:32Z 8.1M followers, 3.2M engagements
"Fractal charm: Space filling curves A montage of space-filling curves meant as a supplement to the Hilbert curve video. https://youtu.be/3s7h2MHQtxc These animations are largely made using a custom python library manim. See the FAQ comments here: https://www.3blue1brown.com/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ You can find code for specific videos and projects here: https://github.com/3b1b/videos/ Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld"
YouTube Link 2016-01-17T01:43Z 8.1M followers, 2.1M engagements
"Solving the heat equation DE3 Boundary conditions and set up for how Fourier series are useful. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/de3thanks Home page: https://www.3blue1brown.com More about the heat equation with a derivation in terms of slope corresponding to heat flow from MIT OCW: https://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006/lecture-notes/heateqni.pdf If you want to learn more about"
YouTube Link 2019-06-16T16:31Z 8.1M followers, 1.6M engagements
"Matrix multiplication as composition Chapter [--] Essence of linear algebra Multiplying two matrices represents applying one transformation after another. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer"
YouTube Link 2016-08-08T22:20Z 8.1M followers, 4.1M engagements
"Why probability of [--] does not mean impossible Probabilities of probabilities part [--] An introduction to probability density functions Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/thanks Curious about measure theory This does require some background in real analysis but if you want to dig in here is a textbook by the always-great Terence Tao. https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf Also for the real analysis buffs"
YouTube Link 2020-04-12T15:41Z 8.1M followers, 3.4M engagements
"How wiggling charges give rise to light Explaining the barber pole effect from the last video: https://youtu.be/QCX62YJCmGk Next video on the index of refraction: https://youtu.be/KTzGBJPuJwM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. This Feynman lecture describes this particular approach in more detail: https://www.feynmanlectures.caltech.edu/I_28.html Timestamps: 0:00 - Recap 0:44 - The radiation law 6:10 - Simulating the radiation law 11:11 - Why the diagonal stripes 16:31 - Why does it twist Thanks to"
YouTube Link 2023-09-01T13:39Z 8.1M followers, 1.8M engagements
"But how does bitcoin actually work The math behind cryptocurrencies. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/btc-thanks This video was also funded with help from Protocol Labs: https://protocol.ai/join/ Some people have asked if this channel accepts contributions in cryptocurrency form. As a matter of fact it does: http://3b1b.co/crypto ENS: 3b1b.eth [----] video: https://youtu.be/S9JGmA5_unY Music by Vincent Rubinetti:"
YouTube Link 2017-07-07T16:51Z 8.1M followers, 18.2M engagements
"How pi was almost [--------]. In some of his notes Euler used to represent [----]. So why did we adopt [----]. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com The idea for this video as well as the live shots came from Ben Hambrecht with the writing and animating done by Grant Sanderson. Special thanks to: - University Library Basel for letting us rummage through their historical collection - Martin Mattmller from the Bernoulli-Euler center for helpful discussion -"
YouTube Link 2018-03-14T13:05Z 8.1M followers, 1.8M engagements
"Visualizing the 4d numbers Quaternions How to think about this 4d number system in our 3d space. Part 2: https://youtu.be/zjMuIxRvygQ Interactive version of these visuals: https://eater.net/quaternions Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/quaternion-thanks Quanta article on quaternions: https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/ The math of Alice in Wonderland:"
YouTube Link 2018-09-06T14:59Z 8.1M followers, 5.4M engagements
"Cramer's rule explained geometrically Chapter [--] Essence of linear algebra This rule seems random to many students but it has a beautiful reason for being true. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ---- If you want to contribute translated subtitles or to help review those that have already been made by others and need approval you can click the gear icon in the video"
YouTube Link 2019-03-17T04:35Z 8.1M followers, 1.5M engagements
"Essence of linear algebra preview Home page: https://www.3blue1brown.com/ This introduces the "Essence of linear algebra" series aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear algebra course. Error corrections: - At one point I mistakenly allude to calculators using the Taylor expansion of sine for its computations when in reality most use CORDIC (or something like it). - Around [--] seconds in there is a typo in how the determinant is written which should be ad - bc Full series: http://3b1b.co/eola Future series like this are funded by the"
YouTube Link 2016-08-05T01:01Z 8.1M followers, 2.7M engagements
"What's so special about Euler's number e Chapter [--] Essence of calculus What is e And why are exponentials proportional to their own derivatives Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/eulers-number#thanks Home page: https://www.3blue1brown.com Timestamps 0:00 - Motivating example 3:57 - Deriving the key proportionality property 7:36 - What is e 8:48 - Natural logs 11:23 - Writing ect is a choice Corrections: 9:40 - I meant to say "*the"
YouTube Link 2017-05-02T15:09Z 8.1M followers, 5M engagements
"This puzzle is trickier than it seems From this full video: https://youtu.be/piJkuavhV50 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-11-19T19:06Z 8.1M followers, 1.4M engagements
"Divergence and curl: The language of Maxwell's equations fluid flow and more Visualizing two core operations in calculus. (Small error correction below) Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/divcurl-thanks My work on this topic at Khan Academy: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives Timestamps 0:00 - Vector fields 2:15 - What is divergence 4:31 - What is curl 5:47 - Maxwell's equations 7:36 - Dynamic"
YouTube Link 2018-06-21T18:34Z 8.1M followers, 5.1M engagements
"The ladybug clock puzzle This is the first in a set of monthly puzzles curated by Peter Winkler. This one was originally suggested by Richard Stanley. You can sign up to hear his description of the answer at http://momath.org/mindbenders Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2026-01-16T14:16Z 8.1M followers, 702.4K engagements
"Backpropagation calculus Deep Learning Chapter [--] Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/nn3-thanks Written/interactive form of this series: https://www.3blue1brown.com/topics/neural-networks This one is a bit more symbol-heavy and that's actually the point. The goal here is to represent in somewhat more formal terms the intuition for how backpropagation works in part [--] of the series hopefully providing some connection between that video and other texts/code"
YouTube Link 2017-11-03T14:08Z 8.1M followers, 3.7M engagements
"Inverse matrices column space and null space Chapter [--] Essence of linear algebra How to think about linear systems of equations geometrically. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld"
YouTube Link 2016-08-15T22:00Z 8.1M followers, 3.6M engagements
"The impossible chessboard puzzle An information puzzle with an interesting twist Solution on Stand-up Maths: https://youtu.be/as7Gkm7Y7h4 Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/chess-thanks Home page: https://www.3blue1brown.com Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ 0:00 Introduction 3:58 Visualizing the two-square case 5:46 Visualizing the three-square case 12:19 Proof that"
YouTube Link 2020-07-05T18:50Z 8.1M followers, 2.2M engagements
"The meaning within the Mandelbrot set The full video dives deeper into the field of math studying this called holomorphic dynamics: https://youtu.be/LqbZpur38nw Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-11-24T17:00Z 8.1M followers, 936.1K engagements
"Error correction is incredible A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/X8jsijhllIA Editing from long-form to short by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2023-12-10T00:00Z 8.1M followers, 5.5M engagements
"But what is the Central Limit Theorem A visual introduction to probability's most important theorem Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these lovely supporters: https://www.3blue1brown.com/lessons/clt#thanks An equally valuable form of support is to simply share the videos. Galton board shown in the video: https://amzn.to/3ZJK8nY Thanks to these viewers for their contributions to translations Hebrew: David Bar-On Omer Tuchfeld Hindi: Tapender1 Italian: anna-lombardo ----------------- Timestamps 0:00 - Introduction 1:53 - A simplified Galton Board"
YouTube Link 2023-03-14T18:36Z 8.1M followers, 4.4M engagements
"Ellipses have multiple definitions how are these the same A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/pQa_tWZmlGs The full video this comes from proves why slicing a cone gives the same shape as the two-thumbtacks-and-string construction which is beautiful. Editing from long-form to short by Dawid Koodziej"
YouTube Link 2024-01-19T19:00Z 8M followers, 63.4K engagements
"A challenging puzzle about subset sums A link to the full video answering this is at the bottom of the screen. Or for reference: https://youtu.be/bOXCLR3Wric Thanks to these viewers for their contributions to translations French: GiveMeChocolate Hindi: rajeshwar-pandey Spanish: Yago Iglesias"
YouTube Link 2024-01-22T06:00Z 7.8M followers, 1M engagements
"Binary Hanoi and Sierpinski part [--] Binary counting can solve the towers of Hanoi puzzle and if this isn't surprising enough it can lead to a method for finding a curve that fills Sierpinski's triangle (which I get to in part 2). Thanks to Desmos for their help in supporting this video. They're hiring and anyone interested should check out https://www.desmos.com/careers Thanks to all Patreon supporters as well you can support and get early access to future "Essence of" series here: https://www.patreon.com/3blue1brown I also want to give a special shoutout to the following patrons: CrypticSwarm"
YouTube Link 2016-11-25T17:30Z 7.9M followers, 768.2K engagements
"What is a group A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/mH0oCDa74tE That video introduces group theory and the monster group. Editing from long-form to short by Dawid Koodziej"
YouTube Link 2023-12-27T19:00Z 8M followers, 156.3K engagements
"Simulating the electric field and a moving charge A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/aXRTczANuIs"
YouTube Link 2024-01-26T06:00Z 8M followers, 1.3M engagements
"tum khud Hi socho chhod dungi to apna aur apne bete ka kharcha #trending #viralvideo #subscribe tum khud Hi socho chhod dungi to apna aur apne bete ka kharcha #trending #viralvideo #subscribe"
YouTube Link 2025-12-17T17:11Z 100K followers, 281.6K engagements
"Why does light slowing imply a bend (Beyond the tank/car analogy) A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/Cz4Q4QOuoo8 That video answers various viewer questions about the index of refraction. Editing from long-form to short by Dawid Koodziej"
YouTube Link 2024-01-11T00:00Z 7.9M followers, 1.4M engagements
"How are holograms possible 3d scenes on 2d film and a diffraction lesson along the way. Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. Hologram credits: The Microscope is by Walter Spierings [----] Donations Hologram by Cherry Optical Holography Lucy in a Tin Hat is by Patrick Keown Boyd [----] The Star Wars-themed Direct-Write Digital Holograms were produced by Zebra Imaging. The 'Shakespeare' embossed animated integral hologram was made by Applied Holographics. Walter Spierings who"
YouTube Link 2024-10-05T15:31Z 8.1M followers, 6.1M engagements
"Order from chaos A link to the full video on the Central Limit Theorem is at the bottom of the screen. Or for reference: https://youtu.be/zeJD6dqJ5lo Thanks to Dawid Koodziej from long-to-short editing"
YouTube Link 2023-12-15T00:00Z 7.9M followers, 14.1M engagements
"The simpler quadratic formula Ep. [--] Lockdown live math Another view on the quadratic formula. Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258217451323416577 Po Shen Loh on quadratics: https://www.youtube.com/watchv=ZBalWWHYFQc Welch Labs on imaginary numbers: https://www.youtube.com/playlistlist=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF Mistakes (there will always be mistakes): At minute"
YouTube Link 2020-04-17T20:04Z 8M followers, 1.5M engagements
"How They Fool Ya (live) Math parody of Hallelujah Happy Tau Day Here's something a bit out of the ordinary for you. Thanks to Matt Parker @standupmaths for the invite. More about the event: https://festivalofthespokennerd.com/show/an-evening-of-unnecessary-detail/ Thanks to Tim Blais @acapellascience for helpful thoughts on the song including the key phrase "How they fool ya" Video about the circle pattern https://youtu.be/YtkIWDE36qU Video about those integrals https://youtu.be/851U557j6HE Video about the primes in base [--] https://youtu.be/jhObLT1Lrfo Timestamps: 0:00 - Intro 1:20 - Song"
YouTube Link 2023-06-28T19:17Z 7.8M followers, 1.2M engagements
"I'm still astounded this is true A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/6dTyOl1fmDo Sliding blocks on a frictionless plane counter their collisions and. Thanks to Dawid Koodziej for editing together this short"
YouTube Link 2023-12-07T01:11Z 8M followers, 66M engagements
"All possible pythagorean triples visualized To understand all pythagorean triples like (3 [--] 5) (5 [--] 13) etc. look to complex numbers. This video was sponsored by Remix: https://www.remix.com/jobs Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/triples-thanks Home page: https://www.3blue1brown.com/ Regarding the brief reference to Fermat's Last Theorem what should be emphasized is that it refers to positive integers. You can of course have things like"
YouTube Link 2017-05-26T17:58Z 7.8M followers, 4.1M engagements
"Q&A with Grant Sanderson (3blue1brown) To commemorate crossing [---] subscribers. FAQ from home page: https://www.3blue1brown.com/faq Subreddit: https://www.reddit.com/r/3blue1brown AMC problem shown on screen: https://artofproblemsolving.com/wiki/index.phptitle=2002_AMC_12A_Problems/Problem_22 Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to stay posted on new videos subscribe:"
YouTube Link 2018-08-24T16:34Z 7.9M followers, 860.3K engagements
"The quick proof of Bayes' theorem Including some added words on independence. Main video: https://youtu.be/HZGCoVF3YvM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks ------------------ These animations are largely made using manim a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out I feel compelled to warn you that it's not the most well-documented tool and it has many other quirks you might"
YouTube Link 2019-12-22T14:45Z 8M followers, 561.5K engagements
"Don't let it fool you A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/YtkIWDE36qU Thanks to Dawid Koodziej for editing together this short"
YouTube Link 2023-12-07T01:11Z 8M followers, 18M engagements
"Why this puzzle is impossible Featuring quite a few science/math YouTubers Vihart response: https://youtu.be/CruQylWSfoU Brought to you by you: http://3b1b.co/mug-thanks And by Brilliant: https://brilliant.org/3b1b Timestamps: 0:00 - Featured guests 4:30 - Why it's "impossible" 12:20 - Surfaces with holes 16:27 - Your challenge 17:35 - Sponsorship and end Thanks to all the following channels for participating. Standup Maths https://www.youtube.com/user/standupmaths Wendover Productions https://www.youtube.com/user/Wendoverproductions Welch Labs: https://www.youtube.com/user/Taylorns34"
YouTube Link 2017-12-23T16:43Z 7.9M followers, 3.3M engagements
"For anyone who might not know how links in shorts work YouTube disabled links in descriptions and comments but we can add links to videos on the shorts player itself. For reference the one at the bottom of this screen is https://youtu.be/KTzGBJPuJwM"
YouTube Link 2023-12-21T00:15Z 7.9M followers, 268.6K engagements
"Hologram preview Full video: https://youtu.be/EmKQsSDlaa4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-10-11T14:00Z 8.1M followers, 67.1K engagements
"What "Follow Your Dreams" Misses Harvey Mudd Commencement Speech [----] I had the pleasure of being invited to give Harvey Mudd's commencement speech this year. Reposted here with permission from the University Timestamps: 0:00 - End of Harriet Nembhard's introduction 0:45 - The clich 2:28 - The shifting goal 5:57 - Action precedes motivation 7:02 - Timing 10:47 - Know your influence 12:05 - Anticipate change ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. If you're reading the bottom of a video description I'm guessing you're more interested"
YouTube Link 2024-05-18T14:50Z 8M followers, 1.5M engagements
"The most absurd product I've made Because why not make a pi creature neck pillow Available at 3b1b.co/store"
YouTube Link 2025-11-24T16:30Z 8M followers, 143K engagements
"Hamming codes part 2: The one-line implementation A cleaner perspective on Hamming error correction codes Part 1: https://youtu.be/X8jsijhllIA Watch Ben Eater's video: https://youtu.be/h0jloehRKas Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/hamming-thanks You can read Hamming's own perspective on his discovery of these codes in chapter [--] of "The Art of Doing Science and Engineering". https://amzn.to/3lwcnmh Heavily related is the chessboard puzzle"
YouTube Link 2020-09-04T15:36Z 7.9M followers, 962.3K engagements
"Binary Hanoi and Sierpinski part [--] After seeing how binary counting can solve the towers of Hanoi puzzle in the last video here we see how ternary counting solve a constrained version of the puzzle and how this gives a way to walk through a Sierpinski triangle graph structure. Thanks to Desmos for their help in supporting this video. They're hiring and anyone interested should check out https://www.desmos.com/careers Thanks to all Patreon supporters as well you can support and get early access to future "Essence of" series here: https://www.patreon.com/3blue1brown I also want to give a"
YouTube Link 2016-11-25T17:30Z 7.9M followers, 330.5K engagements
"A pretty reason why Gaussian + Gaussian = Gaussian A visual trick to compute the sum of two normally distributed variables. 3b1b mailing list: https://3blue1brown.substack.com/ Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these supporters: https://www.3blue1brown.com/lessons/gaussian-convolution#thanks For the technically curious who want to go deeper here's a proof of the central limit theorem using Moment generating functions: https://www.cs.toronto.edu/yuvalf/CLT.pdf And here's a nice discussion of methods using entropy:"
YouTube Link 2023-07-11T15:53Z 7.9M followers, 937.1K engagements
"The power tower puzzle Ep. [--] Lockdown live math A fun puzzle stemming from repeated exponentiation. Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Notes by Ngn V: https://twitter.com/ThuyNganVu/status/1261014161464516608s=20 Play along on Desmos: https://www.desmos.com/calculator/nul32eaaa9 Related videos. Calculus series: https://www.youtube.com/playlistlist=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr In particular look at: https://youtu.be/CfW845LNObM Numberphile on"
YouTube Link 2020-05-12T19:59Z 7.8M followers, 935.4K engagements
"The medical test paradox and redesigning Bayes' rule About Likelihood Ratios also sometimes called Bayes Factors*. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/bayes-factor-thanks Home page: https://www.3blue1brown.com The book by my friend Matt Cook about paradoxes mentioned at the end: https://amzn.to/3aBrEzg On the topic I can't help also mentioning another paradox book I'm rather fond of by Bunch: https://amzn.to/3mBDSKE Another video on Bayes'"
YouTube Link 2020-12-22T17:42Z 8M followers, 1.4M engagements
"Q&A #2 + Net Neutrality Nuance Questions: http://3b1b.co/questions Answers: https://youtu.be/1nxF19qDBQ0 Full net neutrality video: https://youtu.be/hKD-lBrZ_Gg Ben Eater's channel: https://www.youtube.com/user/eaterbc First Q&A Answers: https://youtu.be/8r5WKpK9-m8 CGPGrey's (excellent) video on Net Neutrality: https://youtu.be/wtt2aSV8wdw ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to stay posted on new videos subscribe and click the bell to receive notifications (if you're into that). If"
YouTube Link 2017-12-14T15:57Z 7.9M followers, 153.5K engagements
"A beautiful international math olympiad problem The link to the full video is at the bottom of the screen. For reference here it is: https://youtu.be/M64HUIJFTZM"
YouTube Link 2024-01-03T07:00Z 8.1M followers, 2.7M engagements
"Using topology for discrete problems The Borsuk-Ulam theorem and stolen necklaces Solving a discrete math puzzle using topology I was originally inspired to cover this thanks to a Quora post by Alon Amit Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/borsuk-thanks Home page: https://www.3blue1brown.com Want more fair division math fun Check out this Mathologer video https://youtu.be/7s-YM-kcKME (Seriously Mathologer is great) These videos are supported"
YouTube Link 2018-11-18T14:09Z 8.1M followers, 974.7K engagements
"How to count to [----] on two hands Typically when we think of counting on two hands we count up to [--] but fingers can contain much more information than that This video shows how to think about counting in binary"
YouTube Link 2015-09-18T21:53Z 8.1M followers, 461.4K engagements
"This tests your understanding of light The barber pole effect The barber pole effect of shining polarized light into sugar water. Next video: https://youtu.be/aXRTczANuIs Steve Mould's video on the topic: https://youtu.be/975r9a7FMqc Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. Thanks to Quinn Brodsky for setting up the demo and to the MIT Physics Instructional Resources Lab for their help and materials especially Josh Wolfe and Caleb Bonyun. Thanks to these viewers for their contributions to translations"
YouTube Link 2023-09-01T13:13Z 8.1M followers, 1.4M engagements
"Linear transformations and matrices Chapter [--] Essence of linear algebra Quite possibly the most important idea for understanding linear algebra. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com Full series: http://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld"
YouTube Link 2016-08-07T21:39Z 8.1M followers, 6.7M engagements
"Researchers thought this was a bug (Borwein integrals) A pattern of integrals that all equal pi.until they don't. Next video on convolutions: https://youtu.be/KuXjwB4LzSA John Baez has a really fun article about this: https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/ Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these patrons: https://3b1b.co/lessons/borwein#thanks An equally valuable form of support is to simply share the videos. Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Hindi:"
YouTube Link 2022-11-04T15:54Z 8.1M followers, 4.6M engagements
"Binomial distributions Probabilities of probabilities part [--] Part 2: https://youtu.be/ZA4JkHKZM50 Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/beta1-thanks John Cook post: https://www.johndcook.com/blog/2011/09/27/bayesian-amazon/ ------------------ These animations are largely made using manim a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out I feel compelled to warn you that it's not the most"
YouTube Link 2020-03-15T18:28Z 8.1M followers, 2.6M engagements
"e to the pi i a nontraditional take (old version) Wait There's an improved version: https://youtu.be/mvmuCPvRoWQ Also for the calculus-savvy you'll prefer this one: https://youtu.be/v0YEaeIClKY Home page: https://www.3blue1brown.com/ The enigmatic equation epi i = [---] is usually explained using Taylor's formula during a calculus class. This video offers a different perspective which involves thinking about numbers as actions and about ex as something which turns one action into another. For more information on viewing exponential functions in this new light check out this article:"
YouTube Link 2015-03-05T06:15Z 8.1M followers, 2.8M engagements
"How to derive a formula for A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/NaL_Cb42WyY That video explores how this question leads to a quandary on prime numbers and how a pattern in primes allows for a clean final answer. Editing from long-form to short by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2023-12-25T19:00Z 8.1M followers, 1.1M engagements
"Why 5/3 is a fundamental constant for turbulence Some mathematical order amidst the chaos of turbulence. Vortex rings with Physics Girl: https://youtu.be/N7d_RWyOv20 Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/turbulence-thanks Home page: https://www.3blue1brown.com Thanks to Dan Walsh for many great ideas and thanks to Mike Hansen for many helpful conversations. Error correction: I meant to describe Kolmogorov as a 20th-century mathematician not"
YouTube Link 2018-11-07T20:20Z 8.1M followers, 807.8K engagements
"Olympiad level counting (Generating functions) A lesson on generating functions and clever uses of complex numbers for counting Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. Special thanks: https://3b1b.co/lessons/subsets-puzzle#thanks Artwork by Kurt Burns Music by Vince Rubinetti Nice writeup and video giving solutions to the exercises at the end by Benjamin Hackl https://benjamin-hackl.at/blog/2022/06/generating-functions-3b1b.html https://youtu.be/9SzwfM-S9sk [---] Combinatorial problems by Titu Andreescu"
YouTube Link 2022-05-23T15:55Z 8.1M followers, 2.3M engagements
"What makes a great math explanation SoME2 results Winners and honorable mentions for the SoME2 contest Playlist of all entries: https://www.youtube.com/playlistlist=PLnQX-jgAF5pTZXPiD8ciEARRylD9brJXU Help fund future projects: https://www.patreon.com/3blue1brown Post with links to all entries: https://www.3blue1brown.com/blog/some2 Winners Clear Crystal Conundrums A Multifaceted Intro to Group Theory https://explanaria.github.io/crystalgroups/ The Lore of Calculus https://youtu.be/5M2RWtD4EzI How Realistic CGI Works (And How To Do It Way Faster) https://www.youtube.com/watchv=gsZiJeaMO48"
YouTube Link 2022-10-01T19:23Z 8.1M followers, 800.4K engagements
"The limit of limiting arguments A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/VYQVlVoWoPY That video gives multiple examples of lying with visual proofs Editing from the original video into this short by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2023-12-23T00:00Z 8.1M followers, 2.1M engagements
"Seeing with sound A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/3s7h2MHQtxc Editing from the original video into this short by Dawid Koodziej"
YouTube Link 2023-12-08T00:00Z 5.9M followers, 652.6K engagements
"The barber pole effect A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/QCX62YJCmGk Filming by Quinn Brodsky Editing from long-form to short by Dawid Koodziej"
YouTube Link 2023-12-09T00:00Z 7.6M followers, 511K engagements
"Summer of Math Exposition #4 Teachers I'd love to hear from you Make a math explainer get feedback and receive prizes: https://some.3b1b.co Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. ------------------ These animations are largely made using a custom Python library manim. See the FAQ comments here: https://3b1b.co/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ All code for specific videos is visible here: https://github.com/3b1b/videos/"
YouTube Link 2025-05-05T15:00Z 7.3M followers, 88.4K engagements
"A simple image convolution A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/KuXjwB4LzSA That video introduces convolutions as used in image processing probability and signal processing. Editing from long-form to short by Dawid Koodziej"
YouTube Link 2023-12-12T00:00Z 7.2M followers, 1.1M engagements
"25 Math explainers you may enjoy SoME3 results Playlist of all entries: https://www.youtube.com/playlistlist=PLnQX-jgAF5pQS2GUFCsatSyZkSH7e8UM8 All non-video entries: https://some.3b1b.co/non-videos Thank you to Jane Street both for funding the event and providing eager and able guest judges to the final stages of the process. Organization and logistics were handled by James Schloss aka @LeiosLabs Web development by Frdric Crozatier 0:00 - The event 1:34 - Pixel Art Anti-aliasing 2:26 - The Enola Gay 3:40 - Pitch shifter 4:14 - Cayley Graphs 4:51 - Longest Increasing Subsequence 5:49 - Matrix"
YouTube Link 2023-10-07T14:28Z [--] followers, 537K engagements
"The dynamics of e(i) A fuller version of this explanation also including the reason we care about complex exponents in the first place: https://youtu.be/-j8PzkZ70Lg"
YouTube Link 2025-10-11T21:28Z 7.8M followers, 68.3K engagements
"Q&A with Grant windy walk edition Thank you for [---] subscribers. Store: http://3b1b.co/store Links to things discussed below The Bit Player https://thebitplayer.com/ The Idea Factory https://amzn.to/325PY6W The Information A History A Theory A Flood https://amzn.to/2QhfUtR You can read about Lorenz in "Chaos" also by James Gleick https://amzn.to/3tcXtVF Anthropocene reviewed https://www.wnycstudios.org/podcasts/anthropocene-reviewed Hardcore history https://www.dancarlin.com/ The Numberphile podcast https://www.numberphile.com/podcast Recent Quanta article on the eigenvector discovery"
YouTube Link 2019-11-23T01:00Z 6.6M followers, 455.1K engagements
"The space of musical note pairs Full video: https://youtu.be/IQqtsm-bBRU"
YouTube Link 2025-01-08T21:11Z 6.9M followers, 769.4K engagements
"The DP-3T algorithm for contact tracing (with Nicky Case) This is a video adaptation of a post by my friend Nicky Case: https://ncase.me/contact-tracing/ New post by Nicky on COVID-19: https://ncase.me/covid-19/ Consider supporting their work: https://www.patreon.com/ncase/ Supporters of this video: https://3b1b.co/ctracing-thanks DP-3T Whitepaper: https://github.com/DP-3T/documents/blob/master/DP3T%20White%20Paper.pdf Full repo: https://github.com/DP-3T Where did the number 60% come from https://science.sciencemag.org/content/early/2020/04/09/science.abb6936 The specific figure is Figure 3"
YouTube Link 2020-05-14T15:00Z 7.8M followers, 386.5K engagements
"Snell's law proof using springs This is a supplement to the Brachistochrone video proving Snell's law with a clever little argument by Mark Levi"
YouTube Link 2016-04-01T20:27Z 7.5M followers, 218.1K engagements
"The chessboard and coins puzzle Video with the solution: https://youtu.be/as7Gkm7Y7h4 3b1b on a meta-puzzle: https://youtu.be/wTJI_WuZSwE (These description links aren't active in the shorts player but you can follow the link on the bottom of the video screen itself) This comes from a collaboration I did with Stand-up Maths where on his channel we covered the solution and here on 3blue1brown we analyze a meta-puzzle. Editing from long-form to short by Dawid Koodziej This comes from a collaboration I did with Stand-up Maths where on his channel we covered the solution and here on 3blue1brown"
YouTube Link 2023-12-10T00:00Z 7.1M followers, 4.3M engagements
"When being beautifully wrong leads to discovery Full video: https://youtu.be/YdOXS_9_P4U Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-02-28T15:00Z 8.1M followers, 2.5M engagements
"A cute probability fact (part 1) max(rand() rand()) has the same effect as sqrt(rand()) The next short explains why: https://youtube.com/shorts/sNWDjbaT208 See Matt Parker's video for more: https://youtu.be/ga9Qk38FaHM"
YouTube Link 2024-09-10T15:42Z 6.6M followers, 343.8K engagements
"Other math channels you'd enjoy Think Twice: https://www.youtube.com/channel/UC9yt3wz-6j19RwD5m5f6HSg LeiosOS: https://www.youtube.com/user/LeiosOS Welch Labs: https://www.youtube.com/user/Taylorns34 Infinity plus one: https://infinityplusonemath.wordpress.com/ Check out the ones on relativity https://infinityplusonemath.wordpress.com/2017/03/11/a-mathematical-intro-to-special-relativity/ Music by Enoch Kim https://soundcloud.com/themusemaker ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to"
YouTube Link 2018-06-27T16:29Z [--] followers, 240.1K engagements
"Winding numbers and domain coloring An algorithm for numerically solving certain 2d equations. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/winding-thanks Writing and animations by Sridhar Ramesh with editing and narration by Grant Sanderson. Even though we described how winding numbers can be used to solve 2d equations at a high level it's worth pointing out that there are a few details missing for if you wanted to actually implement this. For"
YouTube Link 2018-03-24T14:42Z 7.2M followers, 978.8K engagements
"How colliding blocks act like a beam of light.to compute pi. The third and final part of the block collision sequence. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/clacks-thanks Home page: https://www.3blue1brown.com Error correction: I wrote the answer as floor(pi/theta) when really it should be ceiling(pi/theta) - [--] t account for values of theta perfectly dividing pi. For example the case of equal masses gives an angle of pi/4 and [--] total clacks."
YouTube Link 2019-02-03T16:23Z 7.2M followers, 1.4M engagements
"Music And Measure Theory A connection between a classical puzzle about rational numbers and what makes music harmonious. Thanks to these viewers for their contributions to translations German: Josh Russian: e-p-h"
YouTube Link 2015-10-04T02:14Z 7.8M followers, 1.7M engagements
"Why do colliding blocks compute pi Even prettier solution: https://youtu.be/brU5yLm9DZM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/clacks-thanks Home page: https://www.3blue1brown.com Many of you shared solutions attempts and simulations with me this last week. I loved it You all are the best. Here are just two of my favorites. By a channel STEM cell: https://youtu.be/ils7GZqp_iE By Doga Kurkcuoglu:"
YouTube Link 2019-01-20T16:40Z 7.1M followers, 7.3M engagements
"A cute probability fact (part 3) Why max(rand() rand()) is the same as sqrt(rand()) See Matt Parker's video for more: https://youtu.be/ga9Qk38FaHM"
YouTube Link 2024-09-10T15:42Z 6.6M followers, 222.4K engagements
"Make math videos Summer of Math Exposition announcement Announcement for the [----] Summer of Math Exposition Details: https://3b1b.co/SoME1 Podcast/New channel: https://www.youtube.com/GrantSanderson Things referenced through the video James Schloss: https://www.youtube.com/user/LeiosOS Free will theorem: https://www.ams.org/notices/200902/rtx090200226p.pdf Kolmogorov complexity and primes: https://people.cs.uchicago.edu/fortnow/papers/kaikoura.pdf Tadashi Tokieda talk: https://youtu.be/tQQ3oiB32GI Boarbarktree: https://www.youtube.com/channel/UCFeIEAkqvS4fJMTwUtF4OFw Mathologer:"
YouTube Link 2021-07-16T18:39Z 7.2M followers, 764.4K engagements
"Infinite Lighthouses and A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/d-o3eB9sfls"
YouTube Link 2023-12-21T00:00Z 7.1M followers, 2.2M engagements
"A cute probability fact (part 2) How do think about max(rand() rand()) The next short finishes the explanation: https://youtube.com/shorts/lpzUZDefha0"
YouTube Link 2024-09-10T15:42Z 6.6M followers, 105.1K engagements
"Pure Fourier series animation montage Because why not Learn the math behind this: https://youtu.be/r6sGWTCMz2k If you're curious about the number of vectors used for each animation: - Eighth note: [---] - Sigma: [---] - Britain: [---] - Fourier drawing: [---] - Nail and Gear: [---] - Treble clef: [---] - Hilbert curve: [---] (relatively small given the detail which is why it looks puzzley) - Seattle: [---] These animations are made using manim a scrappy open source python library: https://github.com/3b1b/manim If you want to check it out I feel compelled to warn you that it's not the most well-documented"
YouTube Link 2019-07-03T04:05Z 8.1M followers, 702.9K engagements
"The twirling tiles puzzle Full video: https://youtu.be/piJkuavhV50 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-11-13T18:01Z 8.1M followers, 257.7K engagements
"Higher order derivatives Chapter [--] Essence of calculus A very quick primer on the second derivative third derivative etc. Next chapter: https://youtu.be/3d6DsjIBzJ4 Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Italian: hi-anji Vietnamese: ngvutuan2811 ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to stay posted about new videos subscribe and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see"
YouTube Link 2017-05-07T14:05Z 8.1M followers, 888.2K engagements
"Zooming out by powers of [--] From this video: https://youtu.be/YdOXS_9_P4U Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-03-26T18:37Z 8.1M followers, 2.8M engagements
"Answering viewer questions about refraction Why bending how can light go "faster" than light and more Lessons are primarily funded directly by viewers who get early access to new videos: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Much of the last video as well as this one is based on the following Feynman Lecture: https://www.feynmanlectures.caltech.edu/I_31.html Looking Glass Universe videos on the refractive index: https://youtu.be/uo3ds0FVpXssi=Q12Rgz9vN1JMo_di Timestamps: 0:00 - Why slowing implies bending 3:36 - Recap for how slowing"
YouTube Link 2023-12-03T11:35Z 8.1M followers, 1.1M engagements
"2021 Summer of Math Exposition results Take a look at the full playlist (really): https://www.youtube.com/watchv=fJWnA4j0_ho&list=PLnQX-jgAF5pTkwtUuVpqS5tuWmJ-6ZM-Z Blog post with more details: https://3b1b.co/some1-results Thanks as always to the supporters of this channel for helping to make this whole project possible: http://3b1b.co/thanks ------------------ Typo at 2:00 it should read "Burkard Polster" Videos and posts mentioned in this video. That weird light at the bottom of a mug ENVELOPES https://youtu.be/fJWnA4j0_ho Hiding Images in Plain Sight: The Physics Of Magic Windows"
YouTube Link 2021-10-23T20:25Z 8.1M followers, 833.7K engagements
"Newtons Fractal is beautiful Full video: https://youtu.be/-RdOwhmqP5s"
YouTube Link 2024-11-16T16:53Z 8.1M followers, 216.3K engagements
"A quick trick for computing eigenvalues Chapter [--] Essence of linear algebra How to write the eigenvalues of a 2x2 matrix just by looking at it. Need a refresher on eigenvalues https://youtu.be/PFDu9oVAE-g Thanks to Tim for the jingle: https://www.youtube.com/acapellascience Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. Special thanks to these supporters: https://3b1b.co/quick-eigen-thanks Lockdown math lecture talking about the mean product formula: https://youtu.be/MHXO86wKeDY Timestamps: 0:00 - Background"
YouTube Link 2021-05-07T21:39Z 8.1M followers, 1.3M engagements
"Fourier series A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/r6sGWTCMz2k That video tells the story of how this concept was originally invented to solve the heat equation. Thanks to Dawid Koodziej for editing together this short Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2023-12-08T00:00Z 8.1M followers, 2.4M engagements
"Triangle of Power Alternate notation for powers logs and roots. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. (This is the corrected version of the one I put out a month or so ago in which my animation for all the inverse operations was incorrect) Here's a sketch from the math redditer Cosmologicon showing how this might be usual with practical space considerations: http://i.imgur.com/hAeJokq.jpg This original comes from an answer to a math exchange post by Alex Jordan which you can find here:"
YouTube Link 2016-06-26T05:51Z 8.1M followers, 835.7K engagements
"Euler's Formula Poem A poem about why e to the pi i equals [---] based on this video: http://youtu.be/F_0yfvm0UoU Full text of the poem here: http://3blue1brown.com/poems/epii Music: "Sundays" by Time for Three http://www.tf3.com/"
YouTube Link 2015-03-05T06:15Z 8.1M followers, 184.4K engagements
"The barber pole optical mystery Series exploring optics: https://www.youtube.com/watchv=QCX62YJCmGk&list=PLZHQObOWTQDMKqfyUvG2kTlYt-QQ2x-ui Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-01-06T15:37Z 8.1M followers, 949.3K engagements
"Thinking through double slits Extracted from this video about holograms: https://youtu.be/EmKQsSDlaa4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-12-26T16:48Z 8.1M followers, 630K engagements
"Exponential growth and epidemics A primer on exponential and logistic growth Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/covid-thanks Home page: https://www.3blue1brown.com Excellent visualization of this kind of growth from Minutephysics and Aatish Bhatia: https://www.youtube.com/watchv=54XLXg4fYsc Data source: https://www.worldometers.info/coronavirus/coronavirus-cases/#case-tot-outchina Some have (quite rightfully) commented on how you shouldn't"
YouTube Link 2020-03-08T16:58Z 8.1M followers, 6.2M engagements
"Temperature in LLMs This comes from a full video breaking down how LLMs work. The link is on the bottom of the screen (in the shorts feed at least) or here for reference: https://youtu.be/wjZofJX0v4M Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-04-28T15:22Z 8.1M followers, 366K engagements
"Incomplete open cubes Full video: https://youtu.be/_BrFKp-U8GI Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-09-07T12:25Z 8.1M followers, 219.3K engagements
"Hilbert's Curve: Is infinite math useful Space-filling curves and the connection between infinite and finite math. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com Supplement with more space-filling curve fun: https://youtu.be/RU0wScIj36o For more information on sight-via sound this paper involving rewiring a ferret's retinas to its auditory cortex is particularly thought-provoking: http://phy.ucsf.edu/houde/coleman/sur2.pdf Alternatively here is the NYT summary:"
YouTube Link 2017-07-21T15:33Z 8.1M followers, 2.4M engagements
"The Wallis product for pi proved geometrically A geometric proof of a famous Wallis product for pi. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/wallis-thanks If you want to dive into the relevant ideas required to make this proof more rigorous the relevant search term is "dominated convergence". https://en.wikipedia.org/wiki/Dominated_convergence_theorem Here's a good blog post on the topic: https://www.math3ma.com/blog/dominated-convergence-theorem"
YouTube Link 2018-04-20T18:59Z 8.1M followers, 912.3K engagements
"How Earth's size was computed by Eratosthenes From this video: https://youtu.be/YdOXS_9_P4U Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-02-12T15:00Z 8.1M followers, 288.1K engagements
"Definition of a "bit" in information theory A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/v68zYyaEmEA That video describes using information theory to write a bot that plays Wordle Editing from long-form to short by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-01-02T00:00Z 8.1M followers, 237.4K engagements
"Cross products in the light of linear transformations Chapter [--] Essence of linear algebra Why the formula for cross products matches the geometric intuition. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ For anyone who wants to understand the cross-product more deeply this video shows how it relates to a certain linear transformation via duality. This perspective gives a very elegant explanation of why the traditional computation of a dot product corresponds to"
YouTube Link 2016-09-01T03:54Z 8.1M followers, 1.5M engagements
"Holograms are wild (full video linked above) Full video: https://youtu.be/EmKQsSDlaa4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-10-05T15:35Z 8.1M followers, 2.1M engagements
"Sphere surface area proof sketch Full video: https://youtu.be/GNcFjFmqEc8"
YouTube Link 2024-11-17T16:00Z 8.1M followers, 1.6M engagements
"Why Laplace transforms are so useful Studying the forced harmonic oscillator by taking a Laplace transform and studying its poles. Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Chapter on the Laplace Transform: https://youtu.be/j0wJBEZdwLs Chapter on the S-plane and Simple Harmonic Motion: https://youtu.be/-j8PzkZ70Lg Timestamps: 0:00 - Opening puzzle 1:06 - Key properties of a Laplace Transform 3:29 - Qualitative analysis with Laplace"
YouTube Link 2025-11-05T13:09Z 8.1M followers, 633.8K engagements
"How word vectors encode meaning This comes from a full video dissecting how LLMs work. In the shorts player you can click the link at the bottom of the screen or for reference: https://youtu.be/wjZofJX0v4M"
YouTube Link 2024-04-11T16:23Z 8.1M followers, 3.4M engagements
"How prisms work (full video linked above) A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/KTzGBJPuJwM There I wanted to dig deeper to understand light slows down and why this would depend on the color. Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2023-12-07T01:31Z 8.1M followers, 8.4M engagements
"The most unexpected answer to a counting puzzle Solution: https://youtu.be/6dTyOl1fmDo Light-based solution: https://youtu.be/brU5yLm9DZM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/clacks-thanks New to this channel It's all about teaching math visually. Take a look and see if there's anything you'd like to learn. NY Times blog post about this problem: https://wordplay.blogs.nytimes.com/2014/03/10/pi/ The original paper by Gregory Galperin:"
YouTube Link 2019-01-13T16:12Z 8.1M followers, 14.5M engagements
"Imaginary interest rates Ep. [--] Lockdown live math Compound interest e and how it relates to circles. Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Great Mathologer video: https://youtu.be/-dhHrg-KbJ0 Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258221677990703105 https://twitter.com/ThuyNganVu/status/1258222002889875457 My other videos on imaginary exponents: https://youtu.be/v0YEaeIClKY https://youtu.be/mvmuCPvRoWQ Mistakes:"
YouTube Link 2020-05-01T20:11Z 8.1M followers, 948.2K engagements
"This open problem taught me what topology is The inscribed square/rectangle problem solved using Mbius strips and Klein bottles. Playlist with more neat proofs: https://www.youtube.com/playlistlist=PLZHQObOWTQDPSKntUcMArGheySM4gL7wS Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. This argument was originally by Herbert Vaughan appearing for examples in this issue of the Topology Proceedings. https://topology.nipissingu.ca/tp/reprints/v06/tp06107.pdf The on-screen argument for"
YouTube Link 2024-12-24T17:50Z 8.1M followers, 2.1M engagements
"Backpropagation intuitively Deep Learning Chapter [--] What's actually happening to a neural network as it learns Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/nn3-thanks Written/interactive form of this series: https://www.3blue1brown.com/topics/neural-networks And by CrowdFlower: http://3b1b.co/crowdflower Home page: https://www.3blue1brown.com/ The following video is sort of an appendix to this one. The main goal with the follow-on video is to show the"
YouTube Link 2017-11-03T14:03Z 8.1M followers, 5.9M engagements
"The Triangle Of Power The referenced stack exchange post by usename 2'5 9'2 http://math.stackexchange.com/questions/30046/alternative-notation-for-exponents-logs-and-roots"
YouTube Link 2024-11-15T15:58Z 8.1M followers, 569.6K engagements
"The topology of two-note chords Based on a construction in this video: https://youtu.be/IQqtsm-bBRU Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-01-30T15:00Z 8.1M followers, 1.3M engagements
"LLMs are next-word predictors Full video: https://youtu.be/wjZofJX0v4M Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-11-04T15:24Z 8.1M followers, 209.3K engagements
"But why would light "slow down" Visualizing Feynman's lecture on the refractive index How the index of refraction arises and why it depends on color (as seen with a prism) Quotebook Notebooks: https://3b1b.co/store These lessons are primarily funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. This video is largely based on the following Feynmann lecture https://www.feynmanlectures.caltech.edu/I_31.html Looking Glass Universe videos on the index of refraction: https://youtu.be/uo3ds0FVpXs The explanation for why the phase of a"
YouTube Link 2023-11-30T18:42Z 8.1M followers, 2.7M engagements
"But what is a convolution Discrete convolutions from probability to image processing and FFTs. Video on the continuous case: https://youtu.be/IaSGqQa5O-M Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these supporters: https://3b1b.co/lessons/convolutions#thanks An equally valuable form of support is to simply share the videos. Other videos I referenced Live lecture on image convolutions for the MIT Julia lab https://youtu.be/8rrHTtUzyZA Lecture on Discrete Fourier Transforms https://youtu.be/g8RkArhtCc4 Reducible video on FFTs https://youtu.be/h7apO7q16V0"
YouTube Link 2022-11-18T16:00Z 8.1M followers, 3.6M engagements
"Large Language Models explained briefly A light intro to LLMs chatbots pretraining and transformers. Dig deeper here: https://www.youtube.com/playlistlist=PLZHQObOWTQDNU6R1_67000Dx_ZCJB-3pi Technical details as a talk: https://youtu.be/KJtZARuO3JY This was made for an exhibit at the Computer History Museum: https://computerhistory.org/ Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support No secret end-screen vlog for this one the end-screen real estate was all full ------------------ These animations are largely made using a custom Python library"
YouTube Link 2024-11-20T15:07Z 8.1M followers, 5.4M engagements
"Beyond the Mandelbrot set an intro to holomorphic dynamics An intro to holomorphic dynamics the study of iterated complex functions. Video on Newton's fractal: https://youtu.be/-RdOwhmqP5s Special thanks to these supporters: https://3b1b.co/lessons/holomorphic-dynamics#thanks Extra special thanks to Sergey Shemyakov of Aix-Marseille University for helpful conversations and for introducing me to this phenomenon. Introduction to Fatou sets and Julia sets including a discussion of Montel's theorem and its consequences: http://www.math.stonybrook.edu/scott/Papers/India/Fatou-Julia.pdf Numberphile"
YouTube Link 2021-10-16T12:39Z 8.1M followers, 1.8M engagements
"The inscribed square problem Full video: https://youtu.be/IQqtsm-bBRU Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2024-12-24T18:46Z 8.1M followers, 4.6M engagements
"The unexpectedly hard windmill question (2011 IMO Q2) The famous (infamous) "windmill" problem on the [----] IMO Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/windmillthanks Home page: https://www.3blue1brown.com The author of this problem was Geoff Smith. You can find the full list of problems considered for the IMO that year together with their solutions here: https://www.imo-official.org/problems/IMO2011SL.pdf You can find data for past IMO results"
YouTube Link 2019-08-04T17:03Z 8.1M followers, 5.7M engagements
"Measuring the speed of light using Jupiter's moons From this video with Terry Tao: https://youtu.be/hFMaT9oRbs4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-04-07T15:57Z 8.1M followers, 2.4M engagements
"The more general uncertainty principle regarding Fourier transforms The meaning of the uncertainty principle in the context of Fourier transforms Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/uncertainty-thanks For more on quantum mechanical wave functions I highly recommend this video by udiprod: https://youtu.be/p7bzE1E5PMY Minute physics on special relativity: https://youtu.be/1rLWVZVWfdY Main video on the Fourier transform"
YouTube Link 2018-02-25T00:25Z 8.1M followers, 2.3M engagements
"Some light quantum mechanics (with minutephysics) The math of superposition and quantum states. Minutephysics channel: https://www.youtube.com/user/minutephysics Help fund future projects: https://www.patreon.com/3blue1brown This video was sponsored by Brilliant: https://brilliant.org/3b1b An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/light-quantum-thanks Huge thanks to my friend Evan Miyazono both for encouraging me to do this project and for helping me understand many things along the way. This is a simple"
YouTube Link 2017-09-13T14:06Z 8.1M followers, 2.2M engagements
"Pi hiding in prime regularities A story of pi primes complex numbers and how number theory braids them together. Mathologer on why 4k + 1primes break down as sums of squares: https://youtu.be/DjI1NICfjOk Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/leibniz-thanks Home page: https://www.3blue1brown.com/ For those of you curious about the finer details here's a writeup from the viewer Daniel Flores justifying the final approximation:"
YouTube Link 2017-05-19T15:41Z 8.1M followers, 2.8M engagements
"Eigenvectors and eigenvalues Chapter [--] Essence of linear algebra A visual understanding of eigenvectors eigenvalues and the usefulness of an eigenbasis. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com Full series: https://3b1b.co/eola Future series like this are funded by the community through Patreon where supporters get early access as the series is being produced. http://3b1b.co/support A solution to the puzzle at the end:"
YouTube Link 2016-09-15T18:22Z 8.1M followers, 6M engagements
"A bizarre probability fact I learned this from Matt Parker who then made a full video: https://youtu.be/ga9Qk38FaHM"
YouTube Link 2024-11-12T23:09Z 8.1M followers, 1.8M engagements
"How secure is [---] bit security How hard is it to find a 256-bit hash just by guessing and checking Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Several people have commented about how [----] would be the maximum number of attempts not the average. This depends on the thing being attempted. If it's guessing a private key you are correct but for something like guessing which input to a hash function gives the desired output (as in bitcoin mining for example) which"
YouTube Link 2017-07-08T14:19Z 8.1M followers, 3.7M engagements
"These integrals all equal until. A link to the full video is at the bottom of the screen. Or for reference: https://youtu.be/851U557j6HE These are known as Borwein integrals Editing from long-form to short by Dawid Koodziej Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2023-12-11T00:00Z 8.1M followers, 829.4K engagements
"How to lie using visual proofs Three false proofs and what lessons they teach. New notebooks: https://store.dftba.com/collections/3blue1brown/products/mathematical-quotebook-notebook Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. Here's a nice short video on the false pi = [--] proof https://www.youtube.com/watchv=6Qnfd5dRyf4 Time stamps: 0:00 - Fake sphere proof 1:39 - Fake pi = [--] proof 5:16 - Fake proof that all triangles are isosceles 9:54 - Sphere "proof" explanation 15:09 - pi = [--] "proof" explanation 16:57 -"
YouTube Link 2022-07-03T15:03Z 8.1M followers, 4.2M engagements
"The essence of calculus What might it feel like to invent calculus Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/lessons/essence-of-calculus#thanks In this first video of the series we see how unraveling the nuances of a simple geometry question can lead to integrals derivatives and the fundamental theorem of calculus. Thanks to these viewers for their contributions to translations Dutch: @LFWarsen Lauri Warsen Hebrew: Imri Omer Tuchfeld Hindi: Vinayak Hungarian:"
YouTube Link 2017-04-28T15:58Z 8.1M followers, 11.2M engagements
"But what are Hamming codes The origin of error correction A discovery-oriented introduction to error correction codes. Part 2: https://youtu.be/b3NxrZOu_CE Ben Eater:'s take: https://youtu.be/h0jloehRKas Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/hamming-thanks Heavily related is the chessboard puzzle I did with Matt Parker: https://youtu.be/as7Gkm7Y7h4 You can read Hamming's own perspective on his discovery of these codes in chapter [--] of "The Art"
YouTube Link 2020-09-04T15:32Z 8.1M followers, 3M engagements
"What does it feel like to invent math An exploration of infinite sums from convergent to divergent including a brief introduction to the 2-adic metric all themed on that cycle between discovery and invention in math. Home page: https://www.3blue1brown.com/ Music: Legions (Reverie) by Zoe Keating Thanks to these viewers for their contributions to translations Italian: Marco Fantozzi Thai: @korakot own doggoVV ------------------ 3blue1brown is a channel about animating math in all senses of the word animate. And you know the drill with YouTube if you want to stay posted about new videos"
YouTube Link 2015-08-14T01:20Z 8.1M followers, 4.6M engagements
"Testing your intuition for quantum computing Full video: https://youtu.be/RQWpF2Gb-gU Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-04-30T12:32Z 8.1M followers, 1.3M engagements
"This pattern breaks but for a good reason Moser's circle problem An apparent pattern that breaks and the reason behind it. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. This is a remake of one of the earliest videos on the channel. It's such a wonderful problem and the audio/pacing in earlier videos was really suboptimal so I wanted to freshen it up a little here. Timestamps 0:00 - The pattern 2:20 - Counting chords 4:03 - Counting intersection points 6:20 - Euler's characteristic formula 11:30 - Connection"
YouTube Link 2023-07-02T04:41Z 8.1M followers, 2.9M engagements
"Exploration & Epiphany Guest video by Paul Dancstep Sol LeWitt's "Incomplete Open Cubes" and rediscovering Burnside's lemma in group theory An interview with the author of this video: https://youtu.be/JEeM2ABUMoo Instead of sponsored ad reads these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to share the videos. Home page: https://www.3blue1brown.com Thanks to the Wadsworth Atheneum for granting permission to use LeWitt's notebooks. Talks by Paul you can find online: What is Category Theory: https://youtu.be/eXBwU9ieLL0 How to Predict"
YouTube Link 2025-09-07T12:25Z 8.1M followers, 472.1K engagements
"How to measure nearby galaxies From this video: https://youtu.be/hFMaT9oRbs4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-04-20T19:36Z 8.1M followers, 180.8K engagements
"Measuring the distance to Venus without radar From this video with Terry Tao: https://youtu.be/hFMaT9oRbs4 Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-04-08T13:45Z 8.1M followers, 428.4K engagements
"The dynamics of e(i) A fuller version of this explanation also including the reason we care about complex exponents in the first place: https://youtu.be/-j8PzkZ70Lg Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue Mathematics three blue one brown [--] blue [--] brown 3b1b 3brown1blue [--] brown [--] blue three brown one blue"
YouTube Link 2025-10-12T12:40Z 8.1M followers, 1.1M engagements
"Logarithm Fundamentals Ep. [--] Lockdown live math Back to the basics with logarithms. Full playlist: https://www.youtube.com/playlistlist=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Triangle of power: https://youtu.be/sULa9Lc4pck Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258222677573001219 Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ The live question setup with stats on-screen is powered by Itempool."
YouTube Link 2020-05-05T20:36Z 8.1M followers, 1.2M engagements
Limited data mode. Full metrics available with subscription: lunarcrush.com/pricing