3Blue1Brown

3Blue1Brown

@3blue1brown · 8.8M subscribers · 247 videos · English

My name is Grant Sanderson. Videos here cover a variety of topics in math, or adjacent fields like physics and CS, all with an emphasis on visualizing the core ideas. The goal is to use animation to help elucidate and motivate otherwise tricky topics, and for difficult problems to be made simple with changes in perspective. For more information, other projects, FAQs, and inquiries see the website: https://www.3blue1brown.com

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Videos

40:44

There's never been a better time to go into math

2.8M views · 28d ago · 40:44

Sharing a few thoughts on the future of math These videos are funded directly by viewers An equally valuable form of support is to simply share the videos. Home page If you want a finger on the pulse of how mathematicians are feeling right now, take a look at this post on Proofs and Prompt

Topics: Math student angst · How does math work? · A proof machine · A conjecture machine · A theory machine · If AI is better at everything

🎵 Mentioned music: Track on vincerubinetti.bandcamp.com · Track on open.spotify.com

▶️ Mentioned videos: Secret Endscreen Vlog

📰 Mentioned news: Mailing list

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51:56

The last IMO problem AI could not solve

3.1M views · 1mo ago · 51:56

A beautiful puzzle that eluded AI, and the intuition it requires. See new videos early An equally valuable form of support is to simply share the videos. Home page Note for the quote at the end: The person who wrote that wanted me to relay a desired edit to the second paragraph, asking that it instead read, "I believe the value of this question as a mathematical discovery is no less real than that of frontier mathematics, albeit different in nature."

Topics: The one that AI missed · Problem statement · Finding the Optimal Construction · A weak lower bound · 3b1b Talent · Proving the Construction is Optimal

🎵 Mentioned music: Track on vincerubinetti.bandcamp.com · Track on open.spotify.com

▶️ Mentioned videos: Video on youtube.com · Secret Endscreen Vlog

📰 Mentioned news: Mailing list

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33:51

But what is cross-entropy? | Compression is Intelligence Part 2

929K views · 4mo ago · 33:51

Where the loss function for training LLMs comes from. Job opportunities aligned to this audience Early views and other perks for supporters Home page Part 1 If you want to learn more about Lagrange Multipliers, I made multiple videos and articles for the topic back in my Khan Academy days

Topics: Language trees and zipping · Defining cross-entropy · Intuition and examples · Application to language trees · Pre-training LLMs · What makes this loss function best?

🎵 Mentioned music: Track on vincerubinetti.bandcamp.com · Track on open.spotify.com

▶️ Mentioned videos: Part 1

📰 Mentioned news: Mailing list

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32:20

Reinventing Entropy | Compression is Intelligence Part 1

1.7M views · 5mo ago · 32:20

Guest: Reinventing Entropy

How to study the compressibility of language. See new projects before they go live Animation credit Manim scenes by Aaron Gostein and Grant Sanderson Shannon’s story, as well as those for various pi creatures, by Mitchell Zemil. Lunar robot and prediction/compression coin by Paul Dancstep NanoGPT animations by Clayton Rabideau

Topics: On “Compression is intelligence.” · The warmup example · What perfect compression looks like · Defining information · Information of language · Defining Entropy

🎵 Mentioned music: Track on vincerubinetti.bandcamp.com · Track on open.spotify.com

📰 Mentioned news: Mailing list

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44:52

How (and why) to take a logarithm of an image

2.4M views · 7mo ago · 44:52

Escher's Print Gallery, and the tour of complex analysis it invites. Explore our virtual career fair Join channel supporters to see videos early An equally valuable form of support is to share the videos. Home page Original paper by de Smit and Lenstra

Topics: The print gallery · Conformal maps from complex analysis · The complex exponential · The complex logarithm · 3b1b Talent · Constructing the key function

📖 Mentioned book: Book on Amazon

📰 Mentioned news: Mailing list

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1:00:24

The most beautiful formula not enough people understand

1.6M views · 8mo ago · 1:00:24

On the volumes of higher-dimensional spheres Explore the 3b1b virtual career fair: See Become a supporter for early views of new videos An equally valuable form of support is to simply share the videos. Home page Thanks to UC Santa Cruz for letting me film there, and special thanks to Pedro Morales-Almazan for arranging everything.

Topics: Random puzzle · Outside the box · Setting up the volume grid · Why 4πr^2 · Archimedes in higher dimensions · The general formula

🎵 Mentioned music: Track on vincerubinetti.bandcamp.com · Track on open.spotify.com

▶️ Mentioned videos: video on Numberphile with a fun application of this problem

📰 Mentioned news: Mailing list

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29:40

Why you can't comb a hairy ball, and why we care

3.7M views · 9mo ago · 29:40

Unexpected applications and a beautiful proof. Supporters get early access to new videos An equally valuable form of support is to simply share the videos. Home page 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

Topics: To comb a hairy ball · Applications · The puzzle of one null point · The proof outline · Defining orientation · Why inside-out is impossible

🎵 Mentioned music: Track on vincerubinetti.bandcamp.com · Track on open.spotify.com

📰 Mentioned news: Mailing list

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23:05

Why Laplace transforms are so useful

876K views · 1y ago · 23:05

Studying the forced harmonic oscillator by taking a Laplace transform and studying its poles. An equally valuable form of support is to simply share the videos. Home page Chapter on the Laplace Transform Chapter on the S-plane and Simple Harmonic Motion

Topics: Key properties of a Laplace Transform · Qualitative analysis with Laplace Transforms · The Laplace Transforms of a Derivative · The forced oscillator · Intuition from the transformed solution · Inverting to find a final answer

🎵 Mentioned music: Track on vincerubinetti.bandcamp.com · Track on open.spotify.com

▶️ Mentioned videos: Video on youtube.com · Video on youtube.com

📰 Mentioned news: Mailing list

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34:41

But what is a Laplace Transform?

2.2M views · 1y ago · 34:41

Visualizing the most important tool for differential equations. Previous chapter An equally valuable form of support is to simply share the videos. Home page Pi creature car artwork by Kurt Bruns Engine animation borrowed with permission from this (excellent) blog

Topics: Understanding the engine · Key background ideas · Definition and intuition · Complex integration · Analytic continuation · The transform of exponentials

🎵 Mentioned music: Track on vincerubinetti.bandcamp.com · Track on open.spotify.com

▶️ Mentioned videos: Previous chapter

📰 Mentioned news: Mailing list

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27:49

The Physics of Euler's Formula | Laplace Transform Prelude

1.3M views · 1y ago · 27:49

Guest: Laplace Transform Prelude

The simple harmonic oscillator and the fundamental role of complex exponents for ODEs. Next chapter on the Laplace Transform video An equally valuable form of support is to simply share the videos. Home page These animations are largely made using a custom Python library, manim. See the FAQ comments here

Topics: Euler's formula explained dynamically · The harmonic oscillator · General linear equations · Motivating the Laplace Transform

🎵 Mentioned music: Track on vincerubinetti.bandcamp.com · Track on open.spotify.com

▶️ Mentioned videos: Next chapter on the Laplace Transform video

📰 Mentioned news: Mailing list

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33:29

What was Euclid really doing? | Guest video by Ben Syversen

824K views · 1y ago · 33:29

What role were ruler and compass constructions really serving? Interview with the author of this video Supporters get early views of new videos Written, produced, edited, and animated by Ben Syversen Additional editing: Jack Saxon 3d Blender model: Jan-Hendrik Müller Additional Blender help: Thibaut Modrzyk (@Deepia) Illustrations: Alex Zepherin/DonDada Studio Camera: Giacomo Belletti Drums: Jeremy Gustin Additional music from Epidemic Sound

Topics: About guest videos · Why ruler and compass? · Diagrams as part of the proof · Geometry as philosophy · Mistakes in diagrammatic reasoning · The parallel postulate

▶️ Mentioned videos: Interview with the author of this video

📄 Mentioned papers: Paper on link.springer.com

📰 Mentioned news: Mailing list

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52:12

Exploration & Epiphany | Guest video by Paul Dancstep

519K views · 1y ago · 52:12

Sol LeWitt's "Incomplete Open Cubes" and rediscovering Burnside's lemma in group theory An interview with the author of this video An equally valuable form of support is to share the videos. Home page Thanks to the Wadsworth Atheneum for granting permission to use LeWitt's notebooks.

Topics: Incomplete open cubes · Sol LeWitt · Goofing around · Size and symmetry · Labelling things · Lookalikes

🎵 Mentioned music: Track on vincerubinetti.bandcamp.com · Track on open.spotify.com

▶️ Mentioned videos: An interview with the author of this video · Video on youtube.com · Video on youtube.com

📰 Mentioned news: Mailing list

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41:03

Simulating and understanding phase change | Guest video by Vilas Winstein

479K views · 1y ago · 41:03

Deriving the Boltzmann formula, defining temperature, and simulating liquid/vapor. @SpectralCollective has the second part You can play with a simulation of this model here These lessons are funded directly by viewers Home page

Topics: What is phase change? · The Boltzmann law and free energy · A preliminary simulation · Defining temperature · Deriving the Boltzmann law · Sampling with MCMC

▶️ Mentioned videos: SpectralCollective has the second part

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37:20

But how do AI images and videos actually work? | Guest video by Welch Labs

2.2M views · 1y ago · 37:20

Diffusion models, CLIP, and the math of turning text into images Welch Labs Book Sections Special Thanks to Jonathan Ho - Jonathan is the Author of the DDPM paper and the Classifier Free Guidance Paper. Preetum Nakkiran - Preetum has an excellent introductory diffusion tutorial

Topics: CLIP · Shared Embedding Space · Diffusion Models & DDPM · Learning Vector Fields · DDIM · Dall E 2

📄 Mentioned papers: arXiv 2006.11239 · arXiv 2207.12598 · arXiv 2406.08929 · CLIP Paper

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