PickVidsBest Recreational & visual math Videos
「Recreational & visual math」下面有141部被不同的人、在不同月份推荐过的视频。挑的时候先看对象：入门35部，适合还没学过的人；进阶22部，适合已经懂术语的人；普通向84部，按兴趣就能看；更硬的0部，留给想看推导或细节的人。这一类数量最多的是讲解，所以它们的共同点是用一个图像或类比把一个概念补上。常出现的频道包括3Blue1Brown、Numberphile、Stand-up Maths。目录给这个主题划的范围是：Math explainers and recreation: 3Blue1Brown, Numberphile, Mathologer, puzzles, fractals, surreal numbers, math history, mathematicians, beautiful proofs, math in everyday life.如果只看三部，就从《Vectors | Chapter 1, Essence of linear algebra》开始，它负责把问题讲出画面；然后看《But what is the Fourier Transform? A visual introduction.》，换一种讲法或例子；最后看《But what is a neural network? | Deep learning chapter 1》，留给已经有基础的人。页面按每页24部切开，顺序看的是被推荐跨越了多少个月，不是播放量。每条标题下面那一句是这部片子自己的内容说明，用来区分它在讲定义、过程、演示还是观点。点进去能看到推荐原话、原文链接和适合谁看。看的时候把强烈推荐当成有人明确叫你去看，把引用当成只是拿来举例，把批评留下来对照，不要把每条评论都当成同一力度。
Vectors | Chapter 1, Essence of linear algebra
The first chapter of 3Blue1Brown's Essence of Linear Algebra series, introducing vectors with animated geometric visuals.
But what is the Fourier Transform? A visual introduction.
3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.
But what is a neural network? | Deep learning chapter 1
3Blue1Brown's first chapter on deep learning explains what neurons and layers are and the math underlying a basic neural network, using handwritten digit recognition with visual animations.
The Beauty of Bézier Curves
Freya Holmer explains how Bezier curves work, from the helper-line construction to their uses in animation, text rendering and shapes.
The Continuity of Splines
Freya Holmer's 74-minute video essay on splines, covering Bezier curves, B-splines, derivatives and the different levels of continuity (C0, C1, C2), built with custom animation tools.
Jim Simons (full length interview) - Numberphile
The full-length Numberphile interview with mathematician and hedge fund founder Jim Simons.
But how does bitcoin actually work?
3Blue1Brown explains the math and mechanics behind Bitcoin visually: ledgers, digital signatures, proof of work and the blockchain, building up a decentralized payment system from first principles.
Conway's Game Of Life in APL
A short Dyalog demonstration building Conway's Game of Life in a single line of APL, step by step.
The essence of calculus
The first video of 3Blue1Brown's Essence of Calculus series, which builds toward integrals, derivatives, and the fundamental theorem of calculus from a simple geometry question.
The man with 1,000 Klein Bottles UNDER his house - Numberphile
Numberphile visits Cliff Stoll, the man behind ACME Klein Bottles, and sees how he stores a thousand glass Klein bottles in a crawlspace under his house.
Essence of linear algebra preview
A five-minute preview of 3Blue1Brown's Essence of Linear Algebra series, which uses animation to build geometric intuition for topics from a standard linear algebra course.
A Swift Introduction to Geometric Algebra
An animated introduction to geometric algebra, presented as a language that can describe most of physics.
The hardest problem on the hardest test
3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.
Imaginary Numbers Are Real [Part 1: Introduction]
The first part of Welch Labs' series on imaginary numbers, presenting them as the natural extension of the number line into two dimensions.
The determinant | Chapter 6, Essence of linear algebra
A 10-minute 3Blue1Brown chapter explaining the determinant as the factor by which a linear transformation scales area or volume.
Math's Fundamental Flaw
Veritasium's explainer on Godel's incompleteness theorems and the limits of mathematical proof, tracing set theory, Hilbert's program and the road to Turing and modern computing.
Fractals are typically not self-similar
3Blue1Brown explains fractal dimension and shows why many fractals are not strictly self-similar.
The Banach–Tarski Paradox
Vsauce's roughly 24 minute explainer on the Banach-Tarski paradox, building from infinity and set theory to the decomposition of a sphere into pieces that form two spheres.
Thinking outside the 10-dimensional box
3Blue1Brown visualizes high-dimensional spheres to explain a surprising puzzle about how a sphere fits in a box as dimensions grow.
Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra
3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series.
Life in life
A two-minute video of Conway's Game of Life running inside Conway's Game of Life, built from OTCA metapixels and Golly.
All the Numbers - Numberphile
Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond.
How Big is Graham's Number? (feat Ron Graham)
Numberphile talks with mathematician Ron Graham about the magnitude of Graham's number, building up from arrow notation to show how impossibly large it is.
The more general uncertainty principle, regarding Fourier transforms
3Blue1Brown shows how the uncertainty principle arises from Fourier transforms.