Best Pure mathematics Videos
「Pure mathematics」下面有97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30部,适合还没学过的人;进阶24部,适合已经懂术语的人;普通向38部,按兴趣就能看;更硬的5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、Mathologer。目录给这个主题划的范围是:Pure mathematics: algebra, group theory, number theory, topology, analysis, geometry, calculus, linear algebra, Euler, prime numbers, Riemann hypothesis, mathematical proofs, famous theorems.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《Lec 1 | MIT 18.06 Linear Algebra, Spring 2005》,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.

Lec 1 | MIT 18.06 Linear Algebra, Spring 2005
The first lecture of Gilbert Strang's MIT 18.06 Linear Algebra course, covering the geometry of linear equations.

The Most IMPORTANT Video You'll Ever See (part 1 of 8)
Part 1 of a lecture by physicist Albert Bartlett on the exponential function and its consequences for population growth, resource use and energy.

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.

Siggraph2019 Geometric Algebra
A SIGGRAPH 2019 course on geometric algebra.

Category Theory 1.1: Motivation and Philosophy
The first lecture in Bartosz Milewski's category theory series for programmers.

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.

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.

The Future of Mathematics?
Mathematician Kevin Buzzard explains why he believes the Lean theorem prover will shape the future of mathematics, and describes digitizing his university curriculum in Lean with undergraduates, plus the cultural challenges.

Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra
3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series.

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.

Visualizing the 4d numbers Quaternions
3Blue1Brown builds visual intuition for quaternions, showing how to think about this four-dimensional number system using stereographic projection and rotations in 3D space.

Pythagoras' theorem (a) | Math History | NJ Wildberger
The first lecture of N J Wildberger's History of Mathematics course, starting with Pythagoras' theorem and following Stillwell's text.

Why can't you multiply vectors?
Freya Holmer's Dutch Game Day 2023 talk asking why vectors can't be multiplied, building from complex numbers to a single axiom and arriving at geometric algebra, quaternions and multivectors.

Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.
Mathologer examines how identities like 1+2+3+...

Taking Vector Transposes Seriously | Jiahao Chen | JuliaCon 2017
Jiahao Chen's JuliaCon 2017 talk argues that vector transposes should be taken seriously in type systems and linear algebra libraries.