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。

Fantastic Quaternions - Numberphile
Numberphile's James Grime introduces quaternions, a type of number beyond the complex numbers, building up from real and complex numbers and explaining why they are useful.

Pi hiding in prime regularities
3Blue1Brown shows how pi emerges from prime numbers via complex numbers and sums of squares, culminating in a formula for approximating pi.

Graham's Number - Numberphile
Numberphile's Tony Padilla and Matt Parker discuss Graham's number, once the largest number used in a mathematical proof, and how enormous it is.

Numberphile v. Math: the truth about 1+2+3+...=-1/12
Mathologer examines the infamous Numberphile claim that 1+2+3+...

Times Tables, Mandelbrot and the Heart of Mathematics
Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set.

Do Complex Numbers Exist?
Sabine Hossenfelder asks whether complex numbers are just a convenient tool or necessary in physics.

Cosmos - Carl Sagan - 4th Dimension
A segment from Carl Sagan's original Cosmos explaining the fourth spatial dimension through analogy with a two-dimensional world and shadow projection.

HACKENBUSH: a window to a new world of math
Owen Maitzen's animated hour-long introduction to Hackenbush, a simple combinatorial game, and how its strategy leads to surreal numbers and the roots of the number system.

1. A strange determinant
Timothy Gowers thinks aloud, in real time, as he tries to understand why Pascal's determinant equals 1.

Pi and the Mandelbrot Set - Numberphile
Numberphile with Dr Holly Krieger shows how the digits of pi surprisingly emerge from the Mandelbrot set.

Euler's formula with introductory group theory
3Blue1Brown builds intuition for Euler's formula, e^(pi i) = -1, using the core ideas of group theory.

Hamming, "n-Dimensional Space" (April 14, 1995)
Richard Hamming's 1995 lecture on n-dimensional space, showing how geometric intuition about spheres and cubes breaks down in high dimensions.

Lecture 7: Introduction to Galois Fields for the AES by Christof Paar
Christof Paar's university lecture introducing Galois fields and finite-field arithmetic as used in AES.

Infinite fractions and the most irrational number
Mathologer uses continued fractions to show why the golden ratio is the most irrational number, comparing it with root 2, e and pi and pointing to where this shows up in nature.

Hyperbolica: A Non-Euclidean Adventure [Old Trailer]
The old announcement trailer for Hyperbolica, CodeParade's Unity game set in hyperbolic and spherical space.

Lec 1 | MIT 6.042J Mathematics for Computer Science, Fall 2010
The first lecture of MIT 6.042J Mathematics for Computer Science, taught by Tom Leighton, introducing mathematical proofs.

What if Current Foundations of Mathematics are Inconsistent? | Vladimir Voevodsky
Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent.

Stanford Seminar: Beyond Floating Point: Next Generation Computer Arithmetic
John Gustafson presents posits, a proposed drop-in replacement for IEEE 754 floats that is simpler in hardware and more flexible in precision.

How Many Holes Does a Human Have?
Vsauce asks how many holes a human has and uses topology to show the answer depends on what counts as a hole, with animations and expert input.

Category Theory in Life - Eugenia Cheng
Eugenia Cheng gives the opening keynote at Lambda World 2017, presenting category theory as very abstract algebra whose abstraction gives it broad applicability.

The Hyperbolic Geometry of DMT Experiences (@Harvard Science of Psychedelics Club)
Andres Gomez Emilsson of the Qualia Research Institute presents a model of DMT experiences using hyperbolic geometry and dynamical systems theory.

Category Theory by Tom LaGatta
Tom LaGatta's talk on category theory at a 2014 LispNYC meetup, covering objects, morphisms and the basic ideas in an informal, conversational style.

The Maths of General Relativity (1/8) - Spacetime and Worldlines
The first of an eight-part ScienceClic series building general relativity, covering worldlines, proper time and coordinate systems with animated visualizations.

Lecture 1 | Convex Optimization I (Stanford)
The introductory lecture of Stephen Boyd's Stanford Convex Optimization I course (EE 364A).