PickVidsBest 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。
Arithmetic, Population and Energy - a talk by Al Bartlett
Physicist Al Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population, energy consumption and resource depletion.
What does it feel like to invent math?
3Blue1Brown explores infinite sums from convergent to divergent, with an introduction to the 2-adic metric, themed on the cycle between discovering and inventing mathematics.
But what is the Riemann zeta function? Visualizing analytic continuation
3Blue1Brown visualizes the Riemann zeta function and the analytic continuation that extends it beyond where its series converges, building toward the Riemann hypothesis.
Who cares about topology? (Old version)
An older 3Blue1Brown video on why topology matters, built around the inscribed rectangle problem.
Special Topics - The Kalman Filter (1 of 55) What is a Kalman Filter?
The first video in a 55-part series by Michel van Biezen that introduces the Kalman filter and builds from the rationale through algebraic examples to the full matrix treatment.
Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations
3Blue1Brown explains why plotting primes in polar coordinates produces spiral patterns, using modular arithmetic, Dirichlet's theorem and rational approximations of pi.
[JSConfUS 2013] Steven Wittens: Making WebGL Dance
Steven Wittens' JSConf US 2013 talk on drawing with WebGL, using animated visuals to walk through vectors, matrices and the rendering pipeline.
How To Count Past Infinity
Vsauce's Michael Stevens takes viewers past infinity using transfinite numbers, ordinals and cardinals, with input from mathematician Hugh Woodin.
Exponential Growth Arithmetic, Population and Energy, Dr. Albert A. Bartlett
A recording of physicist Albert Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population and energy use.
This equation will change how you see the world (the logistic map)
A Veritasium video on the logistic map, showing how a simple population equation leads to chaos and bifurcation.
Preface | MIT Calculus Revisited: Single Variable Calculus
The preface to Herb Gross's MIT OpenCourseWare 'Calculus Revisited: Single Variable Calculus', an older black-and-white lecture series.
The Map of Mathematics
An animated 11-minute tour of the whole field of mathematics as a single map, showing how pure and applied math and their sub-fields relate to each other.
a better way to count
jan Misali presents an humorous but earnest case for counting in base 6 (seximal) instead of base 10 or 12, comparing the arithmetic advantages of each.
But what is a Fourier series? From heat flow to drawing with circles | DE4
3Blue1Brown introduces Fourier series, from the heat equation to drawing arbitrary shapes with rotating circles.
Triangle of Power
3Blue1Brown presents the Triangle of Power, an alternate notation that unifies powers, logarithms and roots in a single triangular symbol.
The Golden Ratio (why it is so irrational) - Numberphile
Numberphile's Ben Sparks shows why the golden ratio is the most irrational number, using seeds, continued fractions and rational approximations.
Real Analysis, Lecture 1: Constructing the Rational Numbers
The first lecture of Francis Su's Harvey Mudd real analysis course, covering the construction of the rational numbers.
Hilbert's Curve: Is infinite math useful?
3Blue1Brown explains space-filling curves and the Hilbert curve, and how infinite mathematical constructions connect to finite, practical approximations.
The Infinite Pattern That Never Repeats
Veritasium explains how Penrose tilings and quasicrystals overturned the belief that 5-fold symmetry and non-periodic crystals were impossible, including an interview with Paul Steinhardt.
Carl Sagan - Cosmos - Eratosthenes
A short clip from Carl Sagan's Cosmos in which he explains how Eratosthenes measured the circumference of the Earth using shadows in two Egyptian cities.
How Imaginary Numbers Were Invented
Veritasium tells the history of how imaginary numbers arose from the quest for a general solution to the cubic equation, including the duels and secrecy among Renaissance mathematicians.
The Simple Essence of Automatic Differentiation - Conal Elliott
Conal Elliott presents his paper on automatic differentiation, deriving a simple, generalized AD algorithm from a natural specification.
e^(iπ) in 3.14 minutes, using dynamics | DE5
A short 3Blue1Brown video explaining Euler's formula e^(i*pi) = -1 through dynamics, treating velocity as the thing that moves a point to a new position.
Four Dimensional Maths: Things to See and Hear in the Fourth Dimension - with Matt Parker
Matt Parker gives a hands-on Royal Institution talk on how four-dimensional shapes appear in a 3D world, with props like straw frames, Mobius strips and a knitted hat.