PickVidsBest Pure mathematics Videos
The 97 Pure mathematics videos here were recommended by different people across different months. Choose by who it is for: 30 introductory, 24 intermediate, 38 for a general viewer, and 5 for someone who wants the harder derivation. Most of them are an explainer. What they share is that one picture or analogy is used to supply a missing concept. Channels you will keep seeing include 3Blue1Brown, Numberphile, Mathologer.
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.