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.
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.