visual math

Mathematician Colin Wright demonstrates juggling and explains the mathematics of juggling patterns, including notation that led to new throwing patterns. It is a public presentation at the Museum of Mathematics aimed at a general audience.

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.

3Blue1Brown explains space-filling curves and the Hilbert curve, and how infinite mathematical constructions connect to finite, practical approximations. It touches on mapping between dimensions and sensory ideas.

Matt Parker's Royal Institution talk based on his book Humble Pi, covering everyday mathematical mistakes and spurious patterns that went wrong in engineering and software. It mixes stand-up comedy with stories of coincidence and error.

A short Great Big Story piece about Hagoromo, a Japanese chalk brand so prized that mathematicians stockpiled it, with some reportedly dealing it on the side. It tells the quirky tale of a writing tool whose supply became scarce.

3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.

3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.

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.

Mathologer examines the infamous Numberphile claim that 1+2+3+... equals -1/12, explaining what is wrong with the calculation and how it connects to real math like the zeta function and analytic continuation.

Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.

Mathologer explains epicycles and complex Fourier series, inspired by an animation of Homer Simpson drawn with epicycles. It covers the shape of the Moon's orbit around the Sun and how to make your own epicycle drawings.

The first part of Welch Labs' series on imaginary numbers, presenting them as the natural extension of the number line into two dimensions. It covers the history and the math with strong visuals.

3Blue1Brown builds visual intuition for quaternions, showing how to think about this four-dimensional number system using stereographic projection and rotations in 3D space. It is part one of a two-part series with an interactive companion site.

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.

3Blue1Brown visualizes the Riemann zeta function and the analytic continuation that extends it beyond where its series converges, building toward the Riemann hypothesis.

The first lecture of N J Wildberger's History of Mathematics course, starting with Pythagoras' theorem and following Stillwell's text. It emphasizes the flow of ideas over proofs.

Thomas Garrity discusses mathematical maturity, a concept mathematicians use for professional development, and how it can inform teaching, mentoring and careers. It was given at the IAS/PCMI Park City Mathematics Institute.

Freya Holmer explains how Bezier curves work, from the helper-line construction to their uses in animation, text rendering and shapes. It uses visuals from her Unity Shapes plugin and was a SoME1 contest winner.

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. It aims to make viewers feel they could have invented calculus themselves.

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.

Veritasium's explainer on Godel's incompleteness theorems and the limits of mathematical proof, tracing set theory, Hilbert's program and the road to Turing and modern computing.

3Blue1Brown introduces Fourier series, from the heat equation to drawing arbitrary shapes with rotating circles. It builds a visual intuition for decomposing functions into sine waves.

Vsauce explores math through card tricks and big numbers, including an animation of how enormous 52 factorial, the number of deck orderings, really is.

A ten-minute clip of Richard Feynman describing how mathematicians and physicists differ in their interests and customs. He argues physics rests on visualizing and applying math rather than pure abstraction.

A Veritasium video on how a feud between Russian mathematicians led to Markov chains and the modern prediction algorithms built on them. It covers the history and the math behind them.

A 21-minute animation showing how a sphere can be turned inside out without creases or tears, known as sphere eversion.

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.

Matt Parker of Stand-up Maths explains why people keep making the same mistake with millions and billions, using a Bloomberg cash calculator example. He looks at the unit slip behind the repeated arithmetic error.

Matt Parker of Stand-up Maths explains single-pile Nim and the trick that wins it, using Dr NIM, a 1960s mechanical plastic computer that plays perfectly. He teaches the strategy so viewers can beat friends.

The first chapter of 3Blue1Brown's Essence of Linear Algebra series, introducing vectors with animated geometric visuals. It begins a series that builds intuition for linear algebra from the basics.

3Blue1Brown's first chapter on deep learning explains what neurons and layers are and the math underlying a basic neural network, using handwritten digit recognition with visual animations.

3Blue1Brown explains fractal dimension and shows why many fractals are not strictly self-similar. Self-similarity turns out to be a special case of the broader idea of fractional dimension.

3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.

Christopher Domas presents his Cantor Dust tool at Derbycon 2012, a 3D visual approach to reverse engineering binaries by visualizing their structure dynamically.

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. It builds geometric intuition for why an exponent with i produces rotation.

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. It is a playful general-audience tour of the fourth dimension.

Christopher Domas's REcon 2013 talk on dynamic binary visualization for reverse engineering. He shows how rendering binary data as interactive visual maps and trigraphs reveals structure that hex dumps hide, leading to his Cantor.dust tool.

Timothy Gowers thinks aloud, in real time, as he tries to understand why Pascal's determinant equals 1. He does not fully solve it in this episode, but shows his exploratory process.

Tom Scott makes the difference between a million and a billion dollars tangible by using distance on a road trip instead of volume. The drive makes the scale of a billion intuitively felt.

The first lecture of MIT 6.042J Mathematics for Computer Science, taught by Tom Leighton, introducing mathematical proofs. It covers propositions, implication and basic proof methods.