math visualization

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.

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.

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

Bret Victor's talk on Drawing Dynamic Visualizations. It argues that visualization tools offer either the directness of hand drawing or the dynamics of programmed graphics, and shows a tool that combines both.

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.

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.

Andrej Bauer's IAS talk introduces constructive mathematics and what it feels like to do mathematics without excluded middle. It is framed as a tour for classical mathematicians.

Chamath Palihapitiya talks with Jason Calacanis about how he bought into the mythology of Silicon Valley, which he calls a Ponzi scheme, and about rebuilding Social Capital. He urges founders to grow slowly and build what matters.

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.

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

Part 2 of Richard Feynman's Messenger Lectures at Cornell, The Character of Physical Law, on the relation of mathematics to physics. He explains why understanding nature requires mathematics.

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.

Chamath Palihapitiya's Stanford GSB View From The Top talk on money as an instrument of change. HN mostly knows it for his remarks on social media's dopamine-driven feedback loops and regrets about Facebook.

A TED interview in which Chris Anderson talks with Jim Simons about his life: code-breaking, math, founding Renaissance Technologies, and his philanthropy in math education and origins-of-life research.

An original recording of a Verizon customer service call in which the rep fails to understand the difference between cents and dollars, known as Verizon Math.

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

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.

Steven Wittens' JSConf US 2013 talk on drawing with WebGL, using animated visuals to walk through vectors, matrices and the rendering pipeline. Despite the title, it works as a visual primer on the linear algebra behind 3D graphics.

Mathologer examines how identities like 1+2+3+... = -1/12 arise in Ramanujan's work, starting from his 1913 letter to Hardy. The video explains the rules for summing infinite series and why such results are meaningful but not naive sums.

Stand-up Maths explains why the perimeter of an ellipse has no simple closed-form equation, showing the infinite series and presenting approximation formulas.

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.

Inigo Quilez live-codes a cartoon character painting entirely from math, using signed distance fields in a Shadertoy shader. He explains each step of building the image from formulas.

An animated introduction to geometric algebra, presented as a language that can describe most of physics. It was made with manim and covers multivectors and how they generalize familiar tools like cross products and quaternions.

Inigo Quilez live-paints a mountain landscape using only math in a shader, building up from a basic polynomial noise surface through fractal terrain, lighting and atmosphere. The code runs in real time on Shadertoy so viewers can edit it as they follow along.

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.

Inigo Quilez live-codes a painting using only mathematics in a shader, building it up step by step. The linked Shadertoy source shows the result.

A 3Blue1Brown live lockdown math episode asking what Euler's formula e^(pi i) is actually saying. It builds intuition through exponentials, rotation and vectors landing on the unit circle.

Gerald Jay Sussman speaks at Dan Friedman's 60th birthday celebration about how programming helps formulate and clarify ideas. He argues that ambiguous mathematical notation hinders understanding.

Philip Roberts explains the JavaScript event loop, call stack, callbacks and asynchronous behavior with live visualizations using a tool he built. It demystifies terms like non-blocking and single-threaded.

3Blue1Brown visualizes high-dimensional spheres to explain a surprising puzzle about how a sphere fits in a box as dimensions grow. It builds geometric intuition for counterintuitive properties of high-dimensional space.

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

Ruben Meerman presents a TEDx talk on the stoichiometry of weight loss, showing with lab demonstrations where fat goes when it is lost. He argues that most of it is exhaled as carbon dioxide.

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. It argues math had to give up the requirement that it mirror reality.

Grant Sanderson of 3Blue1Brown shows his workflow for animating math videos with Manim, with Ben Sparks. He codes scenes live, including a Lorenz attractor, and walks through example scenes.

Physicist Angela Collier rants for 42 minutes about why violin plots are a poor way to show data, citing papers on violin and bean plots. It is part lecture on how to read distributions and part opinionated critique.

3Blue1Brown introduces group theory and abstract groups, then builds toward classification of finite simple groups and the enormous Monster group with its 196,883 dimensions.

Cambridge Analytica CEO Alexander Nix keynotes the OMR 2017 marketing festival on big data and personality-based targeting in political campaigns. It was given before the company's scandal broke.

A Google Tech Talk by Laurens van der Maaten, co-creator of t-SNE, on visualizing high-dimensional data by mapping it to two dimensions. It explains how the technique works and how it compares with other visualization approaches.

Thunderf00t critiques the TeamTrees campaign, doing the math on how little carbon 20 million trees would actually offset. He argues that tree planting is far from adequate against global emissions.