math visualization

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.

The first of an eight-part ScienceClic series building general relativity, covering worldlines, proper time and coordinate systems with animated visualizations.

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.

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.

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 examines the Texas Supreme Court filing claiming Biden's 2020 win had a one-in-a-quadrillion chance. He walks through why the statistical argument is flawed.

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.

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.

Matt Parker of Stand-up Maths asks whether a country's reported land area accounts for hills and mountains, working through how surface area depends on the resolution of elevation data. It follows up on a question from a viewer and work by researchers who measured it.

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

Freya Holmer's 74-minute video essay on splines, covering Bezier curves, B-splines, derivatives and the different levels of continuity (C0, C1, C2), built with custom animation tools. She notes she did not cover non-uniform splines.

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.

ScienceClic explains why the rubber sheet analogy for general relativity is misleading and offers a new visualization that includes the curvature of time and shows gravity as motion through curved spacetime.

Bill Hammack of engineerguy explains how medieval engineers designed stone cathedrals using rules of thumb, with no science, mathematics or literacy. He uses it to define the engineering method.

CodeParade's short devlog on how spherical geometry looks in 2D and 3D and why it feels so unusual, part of the Hyperbolica series on a non-Euclidean game.

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.

Scott Aaronson's Harvard CMSA talk traces what mathematical truths are knowable, from Godel and Turing to the Busy Beaver function. He covers recent work on Busy Beaver values.

Not Just Bikes explains, using Urban3's property-tax analysis, why car-dependent suburbs generate less tax revenue than they cost to maintain, so dense urban cores effectively subsidize them. It is part of a Strong Towns series.

A four-minute tour of the TeXmacs scientific editor, showing math typing, figures, citations, a drawing tool, document styles, HTML export, presentations and animations.

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.

Lex Fridman interviews Stephen Wolfram for about three hours on cellular automata, computation, the Wolfram Physics Project and his career with Mathematica and Wolfram Alpha.

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.

2swap explains how he solved the Klotski sliding-block puzzle by mapping its full state space as a graph and visualizing it. The video includes footage of the Guinness world-record solve and links to an interactive graph.

ScienceClic gives a 15-minute animated introduction to quantum field theory, covering fields, spin, conserved quantities, the standard model and interactions.

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.

A compilation of the hacking scenes from the 1995 film Hackers, featuring flashy visualizations of computer intrusion.

Veritasium explains why no voting system can be perfectly fair, drawing on Arrow's theorem and the work of Eric Maskin. It looks at problems with systems like first-past-the-post and ranked-choice voting.

Matt Parker of Stand-up Maths examines scatter plots that were claimed to show fraudulent vote-switching in Michigan's 2020 election. He recreates the analysis and shows that the pattern arises from comparing percentages across different bases, not from fraud.

3Blue1Brown's visual explanation of how transformers and GPT-style language models work, tracing data through tokens, embeddings and attention.

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.

3Blue1Brown's visual walkthrough of the attention mechanism inside transformers, covering self-attention, multiple heads and cross-attention. It is chapter 6 of his deep learning series.

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.

A PBS Space Time episode on how the Higgs mechanism gives particles mass, prompted by Fermilab's heavier-than-expected W boson measurement. It goes beyond the usual pop-science treatment without heavy math.

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.

Vsauce asks how many holes a human has and uses topology to show the answer depends on what counts as a hole, with animations and expert input.

A Foresight Institute workshop video with two talks: Shawn Douglas on nanoscale instruments for visualizing small proteins, and Bret Victor on Dynamicland. Victor's part shows biomolecular design built in his Realtalk system with physical objects.

ScienceClic visualizes what you would see falling into a black hole, from the approach and the accretion disc to crossing the horizon, in 15 minutes.