math

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.

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.

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 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.

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

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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 short 3Blue1Brown primer on exponential and logistic growth, using early COVID-19 case data to show how epidemics grow and eventually level off. It explains why small changes in growth rate make enormous differences in outcomes.

Veritasium shows how Hilbert's infinite hotel can still run out of room, using infinite buses of guests. It explains the surprising answer in a short animated segment.

Matt Parker examines claims that Biden's 2020 vote counts violate Benford's Law, explaining the law and why it often does not apply to precinct-level election data.

Matt Parker follows the community effort to speed up his slow Wordle-solving code, which ended up running hundreds of millions of times faster. He walks through the techniques contributors used.

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.

A Vsauce video exploring whether chairs exist, through metaphysics, mereology and the philosophy of categorizing objects. It runs about 38 minutes and cites academic work on ontology.

3Blue1Brown builds toy SIR models to simulate how an epidemic spreads and tests scenarios like social distancing, travel restrictions, central gathering places and quarantine. It was made during the early COVID-19 outbreak.

A Veritasium video on the logistic map, showing how a simple population equation leads to chaos and bifurcation. It connects the idea to convection, neuron firing and the Mandelbrot set, with interactive animations.

3Blue1Brown's discovery-oriented introduction to error correction codes, building up Hamming codes from the puzzle of locating a flipped bit. It explains the parity-check idea and why it is so efficient.

3Blue1Brown explains why positive results on accurate medical tests are often false positives, and reframes Bayes' rule using likelihood ratios (Bayes factors) to update odds. It uses visual examples to make the reasoning intuitive.

Sabine Hossenfelder asks whether complex numbers are just a convenient tool or necessary in physics. She discusses a recent paper arguing that quantum mechanics cannot be done with real numbers alone.

3Blue1Brown explains how holograms record a 3D scene on 2D film, using wave diffraction and phase. The video includes demonstrations of several real holograms.

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 old announcement trailer for Hyperbolica, CodeParade's Unity game set in hyperbolic and spherical space. The creator has since posted devlog videos on building it.