learning math

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.

Veritasium debunks the idea of learning styles, such as being a visual learner, with an interview with Daniel Willingham and a memory experiment. It argues that a multimodal approach helps everyone.

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.

Yosh trains a reinforcement learning agent to drive Trackmania until he can no longer beat it. The video explains how the training works and the design choices involved.

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.

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

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.

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.

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.

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 examines which experts have real expertise, drawing on chess research and work by Klein and Kahneman. It explains that expertise comes from pattern recognition built through deliberate practice in valid, feedback-rich environments.

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.

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.

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.

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.

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.

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.

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 Veritasium video on AlphaFold, DeepMind's protein structure prediction system, and the protein design work it enabled. It features interviews with John Jumper and with David Baker's protein design group and explains why predicting protein folding matters.

A Welch Labs explainer on neural scaling laws and the compute-efficient frontier, asking why model loss seems to hit a line it cannot cross. It draws an analogy to an ideal gas law for AI.

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.

Robert Miles covers a paper where researchers ran real versions of his earlier mesa-optimizer thought experiments. They show inner misalignment, where an AI learns the wrong goal in training and misbehaves when deployed.

Matt Parker analyzes the Minecraft speedrunning controversy in which Dream was accused of cheating via improbably lucky drops. He walks through the probability and the statistical arguments in the original accusation and the reply.

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.

Ben Felix argues that common beliefs about renting versus buying are wrong: homes are not great investments, mortgages are not a wealth hack, and ownership does not reliably bring happiness.

Joe Scott takes a serious look at space sunshades as a climate fix, asking how big they would need to be, what they would cost and whether they would work. He draws on Roger Angel's paper and launch options.

Steve Mould shows Spintronics, a set of mechanical components such as resistors, capacitors and transistors linked by chains, that give an intuitive feel for how electrical circuits work.