learning math

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'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's third deep learning chapter gives a visual, intuitive account of backpropagation and what happens to a neural network as it learns. A follow-up video covers the underlying calculus.

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.

Matt Parker of Stand-up Maths demonstrates MENACE, Donald Michie's 1961 machine made of matchboxes that learns to play noughts and crosses through reinforcement. He builds and trains a physical version.

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 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 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.

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

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.

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

3Blue1Brown's chapter 4 on deep learning gives a more formal, symbol-based account of backpropagation calculus, connecting the intuition from the previous chapter to the math found in textbooks and code.

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 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.

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.

A PBS Infinite Series episode explaining the mathematics of quantum computers, including how qubits store complex numbers and how quantum computation differs from classical computation. Hosted by Kelsey Houston-Edwards.

Two Minute Papers covers OpenAI's multi-agent hide-and-seek experiment, in which agents learned emergent tool use and found ways to break the game's rules. It summarizes the 'Emergent Tool Use from Multi-Agent Interaction' paper.

3kliksphilip summarizes Valve's GDC talk on VACNet, a deep-learning system that flags CS:GO cheaters and feeds the Overwatch review queue. It covers Trust Factor, VAC, and how the data is collected and analyzed.

Matt Parker explains the history behind NTSC television running at 29.97 frames per second rather than 30, tracing it to the backward-compatible addition of color. He walks through the arithmetic behind the odd ratio.

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.

Numberphile's James Grime explains Cantor's result that some infinities are bigger than others, including why the reals outnumber the integers. It is a short, accessible introduction to countable and uncountable infinity.

Robert Miles explains reward modelling, in which an AI learns what humans want from their preference comparisons instead of a hand-written reward function. He walks through the 2017 paper on deep reinforcement learning from human preferences.

A minutephysics video explaining why a piano cannot be perfectly tuned, comparing equal temperament with just intonation and the math of harmonics.

Veritasium examines research suggesting science explainer videos like Khan Academy's make students feel they understand while tests show they have not learned, because misconceptions go unaddressed. It suggests how to partly fix this.

minutephysics, in collaboration with the US Census Bureau, explains differential privacy and why the 2020 census adds noise to protect individuals' data. It walks through how statistics can leak private information.

A short TED-Ed animated lesson by Anita Collins on what happens in the brain when people play a musical instrument. It argues that playing engages many brain areas at once, like a full-body workout, with long-term benefits.

A Veritasium explainer on how the brain works and how we learn. It is inspired by Kahneman's Thinking, Fast and Slow and covers System 1 and System 2 thinking and why harder learning builds skill.

Two Minute Papers covers a paper on speeding up fluid and smoke simulation with convolutional networks. It contrasts the approach with earlier regression forest methods.

Yuta asks whether native Japanese speakers can actually write kanji by hand, showing that many struggle to recall characters from memory.

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

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.

jan Misali presents an humorous but earnest case for counting in base 6 (seximal) instead of base 10 or 12, comparing the arithmetic advantages of each.

3Blue1Brown presents the Triangle of Power, an alternate notation that unifies powers, logarithms and roots in a single triangular symbol. The video shows how the inverse operations relate and how the notation could help.

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.

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.

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.