machine learning math

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.

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.

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 second neural network chapter explains cost functions and gradient descent, showing how a network learns by minimizing error during training.

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.

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.

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.

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.

Johnny Harris investigates why McDonald's ice cream machines are so often broken, covering the Taylor machines, the repair restrictions on franchisees and the Kytch workaround device.

Technology Connections takes apart the step-by-step electromechanical logic of a 1970s pinball machine. He shows how relays, steppers and switches track state and score without electronics.

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.

Technology Connections takes a long, detailed look at how a 1970s electromechanical pinball machine works, from relays to stepper motors and mechanical logic. It is the first part of a series.

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'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.

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.

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

3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.

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.

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.

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.

Veritasium short showing Drew Berry's scientifically accurate animations of the molecular machines that drive cell division. It walks through mitosis, chromosomes and motor proteins.

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.

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.

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.

An illustrated 23-minute summary of David Friedman's talk based on The Machinery of Freedom. It describes how law, police and courts could work as market services in a stateless society, covering private law, polycentric law and objections.

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.

Branch Education's animated deep dive into ASML's EUV photolithography machine and how it prints nanometer-scale transistors onto chips. It covers the system's components and the process of chip manufacturing.

Jared Owen's 3D animated breakdown of how a Brunswick GS-X bowling pinsetter works, showing its mechanisms for sweeping, lifting and resetting pins and balls.

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.

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.

A Business Insider World Wide Waste episode on H&M's garment recycling machines, which turn used clothing into new apparel. It asks whether a fast fashion company can solve the waste problem it helped create.