math

Mathematician Colin Wright demonstrates juggling and explains the mathematics of juggling patterns, including notation that led to new throwing patterns. It is a public presentation at the Museum of Mathematics aimed at a general audience.

Matt Parker's Royal Institution talk based on his book Humble Pi, covering everyday mathematical mistakes and spurious patterns that went wrong in engineering and software. It mixes stand-up comedy with stories of coincidence and error.

Mathematician Kevin Buzzard explains why he believes the Lean theorem prover will shape the future of mathematics, and describes digitizing his university curriculum in Lean with undergraduates, plus the cultural challenges.

Matt Parker gives a hands-on Royal Institution talk on how four-dimensional shapes appear in a 3D world, with props like straw frames, Mobius strips and a knitted hat. It is a playful general-audience tour of the fourth dimension.

Lex Fridman interviews mathematician and economist Eric Weinstein about science, mathematics, and society. The conversation ranges across physics, academia, AI and job displacement.

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.

A Computer History Museum oral history with Avie Tevanian covering his math talent, work on the Mach microkernel at CMU, joining NeXT, leading NEXTSTEP development and the 1996 Apple acquisition.

A UCTV panel with endocrinologist Robert Lustig, dentist Cristen Kearns and health policy expert Laura Schmidt on how the US food system and sugar industry influence diet and health, including industry efforts to shape the science.

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's LMS popular lecture on how seemingly incredible results can be meaningless random patterns. He ranges from ancient Woolworths civilisations to shoelaces and DNA.

The full-length Numberphile interview with mathematician and hedge fund founder Jim Simons. He discusses his path from mathematics and codebreaking to founding Renaissance Technologies, his use of algorithms in markets, and his philanthropy.

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.

The first lecture of Francis Su's Harvey Mudd real analysis course, covering the construction of the rational numbers. It begins a full lecture series that follows a standard analysis text.

Tom LaGatta's talk on category theory at a 2014 LispNYC meetup, covering objects, morphisms and the basic ideas in an informal, conversational style. It runs about 97 minutes.

Donald Knuth's 2017 Christmas Tree Lecture at Stanford about a combinatorial geometry problem whose computed numbers matched a striking formula. He tells the story of the conjecture and its sequel.

Christof Paar's university lecture introducing Galois fields and finite-field arithmetic as used in AES. It covers the mathematics behind the AES S-box.

Erik Meijer argues that category theory is the mathematicians' version of interface-based design. He shows that Java 8 lambdas and method references form a Cartesian closed category.

A SIGGRAPH 2019 course on geometric algebra. Charles Gunn gives an intro, then Steven De Keninck gives a programmer-focused course with live examples in ganja.js.

Physicist Al Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population, energy consumption and resource depletion. He argues that steady percentage growth cannot be sustained on a finite planet and that most public discussion ignores this.

A recording of physicist Albert Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population and energy use. He argues that steady percentage growth in a finite world cannot continue and sneaks up suddenly.

Conal Elliott presents his paper on automatic differentiation, deriving a simple, generalized AD algorithm from a natural specification. Varying the representation of derivatives yields forward and reverse mode algorithms that avoid the complexity and statefulness of backpropagation.

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.

John Gustafson presents posits, a proposed drop-in replacement for IEEE 754 floats that is simpler in hardware and more flexible in precision. The seminar includes a live demo and machine learning results.

Andres Gomez Emilsson of the Qualia Research Institute presents a model of DMT experiences using hyperbolic geometry and dynamical systems theory. He describes how different intoxication levels correspond to changing curvature and information content of experience.

The introductory lecture of Stephen Boyd's Stanford Convex Optimization I course (EE 364A). It outlines convex sets, functions and problems, and the course's coverage of least-squares, linear and semidefinite programming, duality and interior-point methods.

A 95-minute recorded debate at the ARITH23 computer arithmetic conference between John Gustafson, proponent of unums/posits, and William Kahan, architect of IEEE 754 floating point. They argue the merits of the new number formats versus conventional floats and interval arithmetic.

A talk by Eric Weinstein on gauge theory and its possible application to economics and inflation. It proposes extending the Wu-Yang dictionary into a geometric tool beyond physics.

Microsoft's Brian Beckman gives an hour-long, whiteboard-style walk through monads, building from function composition and monoids using school-level math. It is aimed at practicing programmers rather than category theorists.

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.

Guy Steele's PPoPP 2017 keynote surveying the history of computer science metanotation, including BNF, inference rules, and overline notation. He argues the field's notations are inconsistent and fragmented.

The first lecture of an MIT course on Douglas Hofstadter's Godel, Escher, Bach, covering themes like self-reference, recursion and incompleteness. The full lecture series is on YouTube.

The first lecture of Andrew Ng's Stanford CS229 Machine Learning course, giving an overview of the course. It introduces supervised and unsupervised learning, learning theory and reinforcement learning.

Andrej Karpathy's three-hour-plus general-audience deep dive into how ChatGPT-style LLMs are built, covering the full training stack from pretraining to post-training. It also gives mental models for their quirks, like hallucination, and how to use them well.

Episode 8 of the Fall of Civilizations podcast, a roughly two and a half hour history of the Sumerians. It covers their mysterious origins, invention of writing and mathematics, great early cities and eventual collapse, with myths, proverbs and recreated music.

Stanford physicist Leonard Susskind explains what the Higgs mechanism is and what it means to give mass to particles. He also covers what is at stake for physics and cosmology.

Gabriel Lebec's Fullstack Academy talk introduces lambda calculus syntax, the history of mathematical logic, and the essence of functional programming using JavaScript. It also covers combinators, currying and Church encodings.

Damian Conway's hour-long keynote at the Perl conference, On the Shoulders of Giants, showing off Perl 6 (Raku) features with history, algorithms and a quantum math operator built with grammars. It is delivered with comic flair.

The first lecture of Caltech's CS 156 Machine Learning course by Yaser Abu-Mostafa, introducing the learning problem and supervised, unsupervised and reinforcement learning. It is one of 18 lectures in the Learning from Data course.

Eric Weinstein's roughly three-hour presentation of Geometric Unity, his proposed theory unifying physics, given as a special episode of The Portal. It includes clarifications at the end.

A 2017 documentary filmed at the Santa Fe Institute in which novelist Cormac McCarthy talks with SFI's David Krakauer. They discuss isolation, mathematics, character and the nature of the unconscious.