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.

Thomas Garrity discusses mathematical maturity, a concept mathematicians use for professional development, and how it can inform teaching, mentoring and careers. It was given at the IAS/PCMI Park City Mathematics Institute.

The first lecture of MIT 6.042J Mathematics for Computer Science, taught by Tom Leighton, introducing mathematical proofs. It covers propositions, implication and basic proof methods.

A clip of Richard Feynman contrasting the Greek and Babylonian traditions of mathematical reasoning. It compares the axiomatic approach of mathematicians with how physicists use mathematics.

Andrej Bauer's IAS talk introduces constructive mathematics and what it feels like to do mathematics without excluded middle. It is framed as a tour for classical mathematicians.

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

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.

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.

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 first lecture of Gilbert Strang's MIT 18.06 Linear Algebra course, covering the geometry of linear equations. It opens a full 35-lecture university course.

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.

Richard Hamming's 1995 lecture on n-dimensional space, showing how geometric intuition about spheres and cubes breaks down in high dimensions. It is part of his course on learning to learn.

Part 2 of Richard Feynman's Messenger Lectures at Cornell, The Character of Physical Law, on the relation of mathematics to physics. He explains why understanding nature requires mathematics.

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.

Part 1 of a lecture by physicist Albert Bartlett on the exponential function and its consequences for population growth, resource use and energy. It argues that steady growth rates quickly lead to enormous quantities.

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.

The first lecture in Bartosz Milewski's category theory series for programmers. It covers the motivation and philosophy behind category theory and why composition matters for handling complexity.

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.

The opening lecture of Steve Brunton's Control Bootcamp, covering the kinds of control and why closed-loop feedback matters. It starts a series that follows the control chapter of the Brunton and Kutz data-driven science book.

The preface to Herb Gross's MIT OpenCourseWare 'Calculus Revisited: Single Variable Calculus', an older black-and-white lecture series. It introduces his approach to teaching calculus from the basics.

A segment from Carl Sagan's original Cosmos explaining the fourth spatial dimension through analogy with a two-dimensional world and shadow projection.

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 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.

A short clip of Richard Feynman on the difference between merely knowing how to reason mathematically and understanding why physical theories work. He discusses holding multiple equivalent ideas and guessing new laws.

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.

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.

Sean Carroll introduces his video series on the biggest ideas in physics, such as symmetry, space and matter, as informal discussions with follow-up Q&A videos. This is the short opening video of the series.

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.

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.

Lecture 1 of Harvard's Statistics 110 with Joe Blitzstein, introducing sample spaces, the naive definition of probability, counting, binomial coefficients and the sampling table.

Leonard Susskind opens Stanford Continuing Studies' Theoretical Minimum series with an introduction to quantum mechanics, a course for people who want real physics rather than popularization. It assumes some calculus and linear algebra.

The first lecture of Leonard Susskind's Stanford Continuing Studies course on modern physics, beginning with classical mechanics. It is the start of a six-quarter sequence on the theoretical foundations of physics.

A detailed 40-minute explanation of the ultraviolet catastrophe, covering Rayleigh and Jeans' classical treatment of blackbody radiation and Planck's quantum hypothesis. It follows the Eisberg and Resnick textbook treatment.