learning math

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.

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.

The introductory lecture of Richard Hamming's capstone course, The Art of Doing Science and Engineering: Learning to Learn. It focuses on style of thinking and on educating rather than training, using technical material only as illustration.

The final lecture of Richard Hamming's Learning to Learn course, from 1995, based on his well-known talk 'You and Your Research'. It covers how to do important work and build a career.

The first lecture of Stanford's Natural Language Processing with Deep Learning course, taught by Chris Manning and Richard Socher. It introduces NLP and word vectors, including SVD, skip-gram, CBOW, negative sampling and word2vec.

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.

Bill Dally of NVIDIA gives a University of Washington lecture on trends in deep learning hardware. It covers numeric formats, specialized instructions, energy per operation and co-design of hardware and software.

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.

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.

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.

Sacha Arnoud, Waymo's Director of Engineering, gives a lecture in MIT's 2018 deep learning for self-driving cars course on the rise of machine learning in autonomous vehicles. It covers how Waymo uses deep learning and how it handles tricky driving situations.

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.

A 15-minute clip of linguist Stephen Krashen discussing language acquisition, drawn from the 1980s. It presents his input hypothesis and the distinction between acquisition and learning.

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.

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.

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.

The first lecture of David MacKay's Cambridge course on information theory, pattern recognition and neural networks. It introduces the core ideas of his book Information Theory, Inference, and Learning Algorithms.

The first lecture of Stanford's CS231n course on convolutional neural networks for visual recognition. It surveys the history and key challenges of computer vision, from the Cambrian explosion and Hubel and Wiesel to ImageNet.

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.

A lecture from the 1980s by linguist Stephen Krashen on how people acquire language. He explains his comprehensible input hypothesis for second-language acquisition.

Richard Hamming's 1995 recording of his talk 'You and Your Research', drawn from his graduate engineering course. He discusses how great scientists pick important problems and build careers, drawing on his years at Bell Labs.

Harvard physicist Eric Mazur explains how he realized his students were memorizing rather than understanding, and how he changed his teaching. He presents peer instruction and data showing improved student performance.

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.

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.

Peter Norvig's UBC distinguished lecture on how massive amounts of simple data, such as for language modeling, can yield understanding that hand-built models could not.

A university lecture from CS480/680 by Pascal Poupart on attention mechanisms and transformer networks, worked through on a chalkboard.

Geoffrey Hinton gives an MIT talk on what is wrong with convolutional neural networks and introduces his capsules project. The description points to the capsule network papers.

Leo Dirac explains how transformer models have replaced LSTMs in NLP. He gives background from bag of words through RNNs and LSTMs, then a technical deep dive into multi-headed self-attention and positional encoding, with sample code.

Russell Barkley gives the keynote at UNC's 2012 Burnett Seminar on ADHD. He presents it as an executive function disorder and discusses its effects and how to help.

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.

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.

The first lecture of Jordan Peterson's 2017 Maps of Meaning course, setting out the Cold War context for his theory of belief and culture. He introduces the narrative structure of culture and archetypal characters for the individual, the known and the unknown.

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.

The opening lecture of MIT 6.824 Distributed Systems (Spring 2020), introducing the course and core challenges of distributed systems. It begins a playlist that goes on to cover Raft and other consensus papers in Go.

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.