formal methods

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.

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.

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.

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 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.

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.

The first of Richard Feynman's 1964 Cornell Messenger Lectures, The Character of Physical Law, focusing on the law of gravitation. Feynman builds up from planetary motion to the nature of physical laws.

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.

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.

Terence Tao's AMS Einstein Public Lecture at UCLA on the cosmic distance ladder, the chain of methods astronomers use to measure distances from the Earth to distant galaxies. It is aimed at a general audience.

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.

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.

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.