computability

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.

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.

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.

A long Lex Fridman interview with Stephen Wolfram on complexity, cellular automata, computational irreducibility and the Wolfram Physics Project.

Polylog explains how algorithms can be turned into circuits and encoded as satisfiability problems, which lets you effectively run them backwards. It uses this to motivate breaking RSA, general reductions to SAT, and what P vs NP is really asking.

The first lecture of Michael Sipser's MIT 18.404J Theory of Computation course, covering course mechanics, finite automata, regular languages and regular expressions. It proves closure of regular languages under union and begins concatenation.

A roughly four-and-a-half-hour Lex Fridman podcast conversation with Stephen Wolfram about his Wolfram Physics Project and a fundamental theory of physics, computation, life and the universe.

2swap explores lambda calculus using John Tromp's lambda diagrams, with animated beta-reductions, asking what PLUS times PLUS gives. It touches on Church encodings and the equivalence of Turing machines and lambda calculus.