computability

Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.

A Computerphile video in which Mark Jago of the University of Nottingham explains Turing's halting problem and how it led to the blueprint for the modern computer.

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.

An 11-minute animated introduction to P vs. NP and the wider landscape of complexity classes, inspired by the Complexity Zoo wiki. It assumes no background in computer science.

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 video in a series on extremely large numbers, introducing the topic with examples. Later parts go deep into the fast-growing hierarchy.

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.