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.

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.