complexity

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.

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.

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.

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

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.

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.

Veritasium explores how synchronization arises spontaneously in nature, with metronomes, fireflies and bridges, drawing on Steven Strogatz's work on chaos and complexity.

A two-minute clip in which Milton Friedman uses a humble pencil to show how thousands of strangers across many countries cooperate, without central direction, to make a simple product. It is a short visual version of the 'I, Pencil' essay's argument about free markets and dispersed knowledge.

Rick Beato analyzes a pop song he argues is among the most harmonically complex ever, breaking down its chords and key changes. It is a music theory deep dive aimed at general music fans.