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.

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.

Jim Weirich's RubyConf 2012 talk derives the Y combinator step by step, live-coding in Ruby lambdas. It builds up an understanding of functional programming and lambda calculus from first principles.

Meredith Patterson and Sergey Bratus argue that networked software stays insecure because protocols and inputs are too complex to recognize safely. They propose using formal language theory and grammars to build secure, verifiable input handling.

Philip Wadler's Strange Loop talk on Propositions as Types, the link between logic and computation (the Curry-Howard correspondence). He traces its history through Church, Godel and Turing and shows how it shaped theorem provers and programming languages.

Christopher Domas's Derbycon 2015 talk on the M/o/Vfuscator, a compiler that emits only x86 mov instructions, showing mov is Turing complete. It explains how a full machine is built from mov and why the output is a nightmare to reverse engineer.

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.

A short SIGBOVIK 2017 presentation by Tom Wildenhain showing that PowerPoint animations are Turing complete, with a working Turing machine built in slides. The talk is delivered deadpan as a serious research result.

A two-minute video of Conway's Game of Life running inside Conway's Game of Life, built from OTCA metapixels and Golly. It zooms smoothly between scales.

Gabriel Lebec's Fullstack Academy talk introduces lambda calculus syntax, the history of mathematical logic, and the essence of functional programming using JavaScript. It also covers combinators, currying and Church encodings.

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.

Tom Stuart's Ruby Manor 3 talk builds FizzBuzz using nothing but Ruby lambdas, working through Church encodings of numbers, booleans and data structures. It is a hands-on introduction to lambda calculus.

David Beazley's PyCon 2019 tutorial derives the lambda calculus from the ground up in Python, using only single-argument functions. He builds booleans, numerals and more with no other language features.

Tom Wildenhain's guest lecture for CMU's Esoteric Programming Languages course shows that PowerPoint transitions and slides are Turing complete without macros, building up to a mind-bending fractal ending.

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.

Matt Might's Curry On talk on ending errors in code, both software and the human genome. He covers conservative approximation of the halting problem via static analysis and a computational approach to precision medicine.

A panel with Tony Hoare, Joe Armstrong and Carl Hewitt, hosted by Francesco Cesarini, on the history and future of concurrency. The three creators of CSP, Erlang and the actor model discuss their differing approaches.

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.

Tom Murphy's satirical SIGBOVIK 2007 presentation, delivered under a pseudonym, proving that generalized Super Mario Bros. is NP-complete. It is a short, deadpan take on a complexity theory result.

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.

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.

Kyle Hill of Because Science explains and demonstrates, using real cards, how Magic: The Gathering can be used to build a Turing machine, a computer inside the card game.

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 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.

John Conway talks in a short Numberphile interview about his mixed feelings toward the Game of Life, his most famous invention. He says he is not especially pleased that it overshadowed his other work.

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.

Find the Longest Path is a comedic song by Daniel J. Barrett, a Billy Joel parody that describes the NP-hard longest path problem in informal terms.

A short demo of a playable Space Invaders game built inside Dwarf Fortress, with a downloadable map. It shows the game's mechanics used as a computing substrate.

An excerpt from Hal Abelson's opening SICP lecture introducing computer science and contrasting declarative and imperative knowledge. He argues that computer science is not really a science and is more like magic or engineering of ideas.

Pro Magic player Luis Scott-Vargas triggers a mandatory-action infinite loop on Magic Online, and the game stalls in a non-terminating state.

An animated, musical visualization of Conway's Game of Life showing patterns made in the Golly program.

Matthias Wandel shows his wooden machine that adds binary numbers using marbles. It demonstrates computation with purely mechanical logic.