Computable Secrets: computer science from first principles

Exploring the limits of the computable and beyond.

27 videos, each with a free companion article

Videos

Browse the library: sort, filter, and track your progress →

• 23:59

  Type-Level Abstraction: System Fω

  Jun 2026 · article

• 20:25

  A Mathematical Theory of Communication (Part 1)

  May 2026 · article

• 23:20

  Kolmogorov Complexity

  Apr 2026 · article

• 16:05

  The Random Graph

  Apr 2026 · article

• 27:29

  Category Theory: What Makes a Construction Natural?

  Apr 2026 · article

• 14:44

  The Polymorphic Lambda Calculus: System F

  Apr 2026 · article

• 35:01

  Categories, Monoids, and Preorders (in Lean 4)

  Apr 2026 · article

• 18:51

  Vanishing Gradients: Why Deep Networks Couldn't Learn

  Apr 2026 · article

• 23:02

  Euclid: the Algorithm and the Format

  Apr 2026 · article

• 8:38

  Bourbaki: A Unified Foundation for Mathematics

  Apr 2026 · article

• 10:05

  The Simply Typed Lambda Calculus

  Apr 2026 · article

• 18:30

  Quantum Computation

  Apr 2026 · article

• 17:03

  Interactive Proofs

  Mar 2026 · article

• 16:15

  The Relativization Barrier: Why It's Hard to Resolve P vs NP

  Mar 2026 · article

• 22:23

  Derandomization

  Mar 2026 · article

• 25:38

  Descriptive Complexity

  Mar 2026 · article

• 8:41

  The Lambda Calculus

  Mar 2026 · article

• 15:05

  Impagliazzo's Five Worlds

  Mar 2026 · article

• 9:52

  The Natural Proofs Barrier

  Mar 2026 · article

• 8:16

  Introduction to Circuit Complexity

  Mar 2026 · article

• 2:40

  Happy Pi Day (What Casinos, Pi, and Your Retirement Have in Common)

  Mar 2026 · article

• 9:55

  History of Computational Complexity Theory

  Mar 2026 · article

• 9:18

  Programs are Proofs: the Curry-Howard Correspondence

  Mar 2026 · article

• 2:22

  Gradient Descent

  Mar 2026 · article

• 7:43

  Turing Machines: How a Simple Machine Shattered Hilbert's Dream

  Mar 2026 · article

• 4:42

  HashMath (Content Addressed Formal Mathematics)

  Mar 2026 · article

• 4:26

  Sigma Protocols: Zero-Knowledge Proofs to Digital Signatures

  Mar 2026 · article

The lab

Workbenches for the machines the videos teach: a multi-tape Turing machine, a lambda calculus reducer, and finite automata you can union, intersect, and complement. They run in your browser, with no sign-in and no setup, and every experiment is a shareable link.

Open the lab →

About

Computable Secrets is a site and YouTube channel about computation, logic, and mathematics, built from first principles: complexity theory, the lambda calculus, information theory, category theory, and proofs you can run.

It's made by Sam Schlesinger. The companion articles are free for everyone; membership ($8/month) adds the ad-free member player.