Computable Secrets: computer science from first principlesSkip to content<br>Computable Secrets<br>Exploring the limits of the computable and beyond.<br>27 videos, each with a free companion article<br>Browse the videosOpen the labSubscribe on YouTube<br>running.cleaning the tape.halts.PBZCHGNOYR FRPERGF#COMPUTABLE SECRETSCOMPUTABLE SECRETSrunning.cleaning the tape.halts.COMPUTABLE SECRETS

Videos<br>Browse the library: sort, filter, and track your progress →<br>23:59<br>Type-Level Abstraction: System Fω<br>Jun 2026 · article

20:25<br>A Mathematical Theory of Communication (Part 1)<br>May 2026 · article

23:20<br>Kolmogorov Complexity<br>Apr 2026 · article

16:05<br>The Random Graph<br>Apr 2026 · article

27:29<br>Category Theory: What Makes a Construction Natural?<br>Apr 2026 · article

14:44<br>The Polymorphic Lambda Calculus: System F<br>Apr 2026 · article

35:01<br>Categories, Monoids, and Preorders (in Lean 4)<br>Apr 2026 · article

18:51<br>Vanishing Gradients: Why Deep Networks Couldn't Learn<br>Apr 2026 · article

23:02<br>Euclid: the Algorithm and the Format<br>Apr 2026 · article

8:38<br>Bourbaki: A Unified Foundation for Mathematics<br>Apr 2026 · article

10:05<br>The Simply Typed Lambda Calculus<br>Apr 2026 · article

18:30<br>Quantum Computation<br>Apr 2026 · article

17:03<br>Interactive Proofs<br>Mar 2026 · article

16:15<br>The Relativization Barrier: Why It's Hard to Resolve P vs NP<br>Mar 2026 · article

22:23<br>Derandomization<br>Mar 2026 · article

25:38<br>Descriptive Complexity<br>Mar 2026 · article

8:41<br>The Lambda Calculus<br>Mar 2026 · article

15:05<br>Impagliazzo's Five Worlds<br>Mar 2026 · article

9:52<br>The Natural Proofs Barrier<br>Mar 2026 · article

8:16<br>Introduction to Circuit Complexity<br>Mar 2026 · article

2:40<br>Happy Pi Day (What Casinos, Pi, and Your Retirement Have in Common)<br>Mar 2026 · article

9:55<br>History of Computational Complexity Theory<br>Mar 2026 · article

9:18<br>Programs are Proofs: the Curry-Howard Correspondence<br>Mar 2026 · article

2:22<br>Gradient Descent<br>Mar 2026 · article

7:43<br>Turing Machines: How a Simple Machine Shattered Hilbert's Dream<br>Mar 2026 · article

4:42<br>HashMath (Content Addressed Formal Mathematics)<br>Mar 2026 · article

4:26<br>Sigma Protocols: Zero-Knowledge Proofs to Digital Signatures<br>Mar 2026 · article

The lab<br>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.<br>Open the lab →

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