Computable Secrets
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 →
23:59Type-Level Abstraction: System Fω
20:25A Mathematical Theory of Communication (Part 1)
23:20Kolmogorov Complexity
16:05The Random Graph
27:29Category Theory: What Makes a Construction Natural?
14:44The Polymorphic Lambda Calculus: System F
35:01Categories, Monoids, and Preorders (in Lean 4)
18:51Vanishing Gradients: Why Deep Networks Couldn't Learn
23:02Euclid: the Algorithm and the Format
8:38Bourbaki: A Unified Foundation for Mathematics
10:05The Simply Typed Lambda Calculus
18:30Quantum Computation
17:03Interactive Proofs
16:15The Relativization Barrier: Why It's Hard to Resolve P vs NP
22:23Derandomization
25:38Descriptive Complexity
8:41The Lambda Calculus
15:05Impagliazzo's Five Worlds
9:52The Natural Proofs Barrier
8:16Introduction to Circuit Complexity
2:40Happy Pi Day (What Casinos, Pi, and Your Retirement Have in Common)
9:55History of Computational Complexity Theory
9:18Programs are Proofs: the Curry-Howard Correspondence
2:22Gradient Descent
7:43Turing Machines: How a Simple Machine Shattered Hilbert's Dream
4:42HashMath (Content Addressed Formal Mathematics)
4:26Sigma Protocols: Zero-Knowledge Proofs to Digital Signatures
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.
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.