Shapes, Colours and Patterns: Convex Geometry and Combinatorics

Deep End Era. Engineering with Sankalp · Oct 12, 2026 · 51m

Combinatorics is the part of mathematics where a twelve-year-old can understand the question and a professional can spend forty years on it. That makes it the perfect place to test what a machine-written proof is worth. Farah and Augustin colour the plane, squeeze convex bodies, hunt arithmetic progressions and tile space with a single strange block. Along the way we separate what OpenAI's manuscripts claim, what a Lean kernel has checked, and what the human community has actually said, including Joshua Swanson's verdict on the Shareshian–Wachs proof.

Chapters

00:00:00 Cold open: the coloured…