Curvature and Spacetime: Geometry's Rigidity Theorems

Deep End Era. Engineering with Sankalp · Oct 12, 2026 · 57m

Curvature is how triangles fail to add up to a hundred and eighty degrees. Rigidity is what happens when a little information about curvature pins down a whole shape. Farah and Augustin walk from the surveyor's triangle to black holes, through a run of famous geometry conjectures that OpenAI's manuscripts claim to settle. We explain each one in words, say exactly what tier each claim is in, and ask why geometry, unlike combinatorics, is mostly beyond today's formal verification.

Chapters

00:00:00 Cold open: the triangle on the pipeline survey

00:01:37 The ground rules, briefly

00:03:03 What…