jphme/math-problems

AI-assisted Lean formalization for Economics and Computation research

Lean 4 port of Gonthier's Coq proof of the Four Color Theorem (4CT), constructed by Claude Opus 5.5

This presents a AI counterexample to a classical problem in differential geometry: are smooth tight surfaces rigid (in the sense that isometry implies Euclidean congruence)? It constructs a band foliated by asymptotic lines, and then uses this to create a torus that allows a pain (in fact infinitely many) of isometric but noncongruent examples.

Multi-agent research program on the Riemann hypothesis: adversarial verification and extension of the 2026 67.25% result (2/3 of zeros on the critical line)

Gabriel Saco.

Proof of Degtyarev–Shimada Conjecture 1.2 for the Fermat varieties of every degree in every even dimension, algebraic core verified in Lean 4; integral Hodge conjecture for prime degree, degree 4, degree prime to (n+1)!. Paper (DOI), Lean project, logs, cold readings, 222 standalone theorems — directed by a non-mathematician, built with Claude.

A registry and coordination layer for Lean workers and Choir members, enabling role-based membership and formal verification of agent state.

ECMA-262 transcribed into a verifiable executable metalanguage (Lean), toward a simulation proof against ovm