AI Proof Systems Breaching the Research Tier
#1DeepMind's AlphaProof (July 2024) solved 4 of 6 IMO 2024 problems — including the hardest problem in the set (P5) — by combining a Gemini-based LLM for proof strategy with Lean 4 formal verification in an iterative self-improving loop. This is not a narrow benchmark achievement: IMO problems require genuine mathematical creativity, multi-step reasoning, and proof construction across geometry, combinatorics, number theory, and algebra. Simultaneously, FunSearch generated new combinatorial constructions surpassing best-known human results, and the Lean 4 Mathlib library reached 100,000+ formalized theorems, providing an executable substrate for automated proof search at industrial scale.