MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling
For the mathematical reasoning community, this work demonstrates that test-time scaling with a generative verifier can surpass human-level performance on competition-level proof problems.
MaxProof achieves 35/42 on IMO 2025 and 36/42 on USAMO 2026, exceeding the human gold-medal threshold on both, by scaling test-time computation over a population of candidate proofs using a generative-verifier RL framework.
We present MaxProof, a population-level test-time scaling framework for competition-level mathematical proof in the MiniMax-M3 series. M3 first trains three proof-oriented capabilities -- proof generation, proof verification, and critique-conditioned proof repair -- using a defense-in-depth generative verifier engineered for low false-positive rate. These capabilities are merged into a single released M3 model. At test time, MaxProof treats the model as a generator, verifier, refiner, and ranker, searches over a population of candidate proofs, and returns one final proof through tournament selection. With MaxProof test-time scaling, the M3 model reaches 35/42 on IMO 2025 and 36/42 on USAMO 2026, exceeding the human gold-medal threshold on both.