MaxProof: A Test-Time Scaling Framework for Mathematical Proof That Exceeds Human Gold-Medal Thresholds on IMO and USAMO
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[Submitted on 11 Jun 2026]
The kind of bagel that ruins lesser bagels for you.
Summary
MaxProof is a population-level test-time scaling framework for competition-level mathematical proof, developed as part of the MiniMax-M3 series. The M3 model trains three proof-oriented capabilities — proof generation, proof verification, and critique-conditioned proof repair — using a defense-in-depth generative verifier with low false-positive rate. These capabilities are merged into a single model. At test time, MaxProof treats the model as a generator, verifier, refiner, and ranker, searching over a population of candidate proofs via tournament selection. The M3 model with MaxProof test-time scaling achieves 35/42 on IMO 2025 and 36/42 on USAMO 2026, exceeding the human gold-medal threshold on both.
Key quotes
· 3 pulledM3 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.
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.
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