MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling
Authors: name: Jiacheng Chen, name: Xinyu Zhang, name: Shunkai Zhang, name: Yanmohan Wang, name: Lin Li, name: Tiancheng Qin, name: Qin Wang, name: Zhengmao Zhu, name: Tianle Li, name: Jingyang Li, name: Zehan Li, name: Binyang Jiang, name: Jin Zhu, name: Han Ding, name: Fei Yu, name: Chenyu Du, name: Zijian Song, name: Jiayuan Song, name: Zhi Zhang, name: Yunan Huang, name: Weiyu Cheng, name: Pengyu Zhao, name: Yu Cheng
Organization: MiniMax

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.