Paper · arXiv 2606.13473
MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling
Jiacheng Chen, Xinyu Zhang, Shunkai Zhang, Yanmohan Wang, Lin Li, Tiancheng Qin, Qin Wang, Zhengmao Zhu, Tianle Li, Jingyang Li, Zehan Li, Binyang Jiang, Jin Zhu, Han Ding, Fei Yu, Chenyu Du, Zijian Song, Jiayuan Song, Zhi Zhang, Yunan Huang, Weiyu Cheng, Pengyu Zhao, Yu Cheng
MaxProof is a test-time scaling framework that enhances mathematical proof generation by combining multiple proof-oriented capabilities and using population-level search with tournament selection to achieve competitive performance on high-level mathematical competitions.
Abstract
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.