数学证明是 AI 推理的硬核测试，MaxProof 用群体搜索和验证器强化学习突破了竞赛级证明的瓶颈，做数学 AI 或推理系统的研究者值得关注其方法。
MaxProof 是一个面向竞赛级数学证明的群体级测试时扩展框架，由 MiniMax-M3 系列模型实现。M3 模型通过深度防御生成式验证器训练了证明生成、验证和基于批评的修复三种能力，并整合为单一模型。在测试时，MaxProof 将模型作为生成器、验证器、优化器和排序器，对候选证明群体进行搜索，并通过锦标赛选择输出最终证明。在 IMO 2025 和 USAMO 2026 上，M3 模型分别达到 35/42 和 36/42，超过了人类金牌阈值。
MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling
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.