MiniMax open-sources MaxProof, an evolutionary math proof framework

MiniMax's developer relations lead, Ryan Lee, announced the open-source release of MaxProof, a test-time scaling framework for large language model mathematical proofs, along with an accompanying technical paper.

MaxProof recasts mathematical proof during inference as an evolutionary search system, achieving test-time scaling through verification, repair, and elimination mechanisms. Underpinned by MaxProof, the MiniMax-M3 model scored 35 and 36 out of 42 on the International Mathematical Olympiad (IMO 2025) and the USAMO 2026 test sets, respectively — both reaching the gold medal threshold.

On the algorithm side, the team built a multi-layered verification mechanism by combining three expert capabilities: generation, verification, and repair. The generation expert is guided by the primary reward signal from a generative verifier and undergoes long-horizon reinforcement learning training. The verification expert focuses on explicit error detection to reduce false positive rates. The repair expert refines corrections to flagged erroneous proofs through fine-tuning under critic conditions. These three expert capabilities were eventually merged into the released M3 model.

At inference time, MaxProof transforms the proof derivation process into evolutionary search. The M3 model is decoupled into four roles: generator, verifier, optimizer, and scorer. The system first constructs a pool of candidate proofs as a population, uses locally repaired patches and re-exploration rewrites for mutation, and finally selects the best derivation through a tournament mechanism. This evolutionary search successfully converts the model's best@K capability on mathematical proofs into more stable pass@1 performance.