# MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling

arXiv: https://arxiv.org/abs/2606.13473 · HTML: https://mlsanity.com/paper/2606.13473/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 5 of its 44 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 5 of 5)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Achieving Gold-Medal-Level Olympiad Reasoning via Simple and Unified Scaling](https://mlsanity.com/paper/2605.13301/) (2026)

## Built on by (most cited first, 4 of 4)

- [Autonomous Research Agents: A Survey of AI Scientists and the Verification Gap](https://mlsanity.com/paper/2608.05179/) (2026)
- [SimpleOPD: Simple Tokenizer-Agnostic On-Policy Distillation for Long-Context Reasoning](https://mlsanity.com/paper/2608.14277/) (2026)
- [Theoretical Foundations of max@k Reinforcement Learning](https://mlsanity.com/paper/2607.17823/) (2026)
- [Self-Evolving Algorithm-Design Agents: Escaping In-Context Evolutionary Stagnation via Population-Curated Policy Optimization](https://mlsanity.com/paper/2609.38757/) (2026)

## Abstract (arXiv)

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.