Year: 2025
Type: preprint
Abstract: LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely using natural language. Dedicated domain-specific languages like Lean provide clear supervision via formal verification of proofs, enabling effective training through reinforcement learning. In this work, we propose \textbf{Seed-Prover}, a lemma-style whole-proof reasoning model. Seed-Prover can iteratively refine its proof based on Lean feedback, proved lemmas, and self-summarization. To solve IMO-level contest problems, we design three test-time inference strategies that enable both deep and broad reasoning. Seed-Prover proves $78.1\%$ of formalized past IMO problems, saturates MiniF2F, and achieves over 50\% on PutnamBench, outperforming the previous state-of-the-art by a large margin. To address the lack of geometry support in Lean, we introduce a geometry reasoning engine \textbf{Seed-Geometry}, which outperforms previous formal geometry engines. We use these two systems to participate in IMO 2025 and fully prove 5 out of 6 problems. This work represents a significant advancement in automated mathematical reasoning, demonstrating the effectiveness of formal verification with long chain-of-thought reasoning.
Source: arXiv (Cornell University)
Authors: Chen, Luoxin, Gu, Jinming, Huang, Liankai, Huang, Wenhao, Jiang, Zhicheng, Jie, Allan, Jin, Xiaoran, Jin, Xing, Li, Chenggang, Ma, Kaijing, Ren, Cheng, Shen, Jiawei, Shi, Wenlei, Sun, Tong, Sun, He, Wang, Jiahui, Wang, Siran, Wang, Zhihong, Wei, Chenrui, Wei, Shufa, Wu, Yonghui, Wu, Yuchen, Xia, Yihang, Xin, Huajian, Yang, Fan, Ying, Huaiyuan, Yuan, Hongyi, Yuan, Zheng, Zhan, Tianyang, Zhang, Chi, Zhang, Yue, Zhang, Ge, Zhao, Tianyun, Zhao, Jianqiu, Zhou, Yichi, Zhu, Thomas Hanwen
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6948301696