title: DeepTheorem: Advancing LLM Reasoning for Theorem Proving Through Natural
    Language and Reinforcement Learning
summary: Theorem proving serves as a major testbed for evaluating complex reasoning
  abilities in large language models (LLMs). However, traditional automated
  theorem proving (ATP) approaches rely heavily on formal proof systems that
  poorly align with LLMs' strength derived from informal, natural language
  knowledge acquired during pre-training. In this work, we propose DeepTheorem, a
  comprehensive informal theorem-proving framework exploiting natural language to
  enhance LLM mathematical reasoning. DeepTheorem includes a large-scale
  benchmark dataset consisting of 121K high-quality IMO-level informal theorems
  and proofs spanning diverse mathematical domains, rigorously annotated for
  correctness, difficulty, and topic categories, accompanied by systematically
  constructed verifiable theorem variants. We devise a novel reinforcement
  learning strategy (RL-Zero) explicitly tailored to informal theorem proving,
  leveraging the verified theorem variants to incentivize robust mathematical
  inference. Additionally, we propose comprehensive outcome and process
  evaluation metrics examining proof correctness and the quality of reasoning
  steps. Extensive experimental analyses demonstrate DeepTheorem significantly
  improves LLM theorem-proving performance compared to existing datasets and
  supervised fine-tuning protocols, achieving state-of-the-art accuracy and
  reasoning quality. Our findings highlight DeepTheorem's potential to
  fundamentally advance automated informal theorem proving and mathematical
  exploration.
paper_authors._id: 68391c6dc4405ad056a9ff79
paper_authors.name: Ziyin Zhang
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-06-02T07:47:09.492Z
paper_authors._id: 6430bdd8cd31d174a9f900fb
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/noauth/Y9SPnRfpKSbYc7MhNdP-H.jpeg
paper_authors.fullname: Ziyin Zhang
paper_authors.type: user
paper_authors.user: Geralt-Targaryen
paper_authors._id: 68391c6dc4405ad056a9ff7a
paper_authors.name: Jiahao Xu
paper_authors._id: 68391c6dc4405ad056a9ff7b
paper_authors.name: Zhiwei He
paper_authors._id: 68391c6dc4405ad056a9ff7c
paper_authors.name: Tian Liang
paper_authors._id: 68391c6dc4405ad056a9ff7d
paper_authors.name: Qiuzhi Liu
paper_authors._id: 68391c6dc4405ad056a9ff7e
paper_authors.name: Yansi Li
paper_authors._id: 68391c6dc4405ad056a9ff7f
paper_authors.name: Linfeng Song
paper_authors._id: 68391c6dc4405ad056a9ff80
paper_authors.name: Zhengwen Liang
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-06-02T07:47:06.128Z
paper_authors._id: 62ffa3f8311cad266f9af236
paper_authors.avatarUrl: /avatars/4c88cb518e000a475f8381573f21aa7f.svg
paper_authors.fullname: Zhenwen Liang
paper_authors.type: user
paper_authors.user: invokerliang
paper_authors._id: 68391c6dc4405ad056a9ff81
paper_authors.name: Zhuosheng Zhang
paper_authors._id: 68391c6dc4405ad056a9ff82
paper_authors.name: Rui Wang
paper_authors._id: 68391c6dc4405ad056a9ff83
paper_authors.name: Zhaopeng Tu
paper_authors._id: 68391c6dc4405ad056a9ff84
paper_authors.name: Haitao Mi
paper_authors._id: 68391c6dc4405ad056a9ff85
paper_authors.name: Dong Yu
paper_title: DeepTheorem: Advancing LLM Reasoning for Theorem Proving Through Natural
    Language and Reinforcement Learning
paper_summary: Theorem proving serves as a major testbed for evaluating complex reasoning
  abilities in large language models (LLMs). However, traditional automated
  theorem proving (ATP) approaches rely heavily on formal proof systems that
  poorly align with LLMs' strength derived from informal, natural language
  knowledge acquired during pre-training. In this work, we propose DeepTheorem, a
  comprehensive informal theorem-proving framework exploiting natural language to
  enhance LLM mathematical reasoning. DeepTheorem includes a large-scale
  benchmark dataset consisting of 121K high-quality IMO-level informal theorems
  and proofs spanning diverse mathematical domains, rigorously annotated for
  correctness, difficulty, and topic categories, accompanied by systematically
  constructed verifiable theorem variants. We devise a novel reinforcement
  learning strategy (RL-Zero) explicitly tailored to informal theorem proving,
  leveraging the verified theorem variants to incentivize robust mathematical
  inference. Additionally, we propose comprehensive outcome and process
  evaluation metrics examining proof correctness and the quality of reasoning
  steps. Extensive experimental analyses demonstrate DeepTheorem significantly
  improves LLM theorem-proving performance compared to existing datasets and
  supervised fine-tuning protocols, achieving state-of-the-art accuracy and
  reasoning quality. Our findings highlight DeepTheorem's potential to
  fundamentally advance automated informal theorem proving and mathematical
  exploration.
paper_ai_summary: DeepTheorem enhances LLM theorem-proving through a large-scale natural language dataset and a tailored reinforcement learning strategy, achieving state-of-the-art results in informal theorem proving.
paper_ai_keywords: DeepTheorem automated theorem proving ATP natural language informal theorem-proving large-scale benchmark dataset IMO-level theorems reinforcement learning RL-Zero verified theorem variants proof correctness reasoning quality