DeepTheorem: Advancing LLM Reasoning for Theorem Proving Through Natural
  Language and Reinforcement Learning
Authors: name: Ziyin Zhang, name: Jiahao Xu, name: Zhiwei He, name: Tian Liang, name: Qiuzhi Liu, name: Yansi Li, name: Linfeng Song, name: Zhengwen Liang, name: Zhuosheng Zhang, name: Rui Wang, name: Zhaopeng Tu, name: Haitao Mi, name: Dong Yu

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.