arXiv:2510.12787cs.AIcs.MA2025-10被引 26

用AI代理系统自动证明数学与量子物理定理,兼顾创造力与形式正确性。

Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics

  • 通过LLM结合Lean工具,实现带形式验证的自主推理。
  • 在抽象代数和量子理论新基准上显著超越现有模型。
  • 适合数学、物理领域专家辅助形式化证明,提升研究效率。

我们提出Ax-Prover,一种用于Lean语言的多代理自动化定理证明系统,可在不同科学领域自主或协同人类专家解决复杂问题。该系统通过形式化证明过程,兼顾创造性推理与严格语法规范。为实现这一目标,我们采用模型上下文协议(MCP)将大型语言模型(LLMs)与Lean工具集成,确保形式正确性。我们在两个公开数学基准及两个自建的抽象代数与量子理论基准上评估性能。在公开数据集上,其表现与前沿证明器相当;而在新基准上则显著优于现有模型。这表明,相较于难以泛化的专用系统,基于工具的智能体定理证明方法具有跨领域通用性。此外,在实际案例中,该系统帮助一位数学专家成功形式化一个复杂密码学定理的证明。

原文摘要 · Abstract (English)

We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover approaches scientific problem solving through formal proof generation, a process that demands both creative reasoning and strict syntactic rigor. Ax-Prover meets this challenge by equipping Large Language Models (LLMs), which provide knowledge and reasoning, with Lean tools via the Model Context Protocol (MCP), which ensure formal correctness. To evaluate its performance as an autonomous prover, we benchmark our approach against frontier LLMs and specialized prover models on two public math benchmarks and on two Lean benchmarks we introduce in the fields of abstract algebra and quantum theory. On public datasets, Ax-Prover is competitive with state-of-the-art provers, while it largely outperforms them on the new benchmarks. This shows that, unlike specialized systems that struggle to generalize, our tool-based agentic theorem prover approach offers a generalizable methodology for formal verification across diverse scientific domains. Furthermore, we demonstrate Ax-Prover's assistant capabilities in a practical use case, showing how it enabled an expert mathematician to formalize the proof of a complex cryptography theorem.

定理证明形式验证AI代理量子物理

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