Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910247050805248 |
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| author | Breen, Benjamin Del Tredici, Marco McCarran, Jacob Mijares, Javier Aspuru Yin, Weichen Winston Sulimany, Kfir Taylor, Jacob M. Koppens, Frank H. L. Englund, Dirk |
| author_facet | Breen, Benjamin Del Tredici, Marco McCarran, Jacob Mijares, Javier Aspuru Yin, Weichen Winston Sulimany, Kfir Taylor, Jacob M. Koppens, Frank H. L. Englund, Dirk |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12787 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics Breen, Benjamin Del Tredici, Marco McCarran, Jacob Mijares, Javier Aspuru Yin, Weichen Winston Sulimany, Kfir Taylor, Jacob M. Koppens, Frank H. L. Englund, Dirk Artificial Intelligence Multiagent Systems 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. |
| title | Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics |
| topic | Artificial Intelligence Multiagent Systems |
| url | https://arxiv.org/abs/2510.12787 |