aiqbench analysis
The paper presents an LLM-based multi-agent system that generates formal Lean proofs, using Model Context Protocol tools to verify each step. It reports competitive results on existing math benchmarks and larger gains on new abstract algebra and quantum theory benchmarks, though these are self-introduced evaluations. For AI readers, the main takeaway is a tool-grounded agent design for verifiable reasoning, with the generalization claim still needing independent testing.
Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics
arXiv:2510.12787v5 Announce Type: replace Abstract: 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.
Abstract: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.
Artificial Intelligence (cs.AI); Multiagent Systems (cs.MA)
arXiv:2510.12787 [cs.AI]
(or arXiv:2510.12787v5 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2510.12787 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 287 words
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