M2F: Automated Formalization of Mathematical Literature at Scale
arXiv:2602.17016v1 Announce Type: new Abstract: Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file dependencies, resolving imports, and ensuring that entire projects compile end-to-end. We present M2F (Math-to-Formal), the first agentic framework for end-to-end, project-scale autoformalization in Lean. The framework operates in two stages. The statement compilation stage splits the document into atomic blocks, orders them via inferred dependencies, and repairs declaration skeletons until the project compiles, allowing placeholders in proofs. The proof repair stage closes these holes under fixed signatures using goal-conditioned local edits. Throughout both stages, M2F keeps the verifier in the loop, committing edits only when toolchain feedback confirms improvement. In approximately three weeks, M2F convert
arXiv:2602.17016v1 Announce Type: new Abstract: Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file dependencies, resolving imports, and ensuring that entire projects compile end-to-end. We present M2F (Math-to-Formal), the first agentic framework for end-to-end, project-scale autoformalization in Lean. The framework operates in two stages. The statement compilation stage splits the document into atomic blocks, orders them via inferred dependencies, and repairs declaration skeletons until the project compiles, allowing placeholders in proofs. The proof repair stage closes these holes under fixed signatures using goal-conditioned local edits. Throughout both stages, M2F keeps the verifier in the loop, committing edits only when toolchain feedback confirms improvement. In approximately three weeks, M2F converts long-form mathematical sources into a project-scale Lean library of 153,853 lines from 479 pages textbooks on real analysis and convex analysis, fully formalized as Lean declarations with accompanying proofs. This represents textbook-scale formalization at a pace that would typically require months or years of expert effort. On FATE-H, we achieve $96\%$ proof success (vs.\ $80\%$ for a strong baseline). Together, these results demonstrate that practical, large-scale automated formalization of mathematical literature is within reach. The full generated Lean code from our runs is available at https://github.com/optsuite/ReasBook.git.
Executive Summary
This article presents M2F (Math-to-Formal), an agentic framework for end-to-end, project-scale autoformalization in Lean. M2F successfully converts long-form mathematical sources into a project-scale Lean library, demonstrating that practical, large-scale automated formalization of mathematical literature is within reach. The framework consists of two stages: statement compilation and proof repair, both of which involve collaboration with a verifier to ensure improvement. M2F achieves a 96% proof success rate on FATE-H, outperforming a strong baseline. The full generated Lean code is available for replication and further research. This breakthrough has significant implications for the field of mathematics and computer science, and its applications may extend to formal verification, education, and research.
Key Points
- ▸ M2F is the first agentic framework for end-to-end, project-scale autoformalization in Lean.
- ▸ The framework consists of two stages: statement compilation and proof repair.
- ▸ M2F achieves a 96% proof success rate on FATE-H, outperforming a strong baseline.
Merits
Strength
M2F's ability to automate the formalization of large-scale mathematical literature, which is a significant improvement over previous methods that were limited to isolated theorems and short snippets.
Scalability
M2F's capacity to handle cross-file dependencies, resolve imports, and ensure end-to-end compilation makes it a scalable solution for large projects.
Collaborative Verification
M2F's interaction with a verifier to ensure improvement is a crucial feature that enhances the accuracy and reliability of the formalization process.
Demerits
Limited Domain
M2F is currently designed for Lean, which may limit its applicability to other mathematical formalisms or domains.
Dependence on Toolchain
M2F's reliance on a specific toolchain may make it challenging to adapt to changing toolchain requirements or configurations.
Expert Commentary
This article presents a significant breakthrough in the field of automated reasoning and formalization. M2F's ability to automate the formalization of large-scale mathematical literature has far-reaching implications for formal verification, mathematics education, and research. While there are limitations to the current implementation, the authors have identified key strengths and areas for improvement. The collaborative verification approach is particularly noteworthy, as it enhances the accuracy and reliability of the formalization process. As the AI and machine learning communities continue to advance, it is essential to explore applications of these technologies in mathematics and computer science. This article serves as a catalyst for such explorations, and its findings should inspire further research and innovation in the field.
Recommendations
- ✓ Future research should focus on adapting M2F to other mathematical formalisms and domains.
- ✓ Investigate the potential applications of M2F in mathematics education and its impact on student learning outcomes.
