Beyond the Library: An Agentic Framework for Autoformalizing Research Mathematics
Arshia Soltani Moakhar, Iman Gholami, Max Springer, Mahdi JafariRaviz, MohammadTaghi Hajiaghayi
Why It Matters
What makes this one worth your time
This work is significant as it enhances the reliability of mathematical proofs generated by LLMs, potentially transforming how research mathematics is formalized and verified.
A novel framework for autoformalizing research mathematics using advanced LLMs.
Summary
The paper presents an agentic framework for autoformalizing research mathematics using general coding LLMs, addressing the limitations of existing libraries by dynamically extending type definitions and validating them through a novel technique before formalizing theorems.
Key contributions
- Introduction of an agentic framework for autoformalization of mathematics using general coding LLMs.
- Dynamic extension of type definitions to accommodate cutting-edge research concepts.
- Validation of generated formalizations through collaboration with human experts.
Notable insights
- The use of a multi-agent pipeline to manage the complexities of research-level mathematics is a clever approach that could improve the efficiency of formalization.
- The Auxiliary Lemma technique for validating type definitions before formalization is a novel contribution that addresses a critical gap in existing autoformalization methods.
Possible limitations
- Not stated in the abstract.
Abstract
arXiv:2606.31134v2 Announce Type: replace Abstract: While Large Language Models (LLMs) have demonstrated exceptional capabilities in mathematical reasoning, they frequently produce subtle errors that evade human detection. Formal mathematical languages like Lean 4 offer mechanical proof checking, strongly motivating the need for autoformalization: the automatic translation of natural language mathematics into verifiable code. Recent trends indicate that general-purpose LLMs, heavily optimized for standard programming, now outperform smaller models explicitly fine-tuned for Lean. Leveraging this shift, we introduce an agentic autoformalization framework powered by general coding LLMs. At the core of our system is an orchestrator that manages a multi-agent pipeline tailored for research-level mathematics. Because cutting-edge research frequently relies on concepts outside the scope of existing libraries like Mathlib, our system dynamically extends necessary type definitions and validates them via a novel Auxiliary Lemma technique before formalizing the primary theorems. We applied our approach to PutnamBench, producing machine-checked Lean proofs for a random sample of 32 problems. Furthermore, we evaluate our system on five papers from the ACM Symposium on Theory of Computing (STOC) spanning combinatorics, communication complexity, mechanism design, and learning theory, successfully formalizing their main theorems and validating the generated formalizations with human experts; for all five we also formalize the proofs alongside the statements, and notably two of them are proved with no axioms beyond Lean's kernel. All of our formalizations are available at https://beyondthelibrary.github.io/formal_arxiv .