Beyond the Library: An Agentic Framework for Autoformalizing Research Mathematics

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arXiv:2606.31134v3 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 *Theo*, 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 seven research papers---five from the ACM Symposium on Theory of Computing (STOC) and two recent OpenAI manuscripts---spanning combinatorics, communication complexity, mechanism design, learning theory, number theory, discrete geometry, and graph theory. We successfully formalize their main theorems and proofs and validate the generated …

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