M2F: Automated Formalization of Mathematical Literature at Scale

TL;DR

M2F is a novel framework that automates the end-to-end formalization of large mathematical texts into Lean, significantly reducing the time and effort needed for project-scale formalization.

Contribution

It introduces M2F, the first agentic framework capable of scaling formalization to entire textbooks by managing dependencies, repairs, and proof completion automatically.

Findings

Formalized 479 pages of textbooks into Lean in three weeks.

Achieved 96% proof success rate, outperforming baseline methods.

Demonstrated practical large-scale formalization of mathematical literature.

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.