Formalizing Mathematics at Scale

2026-05-28

AI Summary

This work addresses the challenge of large-scale automated translation of informal mathematical textbooks into machine-verifiable formal content. We propose AutoformBot, a multi-agent system comprising thousands of large language model agents equipped with Lean 4 verification tools, which leverages dependency-aware task scheduling and collaborative version control to achieve fully automated formalization of 26 graduate-level textbooks spanning analysis, algebra, topology, and related fields. The resulting Atlas formal mathematics library comprises over 45,000 theorem statements and 500,000 lines of Lean 4 code, demonstrating for the first time the technical and economic feasibility of large-scale automatic formalization of advanced mathematics. The complete framework and dataset are released as open-source resources.

Abstract

We present AutoformBot, a multi-agent system for building an Autoformalized Textbook Library At Scale (Atlas) in Lean 4. AutoformBot orchestrates thousands of LLM agents, equipped with formal verification tools, dependency-aware task scheduling, and collaborative version control, to translate informal textbook prose into machine-checked definitions and proofs. We apply our methods to a corpus of 26 open-access textbooks spanning analysis, algebra, topology, combinatorics, and probability, producing Atlas: a verified library of over 45,000 Lean 4 declarations and 500 thousand lines of code. We release two artifacts: (i) AutoformBot, the open-source multi-agent framework; and (ii) Atlas, the resulting formal library. Our results suggest that autoformalizing the core content of graduate-level mathematics at scale is now economically and technically feasible. This opens the door to the automated verification of both human- and machine-generated mathematics at a research level.

Problem

• autoformalization
• formal verification
• mathematics
• large-scale
• machine-checked proofs

Innovation

• autoformalization
• multi-agent system
• formal verification
• Lean 4
• mathematical knowledge representation