Formalizing Mathematics at Scale
This work enables automated verification of research-level mathematics, addressing the bottleneck of manual formalization for mathematicians and AI systems.
AutoformBot, a multi-agent system, autoformalized 26 open-access textbooks into a verified Lean 4 library (Atlas) with over 45,000 declarations and 500k lines of code, demonstrating that large-scale autoformalization of graduate-level mathematics is feasible.
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.