Automatic Textbook Formalization

2026-04-03

AI Summary

This study addresses the efficiency bottleneck in the large-scale automatic formalization of graduate-level mathematics textbooks. By deploying 30,000 parallel AI agents based on Claude 4.5 Opus and integrating version control with the Lean theorem prover, the project achieved the first end-to-end fully automated formalization of an entire 500-page algebraic combinatorics textbook within one week. The resulting artifact comprises 130,000 lines of Lean code and 5,900 formal statements, accompanied by an open-source repository and a side-by-side blueprint website. This effort not only demonstrates the feasibility and economic viability of large-scale formalization—achieving costs lower than expert salaries—but also establishes a new record in scale and efficiency for multi-agent collaborative software engineering.

Abstract

We present a case study where an automatic AI system formalizes a textbook with more than 500 pages of graduate-level algebraic combinatorics to Lean. The resulting formalization represents a new milestone in textbook formalization scale and proficiency, moving from early results in undergraduate topology and restructuring of existing library content to a full standalone formalization of a graduate textbook. The formalization comprises 130K lines of code and 5900 Lean declarations and was conducted within one week by a total of 30K Claude 4.5 Opus agents collaborating in parallel on a shared code base via version control, simultaneously setting a record in multi-agent software engineering with usable results. The inference cost matches or undercuts what we estimate as the salaries required for a team of human experts, and we expect there is still the potential for large efficiencies to be made without the need for better models. We make our code, the resulting Lean code base and a side-by-side blueprint website available open-source.

Problem

• Automatic Textbook Formalization
• Formalization
• Lean
• Algebraic Combinatorics
• Multi-agent AI

Innovation

• automatic formalization
• multi-agent AI collaboration
• Lean theorem proving
• textbook formalization
• large-scale code generation