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ATLAS: Autoformalized Textbook Library At Scale

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Why This Matters

ATLAS is a groundbreaking library that leverages large language models to autoformalize a vast range of mathematical textbooks into Lean code, significantly accelerating formalization efforts in the mathematical and computer science communities. Its scalable approach aims to provide reusable formal building blocks, fostering collaboration and advancing the development of formal mathematics and proof verification tools. This initiative has the potential to transform how mathematical knowledge is formalized, shared, and built upon in the tech industry and academia.

Key Takeaways

ATLAS - Autoformalized Textbook Library At Scale

ATLAS is a Lean 4 library of textbook mathematics autoformalized by LLMs: informal statements and proofs translated into Lean code. It draws from undergraduate and graduate textbooks across analysis, algebra, geometry, topology, combinatorics, probability, statistics, PDEs, number theory, and theoretical computer science.

The goal of ATLAS is to provide reusable formal building blocks for future human- and machine-driven Lean formalization. This is an active effort: we are continuing to scale to more sources, curate the generated material, improve coverage and maintainability, and move the library closer to Mathlib conventions.

ATLAS was generated with AutoformBot, our autoformalization pipeline.

Links

Library Data

Each book directory under Atlas/ contains:

Lean source files for the generated definitions, statements, and proofs.

targets.yaml , listing the textbook statements selected for formalization.

, listing the textbook statements selected for formalization. report.json , containing automated evaluation results for matched Lean declarations, including faithfulness, proof-integrity, and code-quality scores.

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