openai/math is a repository of mathematical manuscripts and formal proof artifacts generated by an AI model during development and evaluation.
The repository addresses the need to document and verify mathematical results produced by machine learning models on open research problems. As the model's performance on existing mathematical benchmarks saturated, the evaluation scope expanded to include novel research problems. The outputs represent various stages of mathematical work, from initial results to formalized proofs in Lean, with some building upon earlier model-generated findings. The collection acknowledges that not all results have been formally verified, and unformalized results may contain errors that the maintainers commit to addressing quickly.
The repository contains manuscripts organized into families that group related papers, including principal results, companion arguments, and alternative proofs, classified by mathematical discipline. Each manuscript is accompanied by source files and citation instructions. A subset of results have been formalized in Lean, with a catalogue describing available formal proofs and their verification configurations. The collection also includes reasoning summaries for selected results, providing abridged accounts of the model's reasoning process. This resource is most valuable for researchers interested in examining AI-generated mathematical work, those studying formal verification practices, or mathematicians exploring novel approaches to open problems. The staged verification status means users should treat unformalized results with appropriate caution while formal proofs provide stronger guarantees.
Development activity shows ongoing commitment to expanding formal verification coverage, with the maintainers continuing to add Lean formalizations as they become available. The project maintains active engagement with the mathematical community through exploration of community-hosted repositories for these materials. Regular updates to the collection reflect sustained effort to improve verification status and address any issues discovered in unformalized results.
