OpenAI has released 722 mathematical manuscripts produced by an unreleased internal model, but the collection does not carry one uniform level of proof checking. Its repository says many results have computer-checkable Lean formalizations, while some do not and could contain errors.
The repository groups the manuscripts into 372 families of related results. OpenAI says the evaluation posed approximately 4,000 open problems, then grouped the model’s outputs into result families and manuscripts after applying a significance threshold. The company estimates average compute per result at roughly the equivalent of three hours of ChatGPT Pro thinking. Those figures describe OpenAI’s process; they are not a count of results independently accepted by mathematicians.
Lean is a proof assistant: researchers encode an argument as formal steps, and software checks whether those steps follow from definitions and earlier results. OpenAI says many manuscripts have Lean formalizations, but the README says the collection contains different verification stages and warns that some unformalized results may have issues. Formalized artifacts can make particular arguments easier to check; the release does not say every manuscript has been independently verified.
The Institute for Advanced Study's Advisory Group on Mathematics and AI published proposed practices for releasing AI-generated mathematics on September 29, after receiving more than 600 responses. OpenAI says the group's advice informed this release. Its public materials include some information in areas the group highlighted: 10 abridged reasoning summaries, attempted-problem statistics, an average compute estimate and Lean formalizations for many proofs. But the repository sits under OpenAI's GitHub organization, while the group recommended deposit in a scholarly repository outside an AI lab's control; the files identify only an unreleased internal model, not per-result model and prompt details. OpenAI says it is exploring community-hosted alternatives and will add formalizations as it obtains them.
Sources
- OpenAI’s announcement, October 6, 2026
- OpenAI’s mathematical manuscripts and proof-artifact repository
- Institute for Advanced Study Advisory Group on Mathematics and AI, “Responsible Release of AI-Generated Mathematics”
Image credit: Preply.com Images via Wikimedia Commons, CC BY 2.0. Illustrative classroom photo; not connected to the OpenAI release.