Summary
OpenAI’s public math repository lists 722 manuscripts across 372 related-work families, produced through an evaluation using an unreleased internal model. The company says the manuscripts are at different stages of verification, and not all have Lean formalizations.
OpenAI has published a public repository cataloguing 722 mathematical manuscripts and supporting proof materials produced as part of its model development. The collection is organised into 372 families of related work, and OpenAI says the results are at different stages of verification: many, but not all, have formal proofs written in Lean.
The repository’s scale is notable, but its catalogue should not be read as 722 uniformly verified mathematical breakthroughs. A family can include a principal result, related arguments, consequences or alternative proofs. OpenAI describes the collection as work on open research problems, with some outputs building on earlier results from its models.
What the collection contains
The repository includes preprints, source files and instructions for citing and building individual manuscripts. An overview describes the research families, while a manuscript map points to papers and supporting materials. The listed subjects range from the irrationality exponent of π and versions of the Mahler conjectures to problems in mathematical physics.
Some manuscripts have Lean formalizations. Lean is a proof assistant: a formalized proof is expressed in a language that software can check according to a defined logical framework. That provides a different kind of checking from reading a conventional mathematical proof written in prose. OpenAI says it will continue adding formalizations as they become available; it also cautions that some results without them could contain errors.
The repository also includes abridged reasoning summaries for ten result families. These are summaries rather than a uniform feature of every manuscript.
How OpenAI says the results were produced
OpenAI says it expanded its evaluations of models on open research problems after performance on its existing mathematical evaluations had saturated. For the vast majority of results, it used the same procedure with an unreleased internal model. The company reports that each result used an average of three hours of ChatGPT Pro thinking compute, and that the model was posed approximately 4,000 problems. OpenAI says it grouped the outputs into families and manuscripts and selected work it considered sufficiently significant for the catalogue.
The process was not identical for every item. OpenAI identifies work on a zero-free region for the Riemann zeta function and a proof of the Hodge Conjecture for CM abelian varieties as exceptions to the standard procedure. It also says the write-up of the zeta-function result for Re(s) > 11/12 was human-edited for readability.
The release therefore offers a substantial, inspectable record of model-generated mathematical work, alongside papers and some machine-checkable proofs. Its value depends on the evidence attached to each result: the repository itself makes clear that formal verification is not yet available for every manuscript.