OpenAI has published a public collection of mathematical manuscripts on GitHub, produced by an unreleased internal model during its evaluation work on open research problems. According to the repository page on GitHub, the catalogue currently holds 719 manuscripts grouped into 372 families, and roughly 42 percent of the top-line results have been formalized in the Lean proof language. The release gives outsiders a rare view of how a frontier AI system approaches unsolved questions, and it comes with an explicit warning that not every result has been checked.
What the repository contains
The collection is organised around families of related papers. A family might include a main result, supporting arguments, consequences, or alternative proofs, and each family is labelled by its mathematical discipline. GitHub's page points readers to an overview that describes each family, a manuscript map for finding individual papers, and a preprints directory holding PDFs, source files, and instructions for citing and building each manuscript.
Formal verification is handled separately. A Lean library and formalization catalogue lists the available formal proofs, the papers they belong to, and the configurations used to verify them. A separate Comparator guide explains further checking steps. GitHub's description makes clear that the material sits at different stages of verification, and that not every manuscript has a Lean version yet.
Reasoning summaries and updates
The repository also says OpenAI is releasing abridged summaries of the model's reasoning for selected results. Changes to the collection are recorded in its history, so readers can track how the material has evolved over time.
How the results were produced
According to the repository, the vast majority of results came from one procedure run on the same unreleased internal model. On average, each result consumed about three hours of ChatGPT Pro thinking compute. Over the full evaluation, the model was given roughly 4,000 problems. The outputs were then grouped into families and manuscripts, and only results meeting a defined threshold of significance were kept, which produced the catalogue now online.
Some work departs from that standard process. The repository names two examples: a zero-free region for the Riemann zeta function and a proof of the Hodge Conjecture for CM abelian varieties. In addition, the write-up for the zero-free region for Re(s) greater than 11/12 was edited by a person to improve readability. These exceptions matter because they show where human involvement entered the pipeline.
Why evaluators moved to open problems
The repository states that OpenAI widened its evaluations after performance on its existing mathematical tests levelled off. When a benchmark becomes saturated, models score so close to the ceiling that the test stops separating strong systems from weaker ones. Open research problems offer a harder and less predictable target, because no answer key exists in advance.
The source also notes that some outputs build on earlier results produced by the models. That detail makes the collection more than a list of isolated answers. It hints at a chain of work in which later results depend on prior ones, which raises the stakes for checking each link.
Caveats and what comes next
- OpenAI acknowledges that some unformalized results could contain issues and says it will work to fix them quickly.
- The company is exploring community-hosted repositories for these materials, which could widen external review.
- Corrections and revisions will be published as new versions, and earlier releases will remain accessible.
- Lean formalizations will be added to the repository as they become available.
For mathematicians and AI researchers, the most useful next step is independent checking of the formalized proofs and the unverified manuscripts. The collection is a meaningful test of what AI systems can contribute to research mathematics, but its value will depend on how much of it survives scrutiny. Readers should watch the repository's version history and its formalization progress, since both will show how many of these claims hold up over time.
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