OpenAI shares mathematics research catalogue

OpenAI has released a catalogue of mathematical research produced by an internal model. The collection consists of 722 manuscripts organized into 372 families, each grouping related papers and potential results. The mathematical discipline classifying each family allows for easy navigation.

The model's reasoning behind these results was made available in abridged summaries. Over 4,000 problems were posed to the model during the evaluation, with an average of three hours of ChatGPT Pro thinking compute required per result. The vast majority of the results were obtained using the same procedure on an unreleased internal OpenAI model.

Some exceptions to the fixed procedure include work on the zero-free region for the Riemann zeta function and the proof of the Hodge Conjecture for CM abelian varieties. The human-edited writeup for the Re(s) ≥ 11/12 zero-free region for the Riemann zeta function is included. Proper citation of individual manuscripts is provided through BibTeX blocks in their respective directories.

Corrections and revisions will be documented as new versions, keeping previous releases accessible. OpenAI plans to continue updating the repository with Lean formalizations as they become available and explores community-hosted repositories for these materials.