OpenAI published hundreds of AI-generated mathematical results, prompting experts to assess their proofs, quality and potential effects on research.
OpenAI’s latest mathematics release has given researchers a large body of AI-generated work to evaluate: 719 manuscripts spanning fields including number theory, geometry, combinatorics, topology and theoretical computer science. The collection includes nearly 400 results, and mathematicians interviewed by The Verge said assessing its claims and significance could take years.
The release contains results that researchers described as potentially important, including work related to the Riemann hypothesis, a special case of the Hodge conjecture and the four-dimensional Kakeya conjecture. Those descriptions are preliminary, however: experts said the volume and uneven presentation make it difficult to determine which claims are correct, novel and properly situated within existing research.
Verification is a particular concern. OpenAI said 300 of the 719 manuscripts had been formalized in Lean, a proof assistant that can support computer-based checking. That is about 42 percent of the collection. Even a formalization needs scrutiny to confirm that it proves the claim made in the paper, and researchers told The Verge that some accompanying code did not clearly match the manuscripts’ assertions.
The repository’s record showed revisions to more than a dozen manuscripts and the removal of three papers after a sign error invalidated an argument, as of October 8. OpenAI said its model had attempted more than 4,000 problems and that a typical result used around three hours of ChatGPT Pro thinking compute. It did not identify the model or disclose its prompts or the full set of attempted problems.
The release has also raised questions about how AI-generated findings affect academic work. Some mathematicians said results may overlap with ongoing research or disrupt plans tied to open problems, while others saw promising contributions that merit careful study. OpenAI said it would fund workshops and conferences to help researchers engage with the material and plans to add more formalizations. It also said future papers would improve in citation, exposition and presentation.