The big picture: OpenAI has published 722 papers generated by an internal AI model, reporting advances across hundreds of mathematical problems. The papers cover number theory, algebraic geometry, and other fields. The release comes amid objections from mathematicians who argue that using proprietary AI models to solve mathematical problems prioritizes results over understanding and leaves researchers unable to examine the systems behind the proofs.
OpenAI organized the results into 372 groups and said it had given the model about 4,000 problems. The release gives researchers a large collection of proofs to examine, but not access to the proprietary system that produced them.
The company reported advances related to three of the five remaining Millennium Prize Problems, including the Riemann hypothesis. That does not mean it has solved all three. Even so, the reported Riemann result prompted a strong response from Rutgers University distinguished mathematics professor Alex Kontorovich.
"If a human did this, it would be an instant Fields Medal, no questions asked," he wrote on X.
Alongside the papers, OpenAI released summaries of the model's "chain of thought" for 10 results. The summaries describe the model's reasoning on selected problems, though they cover only a small share of the published work.
– Alex Kontorovich (@AlexKontorovich) October 6, 2026
OpenAI also said the average result required a fraction of the computing power used for its earlier effort to solve the Navier-Stokes Millennium Prize Problem. The company spent millions of dollars on computing for that project.
The new release therefore offers a broader test of the model than the Navier-Stokes announcement alone. Researchers can now examine results across hundreds of problems rather than assess its abilities through a single heavily funded effort. However, the sheer volume of papers does not establish their accuracy. Mathematicians have begun reviewing the papers, but some question whether they can build on the findings without access to the AI model that produced them.
The model continued producing proofs behind closed doors while researchers debated OpenAI's earlier announcement. The company then faced a publication problem: how to release that work to a community already questioning its methods.
OpenAI said it followed publication recommendations from an independent advisory group of leading mathematicians that it recently helped assemble. The group issued its guidelines last week after gathering feedback from hundreds of researchers.
The company did not accept every recommendation. The committee had asked AI developers to stop using closed systems to test advanced mathematical problems.
"We ask them to stop testing advanced mathematical problems on proprietary models," the mathematicians wrote.
OpenAI defended its decision to continue: "It is important to continue to evaluate our internal frontier models on mathematics and other sciences, so we can accelerate developing the tools to advance those fields."
That disagreement concerns more than how papers should be published. Researchers are being asked to assess discoveries from a system they cannot access, with reasoning summaries available for only 10 results.
The advisory effort followed an open letter signed by more than two dozen Fields Medal winners. Titled "A Severe Misalignment of AI in Mathematics," it warned that the industry's rush to solve problems threatened the purpose of mathematical research.
OpenAI and Anthropic have both used difficult mathematics to demonstrate the capabilities of their advanced models. Their competition helped set OpenAI's Millennium Prize effort in motion: the company said it began that work after hearing that Anthropic had already solved at least one of the problems.
The Navier-Stokes announcement also raised questions about the model's source. An academic collaborating with an Anthropic researcher suggested that the system might have drawn on his unpublished research. OpenAI denies the allegation.
The latest release also put pressure on researchers working with AI. Earlier in the week, as rumors spread that OpenAI was preparing to publish hundreds of proofs, some mathematicians hurried to release their own work before they could be scooped.
OpenAI has now made the papers public while keeping the model internal. Mathematicians have far more material to review, but the company and its advisers remain divided over whether advanced mathematical research should proceed on systems unavailable to the wider field.