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.

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.

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