OpenAI has released 377 AI-generated mathematical results, including work on unsolved problems at the frontier of research. The findings span algebra, number theory, theoretical computer science, mathematical logic and topology.

Released Tuesday, the results came from an advanced model that remains unavailable to the public. 

OpenAI said the average result took about three hours of computing, and it checked many proofs using Lean, a computer language that verifies underlying logic.

The release follows the company’s announcement last month that it had solved the Navier-Stokes problem. 

Together, the claims have intensified debate over whether AI is producing original mathematical insights or completing proofs built on human researchers’ ideas.

OpenAI’s mathematical testing has moved beyond established benchmarks, such as problems set for high school students competing in the International Mathematical Olympiad.

After its models could solve those problems, the company developed new benchmarks involving unsolved questions at the cutting edge of mathematical research. Those problems account for some of the results released Tuesday.

Dan Roberts, OpenAI’s research lead, said testing internal models was important for developing better tools. He described the mathematical proofs as a byproduct of that testing.

For 10 solutions, OpenAI also supplied summaries explaining how its model reached an answer.

The earlier Navier-Stokes announcement concerned one of the Clay Mathematics Institute’s seven Millennium Prize Problems, each carrying a $1 million reward for a solution. 

That claim had already raised questions about the relationship between AI-generated proofs and existing mathematical work.

An independent advisory board hosted by the Institute for Advanced Study in Princeton, New Jersey, has recommended how AI companies should communicate mathematical results.

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