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.

Hundreds of results from an unreleased model

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.

Mathematicians seek transparency and understanding

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

Among its suggestions, the board called for releasing the prompts given to AI agents and the agents’ chains of thought.

In a Tuesday-night statement, it described public release as “the beginning, not the completion, of the process of human understanding and the incorporation of the work into mathematical knowledge.”

“We want to create standards and practices so that results released from AI labs can be understood by mathematicians and can advance the field,” said Harvard mathematician Melanie Wood, a board member.

OpenAI said it had drawn on the board’s advice and public recommendations when preparing its release.

However, the board also opposed using advanced mathematical problems to test proprietary models. 

Human contributions remain a point of contention

Tristan Buckmaster, a New York University mathematician who was working on the Navier-Stokes problem, questioned whether researchers using AI were inadvertently supplying information that helped models reach answers first.

“There’s likely to be a bunch of results where they take someone’s work and then take it to completion,” Buckmaster said.

The advisory board has also asked that AI labs grant “equitable access” to their AI models to the global mathematics community.

The wider concern is whether faster problem-solving advances mathematics when human understanding of the resulting proofs struggles to keep pace.