OpenAI’s math breakthrough is here, but is it really helping mathematicians?

OpenAI released a large collection of mathematical results produced by an internal AI model on October 6. The company says the work could help push mathematics forward and give scientists new tools.

It said the results were produced by an internal “frontier model” and cover a broad range of mathematical problems. The company said it was publishing the work in a GitHub repository. It also included formal versions of many proofs in Lean, a programming language that allows mathematical proofs to be checked by a computer.

OpenAI said it was also sharing information about how the results were produced. This includes 10 summaries of the model’s reasoning, estimates of the computing power used and statistics on the problems it attempted.


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The company explained, “We want this progress to push the frontier of human knowledge and enable further progress in mathematics. We will be funding a series of workshops, conferences, and special programs around the understanding of major results produced by AI, we will share more on this in the near future.”

But publishing the results is only the first step

The Advisory Group on Mathematics and Artificial Intelligence, or AGMAI, responded to the release on October 6. The independent group said OpenAI’s release was an “important event for mathematics." But it also made clear that its involvement should not be seen as an endorsement of the results or the way they were produced. “Making this work public is a first step,” AGMAI said. The group said the release is only the beginning of the process of checking the work and bringing it into mathematical knowledge.

AGMAI says humans must still choose the questions

This is also where the debate becomes bigger than simply asking whether AI can solve difficult maths problems. AGMAI said mathematical research cannot become a process where humans only study results produced by AI companies. The group said mathematicians must still be able to “formulate their own questions, develop their own approaches” and explore areas that AI companies have not selected to demonstrate their systems.

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“Equitable access to powerful research tools and adequate computational resources are essential to that freedom,” AGMAI said.

According to WIRED, mathematicians who had previously spoken with OpenAI wanted the company to provide papers that properly explained its AI-generated results. The concern was that mathematicians need more than a short announcement or a collection of results. They need enough detail to understand the work and build on it. Northwestern University mathematician Bryna Kra was among those raising this concern.

Kra criticized the idea of sharing major mathematical discoveries mainly through short public announcements. She told WIRED, “Math by tweet and math by press release” was not the right way to support the mathematical community.

OpenAI said it has been consulting AGMAI while working on how to share AI-generated mathematical results. The company said it had used the group’s advice and public recommendations when preparing its latest release. OpenAI also said it wants to improve future releases by making the papers clearer and improving their citations, mathematical explanations and presentation. The company said it would continue to “act on feedback from the community” and update its standards for future disclosures.