OpenAI says its artificial intelligence just solved some of maths’ hardest problems

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OpenAI claims that it has made a range of major breakthroughs in mathematics – and appeared to apologise for them.

The company published hundreds of new findings, covering a wide array of mathematical topics, some of which relate to some of the oldest and most important problems in the field. The results came from an experimental model that is yet to be released publicly, OpenAI said, but it published both the findings and the work that had gone into them online.

But OpenAI appeared to acknowledge that the decision to publish them would frustrate mathematicians, who have complained that OpenAI’s work in the field is causing unnecessary disruption and not being done with sufficient care. Once again, some mathematicians suggested that the latest release was unlikely to have been properly checked and could only create unnecessary work for experts.

In its announcement, OpenAI seemed to be aware that the release of the findings could lead to further criticism from mathematicians. It stressed that it had worked with an independent advisory group to decide how to release them, that it would work to improve the quality of future releases, and that it had included detailed information on how the findings came about.

“We want this progress to push the frontier of human knowledge and enable further progress in mathematics,” it said, in an apparent response to the criticism. It said that it would fund a “series of workshops, conferences, and special programs around the understanding of major results produced by AI”.

And it stressed that it aimed to work with researchers to empower rather than upset them. “We want to directly empower scientists with state-of-the-art capabilities and are working to responsibly release the model that produced these results,” it said.

“This is why 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. We will continue to act on feedback from the community and update our standards for future disclosures of major scientific advancements.”

Previous claims by OpenAI to have made progress in maths have been met by some outcry from experts in the field. Last month, for instance, the company claimed to have made substantial progress on a decades-old problem – but it was immediately hit by controversy.

The company said that it had hit a “milestone” on work in the Navier-Stokes equations, which describe the movement of fluids and have troubled mathematicians for 90 years. OpenAI said it had made the breakthrough in a matter of hours, using 10,000 AI agents.

But hours before it announced that breakthrough, Tristan Buckmaster, from New York University, said that he had been working on the same problem with Levent Alpöge, a mathematician at OpenAI rival Anthropic. He claimed that his work had been passed to OpenAI, and suggested that the company’s breakthroughs depended on his own discoveries.

OpenAI denied that it had seen the work while working on the problem. But it said that “we cannot rule out that de-identified data derived from their usage of our products helped improve our models⁠”.

Professor Buckmaster also said that OpenAI’s decision to release its findings had hurried him into publishing his work before it was ready. But he said that his own work had relied on AI models, and acknowledged that their development represented a major breakthrough in mathematics that required a “serious and unhurried discussion about where to go from here”.