OpenAI says its internal model solved over 100 long-standing math problems after just a month of training

Facing growing criticism from mathematicians, OpenAI is setting up an independent advisory group of leading researchers in the field. But not before letting everyone know that a new internal model knocked out more than 100 long-standing math problems after just a month of training.

OpenAI says a new internal model has solved more than 100 long-standing problems across most areas of mathematics, on top of the Navier-Stokes Millennium Problem. The company dropped the claim while announcing a new math advisory group.

According to OpenAI, training only kicked off on August 28, putting the entire run at about a month. Even the company's own mathematicians were "surprised" by how fast things moved, and internal conversations have shifted to how to give the academic community enough warning to prepare. Among the solved problems is reportedly a second Millennium Prize Problem, the Hodge conjecture.

Which problems the model actually solved, how it solved them, and what the results mean for math and science remain open questions. The published Navier-Stokes solution has already sparked heated debate in parts of the scientific community.

The whole thing seems like a pivot. Chief Scientist Jakub Pachocki recently said the team had deliberately chosen not to optimize for math and was focused on recursive self-improvement instead. Skeptics might read the publicity around solving famous math problems as a ploy to keep investors on board and attract new ones, especially since OpenAI admitted it only took on the Millennium Prize Problem after hearing rumors that another team, partly made up of Anthropic researchers, had already cracked it.

Solving problems isn't the same as understanding them

OpenAI's announcement is a direct response to criticism from mathematicians. In the open letter "A Severe Misalignment of AI in Mathematics," they warn against measuring AI performance by how many open problems it can solve. Churning out solutions, they argue, undermines conceptual understanding, which is the whole point of mathematics, and ultimately threatens human intellect.

OpenAI says it's now working with mathematicians who have formed the Advisory Group on Mathematics and Artificial Intelligence, based at the Institute for Advanced Study. The group is meant to connect the company with the math community and the broader public.

The company argues it needs this kind of guidance because math breakthroughs can have far-reaching practical uses, which makes responsible development a concern well beyond the field itself. OpenAI calls the collaboration a "first step," with plenty of " difficult questions ahead about how AI can support mathematical understanding and how the benefits of these capabilities can reach the wider community."

OpenAI keeps control over the pace of research

OpenAI says the group will operate independently. Members can offer advice without being asked, speak publicly about the company's influence on mathematics, and publish their recommendations. OpenAI doesn't pay them, and they can decide who joins the group.

But the group is not allowed to control on how fast OpenAI moves. "Importantly, the group will not be responsible for advising us on how to pace our internal progress on mathematics," the company writes. The group gets a say in how results are shared, not whether or how fast they're produced.

Gowers joins the group but won't sign the letter

One of the group's founding members is Timothy Gowers, the prominent mathematician and Fields Medalist. He didn't sign the open letter from the 25 Fields Medalists and laid out his reasoning on his blog.

Gowers agrees with much of the letter and thinks mathematics is in trouble. Where he parts ways is on what math is actually for. The letter treats conceptual understanding as the main goal, with problem-solving just a means to get there. Gowers sees a spectrum: "At one end of the spectrum you have mathematicians who are primarily motivated by the wish to solve problems, who see conceptual understanding as a very important means to that end. At the other you have mathematicians who are primarily motivated by the wish to attain conceptual understanding, who see problem-solving as a very important means to that end."

His own research project on automated theorem proving at Cambridge lost its reason for existing once large language models (LLMs) got good enough, Gower says. "To put it another way, we have had to swallow the bitter lesson (which of course we were always aware was a distinct possibility, even if the speed at which it happened has taken us by surprise)."

The real risk is that nobody will want to become a mathematician

What worries Gowers most is that the social structures holding mathematical knowledge together could collapse, he says. People who might once have pursued a Ph.D. and become "custodians of the mathematical tradition" may simply decide it's not worth it anymore.

"Speaking for myself, my main motivation for becoming a mathematician was the dream that I would solve unsolved problems — the more famous the better." Take away that dream, and it's not clear what fills the gap.

There's also the funding question. Policymakers could look at AI-powered math and decide human mathematicians are redundant. "We urgently need to come up with good ways of explaining the value of having a large pool of human mathematical experts, even if it is no longer part of their role to find new proofs of theorems," Gowers writes.

He also didn't sign the letter because he couldn't figure out what it was asking for that wasn't already happening. LLMs that can tackle major math problems will be publicly available within months, he expects. "So I felt that there was nothing to be gained from criticizing AI companies for generating too many solutions too quickly."

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