OpenAI claims an internal model solved more than 100 long-standing mathematics problems after training for just one month.
The company announced the figure while introducing an independent advisory group at the Institute for Advanced Study to oversee how results are shared with researchers and the public. The group includes Fields Medalist Timothy Gowers. OpenAI has explicitly excluded the pace of its research from the advisory group’s remit.
The speed of the breakthrough
Training began on August 28. The entire run lasted about a month. Even OpenAI’s own mathematicians were surprised by how quickly things moved. 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. The model also claimed the Navier-Stokes Millennium Problem. The published Navier-Stokes solution has already sparked heated debate in parts of the scientific community.
Which problems the model actually solved, how it solved them, and what the results mean for math and science remain open questions.
A pivot in strategy
Chief Scientist Jakub Pachocki recently said the team had deliberately chosen not to optimise for math. They were 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. 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.
Understanding versus output
Mathematicians are warning that AI-generated solutions could undermine conceptual understanding. In an open letter titled “A Severe Misalignment of AI in Mathematics”, they argue against measuring AI performance by how many open problems it can solve. Churning out solutions, they say, undermines the whole point of mathematics and ultimately threatens human intellect.
OpenAI says it is now working with mathematicians who formed the Advisory Group on Mathematics and Artificial Intelligence. The group is meant to connect the company with the math community and the broader public. 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.
Control over the timeline
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 does not pay them, and they can decide who joins the group.
But the group is not allowed to control 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 are produced.
Gowers joins but does not sign
Timothy Gowers did not sign the open letter from the 25 Fields Medalists. He 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 existence once large language models got good enough. “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),” Gowers says.
The risk to the profession
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 is 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 is not clear what fills the gap.
There is 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 did not sign the letter because he could not figure out what it was asking for that was not 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.”
