OpenAI’s announcement Tuesday that it has solved one of mathematics’ legendaryMillennium Prize problemsshould have been a moment of triumph. The result is both an undeniable achievement and a striking demonstration of just howrapidly AI is transforming mathematics. But before it was even formally announced, the breakthrough had been complicated by the unusual circumstances that prompted OpenAI to pursue the problem: After hearing other researcher…
As Abhishek Saha, a mathematics professor at Queen Mary University of London, explains it, OpenAI has engaged in the “kind of things that mathematicians will generally not do.”
Ina blog post published Tuesday, OpenAI said it took one of its unreleased models just 88 hours to find a solution to the Navier-Stokes problem, a thorny quandary concerning the movement of fluids. On account of the $1 million bounty available for whoever solves it, the problem is among mathematics’ most heavily researched, but it has nevertheless stumped human researchers for close to 90 years. OpenAI said its model solved the problem by focusin…
But the timing of the announcement has raised eyebrows. Just one day earlier, New York University mathematics professor Tristan Buckmasterpublished findingson a related problem with Levent Alpöge, a researcher at OpenAI’s archrival Anthropic (although Alpöge was not, here, working on behalf of his employer). Buckmastersaidhe contacted OpenAI after learning the company had become aware of their progress, to ask when it began working on the problem…
Buckmaster said he asked OpenAI whether it had accessed his sessions on Codex, which he had used while tackling the problem, but that OpenAI grew increasingly evasive, even hostile, in its responses. In statements since, including the blog post announcing the result, OpenAI has flatly denied using any specific user data. “We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in parti…
But OpenAI could not conclusively rule out an indirect influence. “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models,” it said, while stressing that the two proofs differ significantly. Comments from OpenAIresearcherson X echo those denials.
It is difficult to say exactly what happened. Timelines are tangled, research overlaps, and the provenance of AI-generated work is tough, if not impossible, to identify at the best of times. And it’s hardly a surprise that different players might compete to solve one of the most famous mathematical problems in the world, particularly one attached to a hefty prize.
But aspects of OpenAI’s account are hard to explain. By the company’s own telling, the effort was a hurried andincredibly expensive affair, costing it millions of dollars. Yet the company says it has no intention of claiming the bounty, which, in any case, has yet to be awarded by the Clay Mathematics Institute, which administers it. It said its only goal “is to report on the substantial progress of our AI models.” The company does not appear to …
OpenAI’s explanation effectively amounts to a thunderous “Why not?” The company said it began working on the problem after hearing rumors that other researchers were making progress on Millennium Prize problems. It found those rumors “on Twitter,” said OpenAI researcher Sébastien Bubeck at a press briefingreportedon byScience.“So we thought to ourselves: ‘We have such a strong model. Why don’t we try to solve also a Millennium Prize problem?’” Bu…
OpenAI said it only later realized the rumors concerned Alpöge and Buckmaster. Beyond addressing Buckmaster’s allegations about the use of his data, OpenAI has not publicly responded to his other claims and directedThe Vergeto its blog when asked for comment. Bubeck, who Buckmaster named in his account, hasdisputedparts of it, denying he ever asked Buckmaster to remove Alpöge as coauthor.
Even setting aside the most explosive allegations, aspects of OpenAI’s conduct the company has plainly acknowledged have shocked mathematicians. The apparent rush to beat other researchers to a result is simply not how mathematics is done in most cases. Scooping does happen, but it’s not easy, said Saha.
That’s partly because cutting-edge research often requires such deep and specialized expertise that few people are in a position to swoop in even if they wanted to, he explained.
Openness is a deeply embedded virtue in the discipline. “Mathematics depends heavily on an informal norm of trust,” said Matthew Ballard, a professor of mathematics at the University of South Carolina and associate director for scientific activities at the Institute for Computer-Aided Reasoning in Mathematics (ICARM). “Researchers routinely share incomplete ideas and ongoing work with colleagues to sharpen their thoughts. It is done with the expe…
Though unable to comment on whether conversation logs might have been accessed, Carnegie Mellon professor Jeremy Avigad, who is also the director of ICARM, said that even “the thought that AI systems might steal ideas from our queries is chilling.” Mathematicians are accustomed to talking about their work without worrying about being scooped. “Now that even the slightest hint might be enough for someone with sufficient computational resources to …
OpenAI’s unwillingness or inability to say whether its models were informed by the work of other mathematicians compounds the sense of unease in the field. “That is a problem,” Brown University professor Brendan Hassett toldThe Verge,adding that “given the history of the AI companies appropriating copyrighted work without permission or payment, it is natural for people to ask these questions.” He said companies “should be held accountable to deli…
It’s unclear where exactly things go from here. Writing from a conference in Beijing, Yang-Hui He, a fellow at the London Institute for Mathematical Sciences, said he worries that “maths under the big companies is much too secretive.” As someone who says he is “always optimistic about AI,” he admits he is worried mathematics could be reverting to a more secretive state like in the past, when it was funded by patronage from wealthy families like t…
For most researchers, things may not change that much. There are only so many high-caliber problems companies like OpenAI and its rivals would be willing to spend such vast sums solving, Saha speculated. “You would not expect the AI labs to throw everything at most problems people work on because they just won’t get enough publicity.”
Publicity may have been part of the point, which could help explain why OpenAI decided to race after a problem it knew was connected to a researcher at Anthropic, even if he was acting independently. “This is clearly a PR victory for OpenAI,” said Oxford professor Andras Juhasz.
But Juhasz questioned how sustainable that approach could be, wondering whether this might spell the beginning of the end for AI companies’ involvement in research mathematics now that models can tackle some of the biggest problems. Human mathematicians scoop one another, too, he said, though what OpenAI did has shown that this can happen on a much grander scale. “Suddenly, 10,000 mathematicians jump on your problem,” he said.
All that could make OpenAI’s PR victory a Pyrrhic one. The company has,once again, proven that its models can competeat the very frontier of mathematics. In doing so, it appears to have alienated the very community it has been trying to impress.