OpenAI’s sly mathematical breakthrough sends a chill

What happened

OpenAI’s announcement Tuesday that it has solved one of mathematics’ legendary Millennium Prize problems should have been a moment of triumph. The result is both an undeniable achievement and a striking demonstration of just how rapidly AI is transforming mathematics.

“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 OpenAI researchers on 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 and incredibly 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. ” The company does not appear to have expended much effort on tackling Navier-Stokes before September, or if it has, it hasn’t spoken about it publicly.

” 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 briefing reported on by Science. “So we thought to ourselves: ‘We have such a strong model. ’” Bubeck said. OpenAI said it only later realized the rumors concerned Alpöge and Buckmaster.

Why it matters

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 researchers were making progress, it seems to have thrown its considerable resources into a last-minute effort to beat them to the punch.

The ensuing controversy has surfaced allegations of scooping, spying, and flagrant violations of long-standing academic norms that researchers fear could have a chilling effect on the field. ” In a 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. ” But the timing of the announcement has raised eyebrows.

Just one day earlier, New York University mathematics professor Tristan Buckmaster published findings on a related problem with Levent Alpöge, a researcher at OpenAI’s archrival Anthropic (although Alpöge was not, here, working on behalf of his employer). Buckmaster said he contacted OpenAI after learning the company had become aware of their progress, to ask when it began working on the problem and what data its model had been trained on.

” when he said he would go public with what happened. ” OpenAI urged Buckmaster to instead publish the work and credit OpenAI’s internal model, dropping Alpöge as coauthor. 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 particular, no specific user data was accessed in order to solve this problem,” the company said. But OpenAI could not conclusively rule out an indirect influence.

What to watch

Beyond addressing Buckmaster’s allegations about the use of his data, OpenAI has not publicly responded to his other claims and directed The Verge to its blog when asked for comment. Bubeck, who Buckmaster named in his account, has disputed parts 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.