In the past 24 hours, Silicon Valley has erupted in bitter debate over what may seem from the outside to be an esoteric, trivial issue: the solution to a longstanding math problem which, despite its importance among academics, doesn’t have any clear practical applications. And yet it raises urgent new questions about the nature of competition—not only between humans, but also between humans and machines—in the age of AI.
On Tuesday morning, OpenAI published a blog post claiming it had used an unreleased AI model “significantly more capable than GPT-6 Astra” to solve the Navier-Stokes existence and smoothness problem, which is related to the physics of water and other fluids. It’s one of seven “Millennium Problems” laid out by the Clay Mathematics Institute in the year 2000, each of which offers a $1 million prize for the first correct solution. OpenAI wrote in its blog post that it doesn’t intend to accept the prize for its result, which it said was discovered by human researchers collaborating with around 10,000 AI agents working for a little under ninety hours.
The company’s announcement has largely been overshadowed by controversy around how its result was reached. OpenAI said in its blog post that its work on the Navier-Stokes problem started Tuesday of last week, “after hearing a rumour” that two independent mathematicians, Tristan Buckmaster and Levent Alpöge, had achieved a breakthrough in another area, called forced Euler, related to Navier-Stokes. The company says it then reached out to the duo “to offer a concurrent release of our result and to recognize their priority in a joint announcement.”
The previous evening, Buckmaster, a mathematics professor at NYU, published a statement confirming he and Alpöge had been contacted by OpenAI after the company learned of their work on forced Euler, but that the company had played hardball to make sure it wasn’t scooped. Buckmaster said that he first learned about OpenAI’s approach during a Friday call with OpenAI researcher Sébastien Bubeck, which he said sounded suspiciously familiar to the approach he and Alpöge had taken with forced Euler, for which they had used multiple AI models, including OpenAI’s Codex and Anthropic’s Claude. (Alpöge was not on the call.) Buckmaster says he asked Bubeck if the model OpenAI had used to solve the problem had access to his and Alpöge’s Codex logs. “I was told the model did not look up user data,” Buckmaster wrote. “I asked again, about training, and I did not get an answer.”
OpenAI wrote in its blog post that neither its researchers nor its AI agents saw the two researchers’ work before it was published, but also that it “cannot rule out that de-identified data derived from their usage of our products helped improve our models.”
Buckmaster claims Bubeck offered him two potential paths forward to ensure he shared the credit with OpenAI for the pathway that led to the Navier-Stokes solution, both of which involved completely removing Alpöge’s name from the solution; Alpöge has been employed with Anthropic, OpenAI’s biggest competitor, since 2024. Buckmaster says he declined both offers and told Bubeck that if OpenAI opted to move forward with its announcement, he would publish an account of the conversation. According to Buckmaster, Bubeck replied: “Why would you ruin your career?”
In a reply posted Tuesday on X, Bubeck said he “could not consider Levent to be an independent academic” after he learned that Anthropic’s AI models had been used as part of his work with Buckmaster. He also apologized for the threatening-sounding question he posed to Buckmaster, calling it an “extremely poor choice of words” and “the opposite of what I was trying to convey.”
A new era for competition
Historically, the formalizing of a new mathematical proof—even one that doesn’t have any obvious practical application—was a cause for celebration. Science is a collaborative enterprise, and friendly competition is a vital engine for fresh discoveries. There has, of course, been controversy and infighting over the matter of who reached a breakthrough first. But at the end of the day, it was humans bickering among one another, all operating within human limits.
Until now.
With the Navier-Stokes solution controversy, we’ve entered a strange new era of scientific competition: one where humans compete not only with one another, but also with deep-pocketed tech companies wielding powerful AI models, hell-bent on being the first to tout major technical breakthroughs, and operating under the assumption that anything published on the open internet—and perhaps shared with their proprietary AI tools—is fair game.
Money isn’t the issue here. Even if OpenAI were to accept the Millennium Prize for its Navier-Stokes solution, it has no need for the $1 million reward. The computing power required by the agents working on the problem cost millions of dollars, according to OpenAI researcher Noam Brown. “[OpenAI] didn’t do this for the bounty,” one X user wrote on Tuesday. “They needed a headline that says ‘our AI solved one of the hardest problems in mathematics’ and they needed it before someone else got credit.”
Terence Tao, a Fields Medal recipient who’s widely regarded as the greatest living mathematician, had a similar response to the controversy. If humanity’s collective endeavor to understand the universe—which relies not only on friendly competition, but on the free and open exchange of ideas—is subsumed by competition between jealous and power-hungry tech titans, the total store of shared human knowledge is doomed to shrink, rather than expand, contrary to what the AI companies themselves have promised over and over again their technology would deliver.
“We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential,” Tao wrote in a Tuesday post on Mastodon, responding to the Navier-Stokes controversy. “The incentives may now be pointing in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science and do serious long-term damage to the future of the field.”