The big drama in AI land today is decidedly nerdy stuff.
But the hubbub highlights a concern everyone should care about: Can what you type into AI help train a machine that one day beats you at your own game?
On Monday, Tristan Buckmaster, an NYU mathematician, and Levent Alpöge, a mathematician who works at Anthropic, released papers claiming new results related to a famously thorny scientific question: Can the math used to predict the movement of water and air suddenly hit a breaking point?
Solving that problem could lead to a $1 million prize from the Clay Mathematics Institute. While the pair didn’t claim to have achieved that particular breakthrough, Terence Tao, a well-known mathematician, called the work “remarkable” in a Mastodon post.
But it was the four-page statement that Buckmaster published alongside the findings, which included some explosive allegations involving OpenAI, that captured people’s attention. He alleged that OpenAI learned of the pair’s findings — and told him an internal AI model had made progress on solving the $1 million question.
On Tuesday, OpenAI formally claimed it had achieved a solution to the Navier-Stokes Millennium Prize Problem — “one of the deepest problems at the frontier of mathematics.”
Buckmaster — who said that he and Alpöge used AI models from OpenAI and Anthropic to assist in their research — said he does not know whether OpenAI used the pair’s data or chats. OpenAI said “no specific user data was accessed in order to solve this problem,” but said it couldn’t rule out that “de-identified data derived from their usage of our products helped improve our models.”
The episode has set off a dispute over scientific credit, AI training data, and the paper trail behind an AI-assisted discovery. Scientific American said the drama has set up the “biggest day in math in at least two decades.”
What is Buckmaster alleging about OpenAI?
Buckmaster and Alpöge concluded that they found examples where today’s math doesn’t accurately describe smooth air and water flows. They used several AI models, including Claude and Codex, throughout their work.
Buckmaster said that after he told an OpenAI mathematician that he and Alpöge planned to post their work, OpenAI staff, including computer scientist Sebastian Bubeck, told him that their internal model had produced a proof of the Navier-Stokes question (the one that carried the $1 million prize).
Basically, Buckmaster and Alpöge were publishing work that could pave the way to achieving that bigger breakthrough. OpenAI, according to Buckmaster, signaled on the call that it had achieved that bigger breakthrough.
He also said he was offered possible publication arrangements and that OpenAI’s Bubeck wanted Alpöge removed as an author because he works at the company’s rival, Anthropic.
“I have not seen OpenAI’s proof,” Buckmaster wrote. “I do not know whether our data was used. I am not accusing anyone of anything. I am stating what I was told, when, and what was proposed to me. I am stating it because the alternative is to let a sequence of announcements say something I know to be false.”
On Tuesday, OpenAI’s Bubeck pushed back on some of the spiciest elements of Buckmaster’s statement in a post on X, denying he had “ever asked Levent to be removed from authorship of his own work.” He said he tried to “coordinate our releases” of the mathematical announcements, and that OpenAI was motivated to try to solve the problem after “viral Twitter rumors that Anthropic had resolved 2 Millenium problems.”
That followed an earlier post in which he said that “false and inflammatory allegations” against him were circulating.
The dispute has roiled the online math and AI communities. Sholto Douglas, a member of Anthropic’s technical staff, said it was “extremely sad.” Others highlighted the most explosive allegations in the press releases or posted a rundown of the drama.
Questions of scientific credit when AI is used
There are a lot of complexities within this math saga, especially around who gets recognition for what.
Buckmaster credits mathematicians Diego Cordoba and Luis Martinez-Zoroa for helping establish the pair’s underlying approach with their 2024 study. From there, Buckmaster said his work with Alpöge used LLMs to advance their findings.
That account raises new questions about how, or if, researchers should share credit with AI labs — especially if their models are trained on other breakthroughs from leading mathematicians.
It also poses another tricky dilemma: What should AI companies do with the data entered by their customers — and are they using it to compete directly against mathematicians and scientists?
OpenAI, Anthropic, Buckmaster, and Alpöge didn’t respond to requests for comment from Business Insider.
What do OpenAI’s terms say?
Buckmaster said OpenAI wasn’t clear with him on whether its AI models had been trained on the pair’s work. But OpenAI’s policies make it clear that is allowed.
OpenAI’s terms of service state that the company trains on data submitted by its users unless they opt out.
“When you share your content with us, it helps our models become more accurate and better at solving your specific problems and it also helps improve their general capabilities and safety,” the company wrote in a March post.
Users can opt out via the company’s privacy portal by selecting “do not train on my content.”
Buckmaster’s statement said he paid for the tools himself, but it does not identify the particular product, account type, or whether the pair opted out.
OpenAI claims big math breakthrough
OpenAI formally addressed the situation on Tuesday afternoon while announcing that it had solved the Navier-Stokes problem.
The company separately congratulated Buckmaster and Alpöge on their related work, but said that neither its in-house researchers nor its AI agents saw the pair’s work “through any means” until its public release. “No specific user data was accessed in order to solve this problem,” the company said.
But, addressing Buckmaster’s question about AI training data, the company said it was possible the AI models had learned from the pair’s inputs.
“While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models,” OpenAI said. “However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs. unforced).”
The latest from OpenAI suggests the drama is far from over.
The saga is a good reminder that AI companies are constantly working to improve their models — and, unless you explicitly opt out or have an enterprise account that stipulates as much, that includes what you type into them.
