OpenAI says it has solved Navier-Stokes with AI, but the row over credit overshadows the achievement

OpenAI announced that an internal model, described as "significantly more capable than GPT-6 Astra," produced a proof that the three-dimensional Navier-Stokes equations can develop a finite-time singularity, one of the Clay Mathematics Institute's seven Millennium Problems, which carries a one-million-dollar prize. These are equations that describe the motion of fluids and have applications ranging from blood circulation to forecasting weather patterns.

According to the company, the effort began on September 1, after OpenAI researchers heard rumors that two Millennium Problems had already been solved by others, prompting the company to set its new internal model loose on the remaining problems. On a call with reporters, OpenAI executives said they devoted an enormous amount of compute to the task, at a cost in the "millions of dollars" and with roughly 10,000 agents working in parallel. The company itself has said it does not intend to claim the million-dollar prize, presenting the result instead as a demonstration of how fast its most advanced systems are improving.

The problem is the context in which that result emerged. NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had been working for some time on closely related research into fluid dynamics. Buckmaster has publicly questioned whether OpenAI pursued that particular line of research on the basis of information known about their work, and has raised doubts about whether private Codex material may have played a role. He also accused OpenAI researcher Sébastien Bubeck of pushing to strip Alpöge of authorship credit for the result because he works for Anthropic, OpenAI's main competitor. Buckmaster said that when he threatened to make his conversations with Bubeck public, Bubeck replied: "Why would you ruin your career?" (the original English quote cited in the article was "Why would you ruin your career?").

OpenAI has responded to these accusations by saying it did not access Buckmaster's or Alpöge's specific user data while pursuing the proof. The company acknowledged, however, that it cannot completely rule out an indirect connection: "While unlikely, we cannot rule out that de-identified data derived from their use of our products helped improve our models," OpenAI said. The company notes that by default it does not train on its business customers' inputs or outputs, and that users with personal ChatGPT accounts can opt out of having their conversations used for training.

OpenAI CEO Sam Altman himself weighed in on the controversy on X: "Now that we can see their work, the approaches appear to be different," he wrote, while also acknowledging that the company launched the effort after hearing rumors that Anthropic's models had solved a major math problem: "We were curious whether ours could do it too."

The episode raises an uncomfortable question that goes beyond this particular case: what happens when the same company that supplies scientists with AI research tools can also mobilize vastly greater compute resources to compete with them directly on their own lines of work. The dispute goes straight to the question of who owns work done with AI tools, and whether the labs that build those tools are, in effect, competing with their own customers and users.

The case, as the article frames it, is only a first example of a kind of conflict that is likely to recur: disputes over what AI companies know about researchers' and users' work and their use of these tools, and over whether that information — even indirectly or in de-identified form — can end up feeding results with which those same companies compete against the very people using them.