OpenAI and mathematicians clash over credit for Navier-Stokes solution

The Clay Mathematics Institute offers a million dollars to whoever solves one of the seven Millennium Prize problems, the hardest mathematical questions in the world. Among them are the equations describing the behavior of fluids, known as the Navier-Stokes equations, unsolved for more than two centuries. In recent hours, two mathematicians say they have reached a possible solution, partly with the help of artificial intelligence models, and the news has triggered a public dispute with OpenAI.

In the eighteenth century, Leonhard Euler formulated the first equation describing the motion of an ideal fluid, without viscosity. In 1822, the French engineer Claude-Louis Navier introduced viscosity into the model, to calculate how different fluids, from water to honey, behave when subjected to different forces and resistances. The English mathematician George Gabriel Stokes later systematized these equations. Since then, a complete proof for the real, three-dimensional case has been missing: describing every possible behavior of a fluid remains an open problem.

Tristan Buckmeister, a mathematician at New York University, and Levent Alpöge, a mathematician and member of Anthropic's technical staff, have announced a result obtained in a personal capacity, outside their respective jobs. According to Buckmeister, the work had progressed with difficulty for a year before receiving a decisive boost between August 15 and 22 thanks to the use of artificial intelligence models. The two say they proved a blow up, that is, a sudden breakdown in the behavior of a fluid subjected to a regular, continuous force, within a defined time interval: beyond that point, the velocity grows to infinity and mathematics can no longer describe it. The result will still need to be verified under the strict Lean scientific protocol.

The clash with OpenAI

To reach this result, Buckmeister says he used both Anthropic's Claude and several OpenAI models, including Codex and the most advanced versions of GPT, described as the closest yet to general artificial intelligence. Hence the controversy: OpenAI announced that it had produced the proof of the blow up in a short time, with a hundred-page document, describing the two mathematicians' human contribution as minimal and its own models' behavior as largely autonomous.

Buckmeister counters that an entire team at the company instead spent a year analyzing the data he and Alpöge had uploaded to Codex, without ever clarifying whether it was also being used to train the models. The mathematician also denounces pressure to remove Alpöge from the results because he is employed by rival Anthropic: requests he calls "irritating," to which he says he was told, among other things, «Vuoi rovinarti la carriera?» (Do you want to ruin your career?). The phone exchange with Sebastien Bubeck, an OpenAI researcher, was particularly tense: according to Buckmeister, Bubeck insisted on Alpöge's removal, going so far as to tell him: «Se non vuoi che sia gentile, allora vuol dire che non devo esserlo» (If you don't want me to be nice, then I don't have to be).

Buckmeister compares the episode to 1997, when the computer Deep Blue beat chess champion Garry Kasparov, and says he was forced to publish incomplete documentation to avoid being overtaken by OpenAI. The dispute raises a broader question: what role human researchers still play when artificial intelligence contributes decisively to scientific discoveries.