OpenAI announced on Tuesday that its artificial intelligence model had solved a Millennium Prize Problem, a famously difficult mathematical challenge that has remained unsolved for nearly a century. The company stated that its AI, named Astra, proved the Navier-Stokes existence and smoothness problem in 88 hours. This problem, one of seven designated by the Clay Mathematics Institute, carries a $1 million prize for a correct solution.
However, Tristan Buckmaster, a mathematics professor at New York University, has come forward with allegations against OpenAI. Buckmaster claims that scientists from OpenAI attempted to pressure him into a joint announcement of the solution, asserting that they had independently solved the problem. He also alleges that OpenAI may have leveraged his own research, which he had been conducting with Levent Alpöge, a researcher at OpenAI rival Anthropic, on a related fluid dynamics equation.
Buckmaster questioned the timing of OpenAI's claimed discovery, noting it occurred only after the company became aware of his work. He stated that when he asked OpenAI representatives whether their AI systems had access to his research, they declined to answer, leading him to question the speed of their advance.
According to Buckmaster, an OpenAI scientist named Sébastien Bubeck allegedly threatened his career, asking, "Why would you want to ruin your career?" and adding, "If you don't want me to be nice, then I don't have to be nice." Buckmaster described this interaction as ominous.
Bubeck later addressed the alleged threat on X, stating his intention was to warn Buckmaster against making "unfounded claims." He acknowledged that his word choice was a "poor choice of words."
In its announcement, OpenAI insisted that no user data was incorporated into its model to solve the problem, though it noted it "cannot rule out" that anonymized data might have been used to "improve our models." The company extended congratulations to Alpöge and Buckmaster for their mathematical work. Buckmaster responded by questioning the ethics of using customer data to potentially "scoop their customer."
The Navier-Stokes problem concerns whether smooth, three-dimensional fluid flows can always maintain smooth behavior or if they can develop singularities with infinite velocity. Of the seven Millennium Prize Problems established in 2000, only the Poincaré conjecture, solved by Grigori Perelman between 2002 and 2003, has been officially verified and awarded.