OpenAI Says It Has Made ‘Substantial Progress’ on a Second Millennium Prize Problem

Days after claiming a solution to the Navier-Stokes problem, OpenAI told The New York Times it has made “substantial progress” on a second Millennium Prize Problem, Decrypt reported. The company didn’t say which of the Clay Mathematics Institute’s $1 million problems it means or when it might share results.

Online speculation has settled on the Hodge Conjecture, a 1950 problem about how to count the “holes” in high-dimensional geometric shapes, but OpenAI hasn’t confirmed it. It also hasn’t confirmed rumors that the unreleased model behind the work is a version called “Aeon.”

The Navier-Stokes claim

On Sept. 8, OpenAI said an unreleased internal model produced a Lean-verified proof that the Navier-Stokes equations, which describe how fluids move, can “blow up” into a physically impossible infinite speed. The work took roughly 10,000 coordinating AI agents about 88 hours. The Clay Mathematics Institute’s review of the proof is still pending. OpenAI says it isn’t seeking the prize money and is using the problems as a public yardstick for how fast its models are improving.

Mathematician Tristan Buckmaster called it “a Deep Blue–Kasparov moment” in a statement quoted by Scientific American, adding: “The community needs to have serious and unhurried discussion about where to go from here.”

A credit dispute

Buckmaster, of NYU, also alleged that he and Levent Alpöge, a mathematician who works at Anthropic, had made significant progress on the problem before rumors of their method reached OpenAI. He says OpenAI researchers then used the company’s model to finish the job, with a prompt that “had been sent in the past few days, after information about our work had reached OpenAI.” OpenAI denied the allegations at a press conference, according to Scientific American. In a four-page statement summarized by Decrypt, Buckmaster also alleged that OpenAI’s Sébastien Bubeck pressured him over publication timing. That dispute remains unresolved.

The same week, Anthropic said Claude formalized the proof of Fermat’s Last Theorem in 11 days, and mathematician Terence Tao warned that labs racing each other are using up math’s supply of hard, useful problems faster than new ones can be found, Decrypt noted.