OpenAI reports significant progress on a second Millennium Prize problem, following its controversial claim of solving the Navier-Stokes existence and smoothness problem. The company has not officially named the new target, though speculation points to the Hodge Conjecture.
On September 9-10, 2026, OpenAI announced a solution to the Navier-Stokes problem using 10,000 AI agents. The process involved generating a 166-page paper and formal verification code in Lean over 88 hours. The Clay Mathematics Institute is currently reviewing the submission.
The initial announcement triggered significant backlash from the academic community. More than 1,000 mathematicians signed an open letter criticizing the methodology, while 25 Fields medalists issued a statement regarding ethical concerns. OpenAI subsequently withdrew its sponsorship of a Caltech math hackathon.
The Clay Mathematics Institute established the seven Millennium Prize problems in 2000, each offering a $1 million reward. Historically, verification of such proofs takes years; for instance, Grigori Perelman’s proof of the Poincare Conjecture required roughly four years of review before official recognition in 2010.
