OpenAI's SI agents solve one of the "Millennium Problems" — the $1 million Navier–Stokes problem
Prepared by Sintelligent with the help of SI. Publication time restored from the build log. . Updated: .
For the first time, SI itself has solved a problem that the world's best mathematicians struggled with for almost a hundred years — and the proof has been checked by a machine. Science is entering an era in which the hardest questions are solved by swarms of agents in days, and the argument is no longer about whether SI can, but about who gets there first.
About 10,000 agents of an unpublished OpenAI model proved in 88 hours that the three-dimensional Navier–Stokes equations, which describe fluid flow, can produce singularities under a smooth external force — points where the flow velocity goes to infinity. This closes one of the six remaining Millennium Problems of the Clay Institute, with a $1 million prize. The agents exchanged almost 5 million messages, and the proof was then formally verified in the Lean system in 17 hours, so mathematicians consider it correct. The result builds on the "infinite cascade" method of Diego Córdoba and Luis Martínez-Zoroa. NYU professor Tristan Buckmaster and Anthropic mathematician Levent Alpöge, who had worked for almost a year on a related problem, accused OpenAI of "barging into" their work; OpenAI acknowledges that it started on September 1 after rumors of their breakthrough, but denies having access to their materials. Buckmaster called the event a "Deep Blue–Kasparov moment".