On September 8, 2026, mathematicians at OpenAI announced that a group of 10,000 autonomous AI agents, running on an advanced model not available to the public, had found a 'singularity' in the Navier-Stokes equations in three dimensions, thus resolving one of the six remaining Millennium Prize Problems posed in 2000 by the Clay Mathematics Institute, each of which carries a $1 million prize. The model used is significantly more capable than GPT-6 Astra, and the agents arrived at their resolution on September 5, about 88 hours after the first agents were launched, with Lean formalization and verification taking an additional 17 hours via GPT-6 Astra. The agents exchanged about 2.7 million messages and generated roughly 130 billion output tokens on Navier-Stokes alone; across all attempted problems, the larger project involved 4.9 million messages and about 300 billion output tokens. The proposed counterexample resembles a spinning top that tightens to a singularity with diverging velocities.
The announcement arrived entwined in a priority dispute that has shaken the mathematics community. Approximately 12 hours before OpenAI's announcement, NYU mathematician Tristan Buckmaster alleged that his and Levent Alpoge's recent advances on Euler equations had been leaked to OpenAI days earlier and may have inspired OpenAI's prompts for the agents in the process that led to the solution. Buckmaster and Alpoge, who is a mathematician and an employee of Anthropic, had blown up the Euler equations the night before the OpenAI announcement, a result widely seen by the field as a step toward solving the Navier-Stokes problem. The interpersonal dimension proved inflammatory: Buckmaster alleges that OpenAI mathematician Sebastien Bubeck asked him to remove Alpoge's credit as part of a proposed compromise, and that when Buckmaster pushed to make the dispute public, Bubeck replied, "Why would you ruin your career?" and then, "If you don't want me to be nice, then I don't have to be nice." Bubeck subsequently posted a public reply directly apologizing for that specific language.
OpenAI's formal response drew a categorical line on the data question while acknowledging a residual uncertainty. OpenAI said its AI agents did not access the researchers' work through any means before it was released publicly, though the company said it could not rule out that de-identified data from their use of OpenAI products may have contributed to model training. Bubeck said OpenAI's internal model had independently solved the Euler problem by totally different means than those employed by Buckmaster and Alpoge, though OpenAI's solution to the full Navier-Stokes problem did follow a similar method as that used by the two mathematicians. The 165-page paper, titled 'Finite Time Blowup for Navier-Stokes' and authored as 'OpenAI,' states the formal result as Theorem 1.1: for every positive viscosity, there exist a smooth, compactly-supported force and smooth velocity and pressure fields on three-dimensional space starting from zero velocity such that the kinetic energy stays uniformly bounded while the velocity's sup-norm becomes unbounded in finite time.
The mathematical community's response has been admiring but pointedly conditional. Timothy Gowers, a Fields Medal recipient who said he had not yet read the proof, told the Wall Street Journal that the result was 'undeniably a big moment.' The result has been formally checked in Lean, giving mathematicians confidence it is correct, though if it holds up to further scrutiny it is, by a significant margin, the most important mathematical proof to have been arrived at by an AI model to date. Skeptics note the distinction between machine-checkable and community-accepted: as of September 2026, the Clay Mathematics Institute currently considers the problem 'active.' OpenAI has said it does not intend to claim the Millennium Prize for the result. On a call with reporters, OpenAI executives put the cost of solving the problem in the 'millions of dollars.'
Whatever the Clay Institute ultimately rules, the dispute over credit and data provenance has already made clear that the norms governing human-AI mathematical collaboration were not ready for the speed at which the collaboration is now running.