Navier-Stokes solved? What OpenAI's proof shows and why it's disputed
On September 8, 2026, OpenAI published a proof that the Navier-Stokes equations can blow up: a smooth 3D fluid, pushed by a smooth force, can reach infinite velocity in finite time. That would settle a Clay Millennium Prize problem open for about 90 years, and an internal model found it as roughly 10,000 agents running for 88 hours. Twelve hours earlier, an NYU professor had posted a statement…
On September 8, 2026, OpenAI announced a proof of the Navier-Stokes equations, a mathematical problem that had remained unsolved for nearly 90 years. The Navier-Stokes equations describe the motion of fluids, and the proof settled two statements of the Clay Millennium Prize problem. The problem is whether a smooth three-dimensional fluid will always remain smooth or if it can develop a singularity, where the velocity becomes infinite in a finite amount of time.
OpenAI claimed that an internal model, significantly more capable than GPT-6 Astra, produced the proof and a Lean formalization. The proof involved running a model with around 10,000 concurrent agents, utilizing 2.7 million messages and generating approximately 130 billion output tokens, costing roughly $6.5 million at GPT-6 Astra list prices.
A related story involved NYU professor Tristan Buckmaster and Anthropic researcher Levent Alpöge, who had been working on the problem for a year and reached Euler blow-up using Claude and Codex on August 15.
Buckmaster later claimed that OpenAI's first prompt came after they shared information about his work, and OpenAI's model produced a disproof of smoothness, which Buckmaster disputes. The details of the process and the extent of OpenAI's involvement in the proof are disputed, with Buckmaster alleging that OpenAI had a team working on the problem while he and Alpöge were putting in the bulk of the effort.
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