OpenAI Navier-Stokes solution

This is an OpenAI research announcement, published September 8, 2026, of a claimed solution to the Navier–Stokes existence and smoothness problem, one of the Clay Millennium Prize Problems. OpenAI says an internal model, described as significantly more capable than GPT-6 Astra, produced an analytical proof and a Lean formalization. The result shows that an initially smooth fluid at rest, driven by a smooth force with finite energy, can develop a singularity in finite time. OpenAI states this establishes statements "C" and "D" of the official Millennium Prize formulation.\n\nThe described solution is a vortex that spirals inward and elongates while its central region shrinks and speeds up, keeping energy finite. OpenAI says the work used a system of coordinating agents with tools such as a cached copy of the internet and code execution. The Navier–Stokes group involved on the order of 10,000 concurrent agents. The same effort reportedly resolved the unforced Euler regularity question, using nearly 100 agents over about 50 hours. YouTube coverage describes the Navier–Stokes run as about 88 hours and notes that the unforced Navier–Stokes problem remains open.\n\nThis is not a product or model that users can access. It is a published writeup and formal proof, and the underlying model is internal and still in training. The claim is OpenAI's own. This entry does not report independent verification or Clay Institute acceptance.