On the Navier–Stokes Millennium Prize Problem
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OpenAI claims its AI solved the Navier-Stokes Millennium Prize Problem.
OpenAI shares a solution to the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize Problems, produced by an internal AI system. The proof shows that three-dimensional fluid motion can develop a singularity in finite time, with a Lean formalization provided. The solution describes a vortex that spirals inward and stretches, keeping energy finite as velocity grows unbounded. The effort used about 10,000 concurrent agents, 2.7 million messages, and roughly 130 billion output tokens over 88 hours. OpenAI states it does not intend to claim the Millennium Prize for this result.
What commenters are saying
Commenters split on whether this is a genuine breakthrough or a costly brute-force PR stunt. Many question the cost (estimated $15 million at public API pricing) and note the proof required massive compute rather than human insight. A significant thread centers on allegations that OpenAI's work derived from the research of mathematicians Levent Alpöge and Tristan Buckmaster, which OpenAI addresses in the article. Some commenters argue the solution offers no explanatory value despite being technically correct, while a few defend the achievement as unprecedented AI capability.