Károly Zsolnai-Fehér presents OpenAI's announced solution to the Navier-Stokes existence and smoothness problem. The episode treats the result as a major and unusually checkable AI research claim, but it also raises questions about attribution, training-data provenance and what independent mathematical acceptance still requires.
Károly Zsolnai-Fehér explains the equations through advection, pressure, diffusion, external forces and incompressibility. The Millennium Prize problem asks whether smooth three-dimensional fluid motion must remain mathematically well behaved or whether a singularity can develop in finite time.
The claimed construction begins with fluid at rest and applies a smooth external force to create an inward-spiraling, stretching vortex. Its velocity becomes unbounded in finite time while total energy remains finite. The episode explicitly describes this as a mathematical construction rather than a known event in a natural fluid.
The episode reports that the AI search took about three and a half days and argues that mathematics is especially suitable for AI systems because candidate work can be checked automatically at scale. Károly Zsolnai-Fehér closes by connecting rapidly improving capability with a need for stronger coordination on AI safety and alignment.
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