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 provenanceData provenance records where information came from, how it changed, and which people, systems, or processes handled it. 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 alignmentAlignment is the effort to make an AI system pursue intended goals and follow relevant human values, instructions, and constraints..
Watch on YouTube
