09-18-2026, 04:43 PM
In this Numberphile video, Tony discusses the Navier-Stokes equations—the famous fluid dynamics formulas that describe how liquids and gases move—and the recent developments surrounding their associated $1 million Millennium Prize. He explains the physical and mathematical challenges of the equations, noting the delicate push-and-pull between the nonlinear term that attempts to drive infinite spikes or "blow-ups" and the viscosity term that tries to smooth them out.
The conversation highlights how researchers built upon historical breakthroughs by figures like Leray and Terence Tao to understand vortex behaviors, leading up to recent claims that AI systems managed to solve the problem. Tony concludes by exploring the controversial backdrop of how these AI-driven solutions intersected with ongoing human academic work and the broader philosophical questions this raises for the future of mathematical research.
LECTURE
The conversation highlights how researchers built upon historical breakthroughs by figures like Leray and Terence Tao to understand vortex behaviors, leading up to recent claims that AI systems managed to solve the problem. Tony concludes by exploring the controversial backdrop of how these AI-driven solutions intersected with ongoing human academic work and the broader philosophical questions this raises for the future of mathematical research.
LECTURE
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