Tony Padilla walks Brady Haran through the Navier-Stokes equations using a stirred cup of tea. He explains velocity, pressure, viscosity and forcing, then describes how nonlinear growth can compete with the smoothing effect of viscosity.
Tony Padilla distinguishes several formulations of the smoothness problem before outlining the reported AI constructionAI-assisted scientific discovery uses AI to support hypothesis generation, experiment design, analysis, simulation, literature work, and interpretation while researchers retain responsibility.. A rapidly evolving vortex core must be connected to a quiet exterior while respecting smooth-force conditions; the explanation emphasizes scaling and carefully arranged oscillations rather than a simple numerical simulation.
Tony Padilla places the claim alongside earlier work on weak solutions, modified equations and the inviscid Euler equations. The closing discussion raises research-credit questions, but this account does not establish the disputed allegations or imply that a Millennium Prize has been awarded.
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