Science

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1/6 Some of you may know that I’m a sucker for fringe science, of which the Clay Institute’s Millenium Prize Problems are the gold standard when it comes to mathematics.

One of these open problems is the Navier-Stokes (NS) existence and smoothness problem.

Aviator, diver, Etherean, nexialist, PhD in aviation and climate science, host of /diving /ethfinance /forteantimes /geopolitics /science /singapore /thomas

2/6 NS are partial differential equations that describe the flow velocity of every point in a viscous fluid. They are ubiquitous anywhere something flows: weather and oceanic forecasts, car and wing design, behavior of liquids in a pipe, etc.

5/6 The idea is to use machine learning (specifically, neural networks) at hyperscale to explore the NS search space.

The team is pursuing two avenues: a constructive proof (showing that the NS equations always return well-behaved/smooth solutions) and a counterexample proof (finding a single singularity).

4/6 And yet this is exactly what Spanish mathematician Javier Gómez Serrano has been working on in collaboration with Google’s DeepMind for the last three years. The effort has only recently been made public.

3/6 We just don’t know whether those equations have solutions for every point, and whether they always remain bounded or can blow up to infinity. Proving either way is worth a $1M prize from the Clay Institute.

(It’s an understatement to say that there are easier ways to earn $1M.)