Comment by bmacho

14 hours ago

Article says that there are 2 formulations of the NS problem and both are interesting: one is about fluid behaviour with no external forces, other is about fluid behaviour with external forces.

For a counter-example the latter is easier since you can have a tricky external forcefield.

3 comments

bmacho

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HarHarVeryFunny  2 hours ago

Right - OpenAI proved the forced blow-up case rather than the harder unforced one, with the Millenium Prize problem statement saying it would be awarded for either one.

The forced version is easier since you can custom design the force function to get the result (it doesn't have to be a realistic force like stirring), so getting the blow-up might be regarded just as much a function of your bespoke force function as of the fluid dynamics itself, which is apparently what OpenAI did, pushing the definition of the force function being "smooth" to it's limit.

So, it appears OpenAI did legitimately meet the Millenium Prize solution criteria, but in the most unrealistic, and therefore least interesting, way possible.

  • adriand  1 hour ago

    My friend, who is a mathematician, sent this in our group chat:

    The title is a bit misleading. The variant with a smooth forcing was one of the four valid variants in the Clay formulation. It is interesting to solve it. It is still an interesting and impressive result. The no force version is also interesting and remains unsolved. It isn’t reasonable to just dismiss the proof on the grounds that 26 years later we claim it was never that interesting. This is the first time I’ve seen this attitude.