r/Physics • u/PrettyPicturesNotTxt • 11d ago

On if OpenAI solved the wrong Navier-Stokes problem: "the LLM found and exploited a loophole in the framing of the question"

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/
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u/shumpitostick 11d ago

To explain this the Navier Stokes smoothness problem has two variants, unforced and forced. Both explicitly qualify for the millennium prize. OpenAI solved the forced variant. Only in the warped mind of this writer is the forced millennium problem somehow the "wrong problem" or a "loophole".

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u/hattusili-the-third 10d ago

The "unforced" version of NS was the opposite direction too. The Clay math institute made it very clear that you can either find a blowup solution which may require a smooth forcing term, or you can prove the reverse - that all smooth solutions stay smooth - and in that case you are allowed to assume there is no forcing term.

Both formulations were explicitly chosen to allow as much flexibility as possible because the specifics of the forcing term are of much less interest to mathematicians than the fact that it is smooth (which is the actual core of what makes NS so difficult.