Comment by jonlong
5 hours ago
No, OpenAI did not solve the "wrong" Navier-Stokes problem. OpenAI did not solve the hardest version of the problem (unforced blow-up), but did give a solution to the Clay Millennium Prize Problem as written and understood, choosing the explicitly allowed forced option.
SciAm writes "in a sense, the LLM found and exploited a loophole in the framing of the question". This is pure sensationalism. Choosing option (C) (out of an explicit list of four options) is neither a "loophole" nor something "found by the LLM"; everyone involved knew this was the option they were pursuing.
With the grumbling out the way, there is some actual scientific content to the article: there's a strong argument that OpenAI's method will not extend to the unforced case, leaving our understanding of NS incomplete. This negative result is itself new and interesting (and predicated entirely on the solution found by OpenAI)!
As I understand it the "loophole", if you want to call it that, is that OpenAI's custom-designed forcing function was smooth, as the rules said it had to be, but was non-analytic, consisting of some construction of "compactly supported bump functions", meaning a mass of tiny little pushes at precise points of space and time to push a vortex into blowing up the math.
Reminds me of Maxwell's Demon.
Or a better framing: Clay Institute chose the wrong Navier-Stokes problem for a Millennium Prize.
> SciAm writes "in a sense, the LLM found and exploited a loophole in the framing of the question".
God, it’s embarrassing to read stuff like this. They’re making it seem as if everyone involved was either stupid or dishonest just so they can pretend they have a scoop here.
There's a big market in journalism to take down the popular thing in the news. "Everyone is wrong" and here is my article where I wildly exaggerates some minor details to justify the headline which made you click on the article.
Totally agree. I wouldn't quite call it clickbait, but the article does this thing I find annoying where it puts the "sensationalist" framing at the beginning (the "loophole" quote you put), but then closer to the end fully admits that it wasn't really a loophole in any case:
> It did, however, unambiguously solve the problem according to the Clay Institute’s original formulation. The official problem statement, penned in 2000 by mathematician Charles Fefferman, offers an option called “C,” in which solutions are allowed to use an external force like OpenAI’s.