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.

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.

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.

It's just moving the goalposts, this happens every time an AI solves a problem, doesn't matter if the goalposts were there for 26 years.

What's interesting is that there are a set of people who are "in charge" and can as they wish arbitrarily set the goalposts to the thing that they happen to be best at. While this might be satisfying for an Humanity vs AI narrative, it's concerning for an us vs them one. Are these people really special? or do they just change the rules of the game so that outsiders (human or AI) can't win.

If it was you or I that solved this problem our would our rewards stop at $1M? Or would we get authority? If the achievement earns that for an insider but becomes 'just a solved problem' when an outsider does it, what exactly is being rewarded?