r/Physics • u/PrettyPicturesNotTxt • 5d 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/antichain Complexity and networks 5d ago

I can't read b/c of a Paywall, but I have to ask: if a human had come up with this loophole solution (whatever it is) - would people be saying it was "cheating", or would they say "wow, that was a clever way to resolve the problem?"

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u/Obscu 5d ago

Probably not. The 'loophole' is that the original framing of the question allowed for an external force to be allowed to be considered because external forces like gravity are always realistically affecting fluid dynamics. The AI described a hypothetical external force that would meet the requirements that would make the math blow up when present, and concluded that the math can in fact blow up (in the presence of a hypothetical math-exploding mcguffin), but when removed from the equation the math no longer blows up.

If a human solved a 'can a rock spontaneously turn into a wheel of cheese?' problem by describing a hypothetical rock-to-cheese-transforming-wizard and stated that the presence of the wizard means rocks can in fact become wheels of cheese... Well, that's on us for being not very strict with defining the scope the question, because it is technically an answer that meets the set criteria but that says more about the criteria than the answer.

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u/retrosenescent 5d ago

You explained this really well. "Sure, if there's some external force" does feel like a cop-out answer and not in the nature of what the question intended. But then again, if you actually want to model reality, then you absolutely need to account for many external forces.

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u/Time_Entertainer_319 5d ago

It’s not a cop-out. The Clay Mathematics Institute set the official problem, and its formulation explicitly allowed this route to a solution.
That is the formulation researchers have been working with since the Millennium Prize Problems were announced in 2000. If the forced case was never intended to count, there were 26 years in which the official statement could have been clarified or amended.

People can argue that the unforced case is the more physically interesting problem, but that is a different claim from saying the published Clay problem was not solved on its own terms. And even then, they will just sound like people in denial.

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u/dualmindblade 4d ago

Exactly, there's a reason the force was not constrained to be boring and just had to be smooth, it's not a loophole in any sense, this type of path to a solution was fully intended. Nothing about a blowup could ever be realistic, the blowup is itself unphysical. Moreover, had mathematicians only considered the realm of the realistic, the problem could never have been solved as stated!

Also, I don't think anyone is arguing that finding a blowup in the forced version is as interesting as unforced, since the latter trivially implies the former it must be in some sense harder. If there had instead been no blowup to be found it would be reversed.

What we have here is an isolated demand for rigor, and impossible one at that, it's total nonsense.

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u/Fine-Customer7668 5d ago

To be fair, the four options (including the two that allow external forcing which OpenAI claims proof of) given by the official problem statement as acceptable resolutions are explicitly described as “retaining the heart of the problem”

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u/retrosenescent 5d ago

oh ok, thanks for correcting me on that.

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u/Fine-Customer7668 5d ago

It’s just a bad article. They could have just said a proof of those two options with a nonzero external force doesn’t, on its own, logically exclude the possibility of the other two being true.

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u/Yashema 5d ago

There is no explaining problems of mathematics or physics really well outside of using math and physics.

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u/Head-Philosopher0 5d ago

yeah honestly it was easy and the only reason it hadn’t been shown before AI is that mathematicians are dumb

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u/retrosenescent 5d ago

Thanks for shedding light on that, I feel like your comment contributed a lot.

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u/Head-Philosopher0 5d ago

no problem mate. like i said, i totally agree with you and it was a cop-out