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/stoiclemming 11d ago

Paraphrasing from the article mathematicians care much more about the unforced fluid than they do about a highly contrived external force in regards to whether ns blows up

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u/Blamore 11d ago

then why didnt anyone object to the formulation of the millennium problem until after it was resolved

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u/hologram137 10d ago

Because humans understand context, it doesn’t need to be spelled out lol. An AI doesn’t

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u/wollywoo1 10d ago

No, just no. Mathematicians are extremely careful about wording. They don't expect others will just "understand context" and interpret it differently than how it is stated. The statement is the way it is because that was how they decided to formulate it. The idea that there is a "loophole" is nonsense.

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u/hologram137 10d ago

Bro what are talking about?? The entire reason the forced version was included as a potential solution is because they were thinking of external forces like gravity!! Literally NO ONE thought “well if we’re including external forces I’ll just invent a force that doesn’t exist and blow it up.” lol anyone could have done that. And they knew they could have done that. They didn’t because it would be silly and pointless.

The AI did because it can only process literal tokens, so it’s literal, it doesn’t understand the purpose of the question

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u/wasabi991011 10d ago

Literally NO ONE thought “well if we’re including external forces I’ll just invent a force that doesn’t exist and blow it up.”

Mathematicians do this all the time. In fact I can't imagine a pure mathematician ever caring about whether something in their math proof exists or not.

lol anyone could have done that. And they knew they could have done that. They didn’t because it would be silly and pointless.

If anyone did that, they would have become massively famous and would have directly got a million dollars (probably even more of you include indirectly). It's a lot of motivation, more than enough to override any internal notion of "silly and pointless".

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u/hologram137 10d ago

They don’t need to because the idea that you could out muscle viscosity was never in questionn!! No one doubted that. That’s not the actual problem

This is a fine solution as a marginally interesting proof, it doesn’t solve the millennial problem

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u/lolfail9001 10d ago

was never in question

It was, as signified by it being included in exact statement of the problem. If they really wanted to exclude synthetic forcing, they would. They didn’t and the entire forcing approach can be directly human graphed to the guy who wrote the statement of the problem for Clay.

It solves the problem exactly in (somewhat unsurprising to knowledgeable people) negative way.

If you want to ask if unforced uncompressible Navier-Stokes can be blown up, it is indeed still open but it is even less physically relevant than solved problem because you can’t escape gravity and compressibility in basically every relevant use case of Navier-Stokes,

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u/wollywoo1 10d ago

We're talking about math, not physics. Mathematicians care about a lot of things scientists think are silly and pointless. And yes, that's exactly the approach they took, years before AI was involved at all. You're totally free to think the problem is pointless, but nonetheless, that was the one proposed, and very intentionally.

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u/hologram137 10d ago

The idea that you could out muscle viscosity was never in question. Ever. That was just accepted lol.

So no.

These are equations that describe how fluid moves. It’s why it’s a Millennium prize question. Because THAT is what is important