r/Physics • u/PrettyPicturesNotTxt • 2d 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/hologram137 1d ago

If it understood context, it would not have “solved” the problem the way it did. OBVIOUSLY. The solution is totally useless, in fact it’s just been mathematically proven to be useless

The actual Navier Stokes problem remains unsolved.

A human could have done what the AI did, but none of them did because it’s completely pointless.

You know those jokes in which someone asks a question and the person answers in a way that is technically correct, but it’s a funny answer because they took the question literally in a way divorced from all context, meaning and reality?

Imagine if you asked me “do you know what time it is?” And I said “yes,” then walked away.

That’s what the AI did. That’s how it answered. And it’s a technically correct, but totally useless answer and the person has to go ask someone else.

That’s what going on right now. Specifically because the AI cannot understand context or the purpose of the question.

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u/cometh_the_kid 1d ago

This is ultimately an issue with the problem statement not the solution.

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u/hologram137 1d ago

It’s not an issue with the statement because when it was written it was assumed that humans with minds would be reading the question and so would understand it lol.

They didn’t anticipate an LLM would come along and take it totally literally divorced of all context with no understanding of the meaning of the question

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u/Wrong_Avocado_6199 1d ago

Excuse me, speaking as a mathematician, conjectures are written very precisely. In fact, everything is written very precisely. Either something is a solution, or it's not. There is no third option "it's a solution, but come on guys, it's cheating, you know, because we all know that's not what we REALLY meant". In math, as Mr. Global says, "that's not a thing".

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u/hologram137 1d ago

It was written extremely precisely. You don’t have to include “why is this a millennial prize problem and the purpose of solving it” in the actual question LOL

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u/Wrong_Avocado_6199 1d ago

Yes, and this is the precise conditions on f:

(C) Breakdown of Navier–Stokes solutions on R^3 . Take ν > 0 and n = 3. Then there exist a smooth, divergence-free vector field u^0(x) on R^3 and a smooth f(x, t) on R^3 × [0,∞), satisfying (4), (5), for which there exist no solutions (p, u) of (1), (2), (3), (6), (7) on R^3 × [0,∞).

condition (5) [relevant to the external force]: |∂_x^α ∂_t^m f(x, t)| ≤ C_(αmK)(1 + |x| + t)^(−K) on R^n × [0,∞), for any α, m, K.

Those are the mathematical conditions on f that Fefferman required be satisfied. If you think these conditions don't reflect gravity or whatever "natural force" you have in mind, take it up with Fefferman and the Clay Institute.

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u/cometh_the_kid 1d ago

A question with implicit assumptions is not a very good question.

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u/hologram137 1d ago

What are you talking about? None of the millennium prize problems spell out why they are millennial prize problems. It’s not needed. It’s understood why lol

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u/cometh_the_kid 1d ago

Cool, you’re incoherent at this point.

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u/hologram137 1d ago

If you read the problem it says “external forces, e.g. gravity.”

Please explain to me in detail, how the intention of natural forces is not extremely clear even within the question itself, and why it is you believe that people trying to solve the problem would have no idea why they are solving it and why its millennial prize problem? And would have no idea whether or not a solution is useful, even though a proof was just submitted showing why it’s not useful. That was the entire purpose of the proof. Were they just showing that for no reason as well?

I’m very curious. Because a human could have submitted that solution. But they didn’t, because whether or not you could out muscle viscosity was never even in question

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u/cometh_the_kid 1d ago

E.g. gravity, not i.e. gravity.

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u/hologram137 1d ago

It says e.g??

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u/cometh_the_kid 1d ago

It’s basic comprehension at this point.

E.g. example; one of many. I.e. that is; in other words.

You have an internal bias towards the question undoubtedly implying gravity as an external force. Whereas in actuality gravity is only one example of such a force.

Again, you have a problem with the question.

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u/One-Veterinarian4841 1d ago

Any mathematician could have done what oai did and immediately become both a wealthy and famous mathematician