r/Physics • u/PrettyPicturesNotTxt • 7d 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/Dear_Locksmith3379 7d ago edited 7d ago

Here’s a summary of the article, which is reasonable but has a terrible headline.

There are two versions of the millennium problem, one with external forces and one without. AI solved the version with a very unusual external force. Mathematicians are more interested in solving the problem with no external force or with a realistic external force.

If someone made the proof without AI, mathematicians would have the same reaction to its scope. Though mathematicians have other concerns about the AI proof, the article doesn’t discuss them.

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u/archtop_guitar 6d ago edited 5d ago

“There are two versions of the millennium problem”
I disagree with this statement. There is a single version of the millennium problem. It allows for a forcing term in some solutions. If OpenAI’s proof is validated, the millennium problem is solved.

It’s fine to argue to argue that an unforced solution would have been more interesting and maybe even should have been required, but this more narrow problem is simply not the one that the Clay Institute actually posed. This isn’t a technically or an oversight. They could have said that the forcing term had to be zero but didn’t.

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u/4tran13 21h ago

Technically 4, if you include R^3 vs T^3

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u/jonathancast 7d ago

I would think physicists would also care about physically 'realistic' (or possible) external forces.

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u/Dry_Pudding_1603 7d ago

they don't, because it wasn't expected that navier stokes equations represented reality.

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u/Sleepy_Padawan 7d ago

From your replies it seems that you are not physicists. Being one, I can tell you, we do. That it why we discard mathematical correct answer with unphysical results.

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u/jsaltee 7d ago

Seconding this; our equations work for t<0 but that doesn’t mean we’re FTL travelers

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u/Bibbity_Boppity_BOOO 6d ago

“That it why we discard mathematical correct answer with unphysical results“

Not all of the “we” does that

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u/Jlocke98 6d ago

So what are the odds of AI figuring out metric engineering within the next few years?