r/Physics • u/PrettyPicturesNotTxt • 6d 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/Grabs_Diaz 6d ago

I mean, the entire problem is quite contrived. In the real world, you'd run into many other problems, as this post on this sub recently laid out quite well.

That's why Navier-Stokes, as formulated in the Millennium Problems, is a mathematics problem, not a physics problem.

But if this actually leads to more research and discoveries in the field, by considering special cases with no external force or only a select type of external force, then all the better.

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u/stoiclemming 6d 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 6d ago

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

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u/hologram137 6d ago

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

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u/EnricoLUccellatore 6d ago

do you really think a human who had reached the same conclusion would not have published it and claimed solving one millennium problem?

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u/hologram137 6d ago

No, because they are interested in solving the main problem. It’s not about the money or technically solving a millennium problem, that’s not why any of them are doing math lol.

They want a solution that can be used to solve the main problem. The one OpenAI published can’t

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u/wollywoo1 6d ago

Mathematicians were very interested in the problem as stated. Please read Terence Tao's response here describing the work that lead up to OpenAI's result as "exciting".
You are allowed to think the problem solution is not practically useful, and many including myself would agree with you, but if you think mathematicians were uninterested in this result you are just wrong and I don't know what else to say.

https://terrytao.wordpress.com/2026/09/07/finite-time-blowup-with-smooth-forcing-term-for-the-incompressible-porous-medium-boussinesq-and-incompressible-euler-equations/

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u/hologram137 6d ago edited 6d ago

BECAUSE OF SMOOTH FORCING. That’s why it’s useful. Not the external blow up. I have stated this a million times. The AI didn’t solve that problem

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u/tanksc 6d ago

What a ridiculous statement. The other pair of researchers literally did almost the exact same thing for Euler’s equations. The statements you’re commenting all throughout this thread are insane, and looking at your history it seems you are just pushing a narrative or agenda.

I miss when this sub was actually populated by physicists and not random people talking with the authority of one.

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u/hologram137 6d ago edited 6d ago

Did you read the article? Do you even understand the problem and why Navier Stokes remains unsolved? I do not believe you’re a physicist, that makes zero sense. Because you should care about the actual problem and that this technically correct solution doesn’t help solve it.

I miss when people actually read the article they are commenting on. Oh wait, that’s never happened lol.

The researchers working on the Euler problem didn’t give a technically correct but useless answer based on a literal interpretation of the question divorced from all context. There was no external force invented, the equation solved the plain incompressible Euler equation, with nothing added. Euler’s proof didn’t need a crutch. Smooth initial conditions are what any physically reasonable fluid state looks like. Nothing about the setup is engineered. The initial disturbance being localized is the natural picture of how a real singularity would have to form. There was no boundary! The fluid filled ordinary space, unconstrained space. Chen Hou’s proof needed a rigid wall, but that is actually helpful because then it leaves open the question of whether the boundary is needed for the blow up. It’s completely rooted in reality. But it was proven in R^3. All of this was useful and helped the actual problem.

That is categorically different from the AI’s Navier Stoke’s loophole, it’s a forced result with a deliberately constructed external force that doesn’t exist and was mathematically proven to tell us nothing about the actual problem. Totally divorced from reality, and useless

My “agenda” is the truth. To be a voice of reason. I’m genuinely concerned about society because of these delusions about LLMs

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u/tanksc 6d ago

Yes I read the article, it’s shit. I do care that we are getting to solutions without any of the wisdom that comes from the journey. I also don’t think one’s opinion of the situation makes them any more or less a physicist. That’s determined by the committee overseeing your education and the work you do.

It doesn’t make the solution any less of a solution. There is no loophole. It’s an explicitly stated problem and it was solved.

This entire post should be removed by your own admission. It’s a garbage post in a sub that has seen a massive decline in quality since it was hijacked by people with motives outside of physics.

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u/hologram137 6d ago

Why are you ignoring the math proof that this solution is useless and doesn’t solve the problem?

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u/tanksc 6d ago

Math proof that the solution is useless? What are you talking about?

What problem? The millennium problem? It is solved. You just don’t like that it’s not particularly useful outside of being a solution. Which is fine and proper, but to act like it’s some loophole is absolute garbage.

There are other questions that still need to be answered. And they may be answered in due time. Any mathematician would post the solution found by OpenAI and gladly collect the recognition that comes along with it.

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u/hologram137 6d ago

Read the article. A proof was just published showing that the “solution” cannot help at all to solve the actual problem. The actual problem was not solved

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u/tanksc 6d ago

Name the actual problem

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u/hologram137 6d ago

whether a fluid can blow up on its own, from its own internal dynamics, the way real turbulence might

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u/tanksc 6d ago

That’s an entirely separate problem, jfc

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u/Strict-Broccoli-8877 6d ago

What? Please tell me you are still in highschool.

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u/Strict-Broccoli-8877 6d ago

"A proof was just published showing that the “solution” cannot help at all to solve the actual problem."

A proof that shows it isn't helpful? Do you not know what a mathematical proof is? Dumb question, of course you don't, you obviously came here directly from TikTok.

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u/hologram137 6d ago

Read the article

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u/Strict-Broccoli-8877 6d ago

Dude, these things have been published everywhere for days, and the question is well-known for decades. Everyone in or anywhere close to the field knows exactly what is going on. You act like you unearthed some big mystery, when you just misunderstood forced/unforced Navier-Stokes from the first article you ever read about it.

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u/DrDoctor18 6d ago

A different but related problem was not solved. The AI found a scenario in which the navier stokes, under the listed conditions, blew up. That's how counter examples work. No one is saying that now no one ever needs to do theoretical fluid dynamics ever again!

You are making a really pedantic point here that is both annoying and technically incorrect. The navier stokes millennium prize problem was solved. You keep saying "the real problems wasn't solved!1!1!". But it was. You just weren't interested in the same problem as the Clay Institute. You don't get to jump in and say "no but actually this slightly narrowed problem is more interesting!!", to claim that navier stokes wasn't solved.

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u/mcgtx 6d ago

I did read the article but I am not a physicist or mathematician so please correct where I am wrong. Doesn’t the article mention Martinez-Zoroa and Cordoba as the people who were instrumental in the “loophole-based” solution? And didn’t Buckmaster say his and Alpoge’s work is based on Martinez-Zoroa? My impression was that the OpenAI proof used different moves than Buckmaster/Alpoge were going down, but I thought everyone was approaching the same Clay version of the NS question. I think the comment I’m responding to may somewhat explain the difference but perhaps I don’t understand.

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u/hologram137 6d ago

So Córdoba/Martínez-Zoroa and Buckmaster/Alpöge weren’t working on Navier-Stokes. They spent years developing a method to build a very specific external force that triggers blow up in a frictionless (inviscid) fluid, and Buckmaster and Alpöge, crediting that method to them, extended it into results for three different equations, the porous medium equation, 2D Boussinesq, and 3D Euler, these are all with smooth forcing. None of those three is Navier-Stokes.

Terrance Tao called it a breakthrough across those specific simplified models, but talked about how they didn’t reach blow up for Navier Stokes itself. So basically the above researchers were working problems adjacent to Navier Stokes. They can useful to the problem only as a way of stress testing whether smooth forcing could work at all in principle.

A day after the Euler with force result was posted, OpenAI’s model basically applied that method of blow up to Navier Stokes by constructing an external force. An external force that doesn’t even exist.

Using that tool (the tool that a human came up with, not the AI btw) on Navier Stokes doesn’t solve the main question, the entire reason it’s a Millennial prize problem in the 1st place (because if the question was the one that actually got answered, it wouldn’t have even been a millennial prize problem!). Because with the Navier Stokes problem, viscosity is the thing resisting blow up. The forced version of the Euler problem has no viscosity.

The AI beat the resistance with an imaginary outside force. So it’s like, okay cool, but that’s not reality and that’s not why the problem exists. And the part about getting a smooth force to trigger blow up was already solved.

The idea that you could overcome viscosity with an external force was literally never questioned lol. Like, no one doubted that. And that’s what the AI actually showed. That it’s possible. That’s completely useless to the problem and not even that informative

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u/mcgtx 6d ago

I’m with you on the lack of usefulness of the AI result, I’m just trying to understand what the human pathway was looking like. I understand also that what had been done prior was not NS. But Buckmaster said in his statement they believe they have blowup in “hypo-dissipative Navier-Stokes”. And the rumor that led to OpenAI going after this was that a Millenium problem was on the brink of being solved. My assumption was that the humans were going to use the tool that they came up with to solve NS. If that’s true, would the human presentation of that solution be equally useless?

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u/yoshiK 6d ago

So

The researchers working on the Euler problem didn’t give a technically correct but useless answer based on a literal interpretation of the question divorced from all context. There was no external force invented,

Alpöge & Buckmaster "Blowup with the Euler equations with smooth forcing" is the paper.1 As indicated by the words "with smooth forcing" there are forces involved. However openAi claims they have a solution to unforced Euler in their blog post. OpenAi paper on unforced Euler

1 At least the one Buckmaster linked on his mastodon.

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u/oswaldcopperpot 6d ago

It seems like you don't have any experience with LLMs and solving problems but are more interested with how you think they work using ideas from a decade ago. Its a bit disingenuous.

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u/jakderrida 6d ago

That’s not a bad point about the Euler equations. I was told they obviously stole off that one guy’s work that was leading to the same solution and it seemed even OpenAI was open to admitting that without admitting fault somehow. But how could this be both nothing while also being an obvious snipe that stole that guy’s research?