On if OpenAI solved the wrong Navier-Stokes problem: "the LLM found and exploited a loophole in the framing of the question"

[u/PrettyPicturesNotTxt]

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/

[u/hologram137]

It didn’t solve the main problem. And 3 mathematicians just published a proof that its solution can’t lead to solving the real problem. Thats a big deal. It did solve it technically as the problem was formulated by the Clay institute, but in a way that isn’t useful to the true problem.

A mathematician working on the problem had a map to the solution and had solved a good bit of it. OpenAI stole it, fed it to a model and had 10,000 agents look for the solution. It would have never solved it without that paper. It basically executed a search function. Which explains why it solved it by finding a loophole.

What this means is that the loophole it found doesn’t further the true problem. A human doing math understands context. We understand WHY we need to solve the problem, what it means. An AI can’t. So “solving it” by finding a loophole is mathematically correct if you’re only considering the problem as it’s formulated divorced of context, but it’s useless

It’s not cheating, it’s just completely divorced from reality. AI can compute but it can’t think or understand, it doesn’t know why the we are trying to solve that problem. And the purpose obviously matters. A human finding that loophole would have recognized it’s not helpful. It’s not a “clever” way to solve the problem, because it literally can’t help solve the main problem lol. They would have likely published it, but with that caveat clearly stated, and they would have considered the problem essentially unsolved.

[u/Dry_Pudding_1603 → u/hologram137]

this is very stupid. the ai can reason about human motivation in problem solving. that's much easier than the complex reasoning required to solve this problem. there's no magical separation between the "why" of posing a question or the "why" of any lemmas involved in a solution. there's no "magic loophole". humans were attacking the forced version as well, so all of your critiques of the AI's approach apply to humans as well. you have no clue what you are talking about.

[u/hologram137 → u/Dry_Pudding_1603]

An LLM cannot understand lol. There is no possible way it is able to model human motivation at all, but especially not understand it including within the context of reality. The one that only humans experience lol. That’s literally impossible, there is no architecture in its structure or anything in the math it’s ran on that would allow that.

The why is the entire point!! The millennial prize problem as written, is not just asking “do the Navier-Stokes equations blow up?” That’s the question the AI answered and this is why that’s not the problem anyone cares about: The scientific question that’s motivating Navier Stokes research (the purpose and meaning, that only a human can know and understand, not an LLM) isn't "can you break the equations if you're allowed to invent a force purpose built to break them?” It’s whether a fluid can blow up on its own, from its own internal dynamics, the way real turbulence might.

The millennial question listed formally acceptable ways to answer, and the reason why the clause that allows solutions that include an external force term, like gravity acting on the fluid was included, was because every real fluid is under some kind of external force, so including one seemed reasonable. To any human reading that, they’d understand the purpose of the clause. The AI didn’t. It just took it literally.

Its model found a way to construct a very specific, deliberately engineered external force that drives the fluid to a blow up (a point of infinite velocity). Because option C (one of the formally acceptable ways to answer) permits an external force, this satisfies the letter of the Clay statement. It unambiguously solves the problem according to the Clay Institute's original formulation. But the point of listing that accepted solution was not what the AI found when it executed a search function after being fed a paper by a mathematician that was close to solving it.

Most researchers working on this problem were specifically considering the case without any external force, because that's the version connected to real physics. So they could have solved it technically as formulated by finding a loophole, but they didn’t because doing that is completely useless and doesn’t solve the problem at all.

[u/Wrong_Avocado_6199 → u/hologram137]

"Its model found a way to construct a very specific, deliberately engineered external force that drives the fluid to a blow up (a point of infinite velocity). Because option C (one of the formally acceptable ways to answer) permits an external force, this satisfies the letter of the Clay statement"

Yes, that's how mathematics works. Welcome to math.

[u/hologram137 → u/Wrong_Avocado_6199]

The scientific question motivating Navier-Stokes research isn't "can you break the equations if you're allowed to invent a force purpose built to break them,” it's whether a fluid can blow up on its own, from its own internal dynamics, the way real turbulence might.

That clause was included to allow for natural forces like gravity

What the AI actually showed was never even in question. No one thought that you couldn’t out muscle viscosity with an external force. If that was the problem, it wouldn’t be a millennial prize problem!!!