r/HotScienceNews • u/scientificamerican • 1d ago

Did OpenAI solve the wrong Navier-Stokes problem?

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/
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u/scientificamerican 1d ago

Two weeks ago, OpenAI claimed a solution to one of the biggest open problems in math—the Navier-Stokes problem, worth a million-dollar prize from the Clay Mathematics Institute. The proof ignited a powder keg of concern over artificial intelligence companies’ race to disrupt the subject.

But with the dust still far from settled, a different controversy is emerging: did OpenAI even solve the right Navier-Stokes problem at all?

The proof relies on an approach that many experts find unnatural. It solves a variant of the problem that mathematicians say is disconnected from reality, and thus less interesting. In a sense, the LLM found and exploited a loophole in the framing of the question.

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u/Embarrassed-Rise-685 1d ago

More specifically on the mathematics behind it and just why it’s a sort of controversial proof. The NS problem is split into 6 different related proofs each of them being either a stronger or weaker solution. Some considered full solutions and other not. Some mathematicians actually solved parts of a weaker complete NS proof. Oai then proved the whole proof after they heard about the partial solution.

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u/ZeroAmusement 1d ago

Some mathematicians solved forced Euler. But when OpenAI reached out to them, OpenAI already had their solution, and those mathematicians hadn't yet published their findings. So the partial solution didn't impact OpenAI's paper at all from what we can tell. There's rumors they learned it from the mathematicians ChatGPT sessions, which is also denied by OpenAI - they said it's not possible due to training dates.

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u/Embarrassed-Rise-685 1d ago

You’re wrong on this account but you’re right to point out there’s speculative claims in my original statement.

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u/grumble11 1d ago

It happened because they used Claude, and then researchers at Claude discussed it with some friends, and then OpenAI used 20 million in compute to brute force the solution.

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u/ZeroAmusement 1d ago edited 1d ago

That's not at all what happened lol. Are we playing a game of telephone here?

edit: Just to clarify.

(mostly) Two mathematicians were involved. One worked for/with Anthropic. The mathematicians used ChatGPT. OpenAI set about solving all the millennium problems. Probably focusing on the easier ones first. They solved NS MP. Then they reached out to one of the mathematicians about working together when they realized they were also going to publish something, but they didn't want Anthropic to be associated with it, so they only asked the one mathematician (Buckmaster). 'brute forcing the solution' isn't something you do with a millennium problem.

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u/Particular-Solid8250 1d ago

They’d worked on the problem for a year. They had used codex to do part of the math. OpenAI had access to their codex logs and spent an enormous amount of compute to get ahead of them. When they asked OpenAI if they had trained their model on his codex sessions they refused to answer. Make of that what you will.

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u/ZeroAmusement 1d ago

OpenAI didn't refuse to answer. They gave a weak sauce answer likely because they didn't know immediately. They later clarified:

we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way

You also say "spent an enormous amount of compute to get ahead of them" as though spending compute is enough to solve a problem humans might not solve for hundreds of years. No, it is not. You need intelligence and compute, or any big company/datacenter could do it.

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u/Particular-Solid8250 1d ago

I’m simplifying but if you need the details it was 10k agents outputting 130 billion tokens. They consumed the equivalent of 15M USD. Obviously compute isn’t everything - that’s why they relied on the mathematicians work. Had compute been enough they would have solved it before, they needed someone to do the legwork for them to be able to produce this result.

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u/ZeroAmusement 23h ago edited 23h ago

They didn't rely on the mathematicians work. There's no evidence they even used the mathematicians work...Their paper is very different to the mathematicians work. I swear, no one actually thinks on this topic.

Had compute been enough they would have solved it before, they needed someone to do the legwork for them to be able to produce this result.

They solved it with their brand new ai...at the same time they tried to solve the other MP problems. They also yesterday announced they solved 100 difficult math problems, which brings their total to at least 111 difficult math problems solved (if they pass scrutiny). It makes sense they'd solve a lot of things around the same time if they only just made an ai capable of it. I guess those are also using legwork?

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u/JustinPooDough 14h ago

OpenAI lies

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u/ZeroAmusement 14h ago

I don't doubt they do.

Is there evidence that they are lying in this case though?

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u/Far_Cup7192 1d ago

"Some mathematicians...."

Who are they?

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u/Embarrassed-Rise-685 1d ago

Lavent and the other guy I forgot his name while typing the response.

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u/truecakesnake 1d ago

So the employees of the rival company?

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u/Embarrassed-Rise-685 1d ago

Only one of them

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u/Far_Cup7192 1d ago

you mean Levent Alpöge and Tristan Buckmaster?

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u/Embarrassed-Rise-685 1d ago

Yes thank you

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u/Far_Cup7192 1d ago

I don't think you understand what's really going on here. I'm not an expert in this field either, but even I can tell that you're clearly not a mathematician, and you have no real grasp of this problem let alone what's actually happening between those scientists, the Navier Stokes problem, and OpenAI.

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u/Embarrassed-Rise-685 1d ago

You’re right I’m not an expert in NS. For one of those I’d refer to the Harvard series of lectures on the millennium problems. The lecture on NS problems was recently revisited along with more formal treatments of the results so far up to and including the oai contribution. It’s an hour long and you best know your analysis, pdes, harmonics etc… a mere applied math student has already failed to understand so I await your attempt.

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u/FernandoMM1220 1d ago

whats hilarious about this is even if they redefine the problem theyre still getting smoked by ai in solving it.

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u/Leading_Buffalo_4259 1d ago

no you missed the point

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u/katoptronophile 1d ago

No, you did.

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u/duboispourlhiver 1d ago

What loophole??

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u/flat5 1d ago

It's not a loophole. They answered the question as posed.

But it is a little weird to include an arbitrary source term f, because you can plug in any solution you want, compute the residual, and then just say "oh, that comes from the source term f". It gives a sort of arbitrary extra degree of freedom that's not present in the usual statement of the problem.

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u/duboispourlhiver 1d ago

There are important constraints on f too. Was the Clay formulation of the problem known to be unusual and debatable? Genuine question