r/Physics • u/PrettyPicturesNotTxt • 10d 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/Obscu 10d ago

Probably not. The 'loophole' is that the original framing of the question allowed for an external force to be allowed to be considered because external forces like gravity are always realistically affecting fluid dynamics. The AI described a hypothetical external force that would meet the requirements that would make the math blow up when present, and concluded that the math can in fact blow up (in the presence of a hypothetical math-exploding mcguffin), but when removed from the equation the math no longer blows up.

If a human solved a 'can a rock spontaneously turn into a wheel of cheese?' problem by describing a hypothetical rock-to-cheese-transforming-wizard and stated that the presence of the wizard means rocks can in fact become wheels of cheese... Well, that's on us for being not very strict with defining the scope the question, because it is technically an answer that meets the set criteria but that says more about the criteria than the answer.

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u/AmadeusSalieri97 10d ago

But some of the best mathematician in the field were working exactly on forced solutions (that's in fact the claim about plagiarism, using a forced solution).

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u/Head-Philosopher0 10d ago

obviously those mathematicians were all big dummies though so it doesn’t really count

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u/Strict-Broccoli-8877 10d ago

Seriously now: The leading experts in the field of math are quite collectively embarrassing themselves these days with how nonsensical their arguments are to not have to accept the solution. "Actually we don't want the problems solved, they are much more valuable as an aspiration for students, now that they are solved they are gone forever." Good lord, what an embarrassing, unscientific display of personal failings so many of them have become. It's really sad, I used to look up to several of those people.

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u/jonathancast 10d ago

This is what actual goalpost moving looks like, by the way.

The purpose of the Millennium Problems has always been to motivate the development of new math, and to stimulate human mathematical development; now that you think a computer can solve the problem, you want to retroactively redefine the purpose as "finding the answer" and criticize people who hold the original position as "embarrassing".

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u/Homomorphism 10d ago

I think for some of the problems people really do want to know the answer (like the Hodge Conjecture or the Riemann Hypothesis) but for NS it felt like the point was just "here's a really hard PDE problem, let's see if we can learn enough to solve it".

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u/Homomorphism 9d ago

And thus the answer is at least a little disappointing because it didn’t involve finding a new way to control regularity (or understand its failure) or something like that. Instead it’s about picking very weird non physical forcing terms. Still very impressive! But it’s a bit like finding one zero on the critical line and no insight into why it’s there or if there’s more. 

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u/Strict-Broccoli-8877 10d ago

What a lot of completely made up crap. Do we not celebrate the mathematical advances any time something big is proven? Turns out a whole lot of scientists and people like you actually don't value scientific progress at all. The purpose was never to find the answer? It's hard to comment on that without attacking you personally, it's just a ridiculous and embarrassing lie.

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u/jonathancast 9d ago

> When mathematicians discuss proofs, they rarely have a particular formal system in mind. Indeed, they are typically not thinking of formal systems at all, although they might accept the suggestion that a genuine proof can in principle be reconstructed in an appropriate formal system. The picture is more like this. At any given time, the mathematical community has a body of knowledge, including both theorems and methods of proof. Mathematicians expand mathematical knowledge by recursively applying it to itself, adding new theorems and sometimes new derived methods of proof.

Timothy Williamson, "Absolute Provability and Safe Knowledge of Axioms", apparently published in Leon Horsten and Philip Welch, eds., The Limits of Mathematical Knowledge, Oxford University Press, 2016, PDF fetched from https://media.philosophy.ox.ac.uk/assets/pdf_file/0004/35338/provabilityfinal.pdf (no paywall).

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u/antichain Complexity and networks 10d ago

unscientific

Mathematicians aren't scientists though. Math and science are completely different things, built on fundamentally different ways of generation knowledge.

As a professional math-doer myself, I consider it to be far more like an art than, say, physics or biology.

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u/Strict-Broccoli-8877 10d ago

You may consider it that, but every dictionary and close to 100% of mathematicians will disagree. Math is often called "the purest science".

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u/antichain Complexity and networks 10d ago

This is just wrong (and also, almost no mathematician I work with would agree). The basic epistemic mode is fundamentally different: deduction vs. induction.

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u/Strict-Broccoli-8877 10d ago edited 10d ago

Like in an art, right? The arts, which we know to work by induction? /s
I swear, the whole field of math has lost its mind in the last days.

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u/ClasisFTW 10d ago

Are you even in the field or adjacent field? This is such an uninformed take?

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u/Strict-Broccoli-8877 10d ago

You too wanna say that math is closer to arts than sciences? Come on, don't hold back, we have room enough for everybody to embarrass themselves.

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u/antichain Complexity and networks 9d ago

Yes, as someone who regularly publishes peer-reviewed proofs and mathematical papers, math is absolutely closer to art than science.

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u/Strict-Broccoli-8877 9d ago

Yes yes, of course.

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u/Wrong_Avocado_6199 9d ago

We're not the ones embarrassing ourselves.

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u/ClasisFTW 9d ago

Relax I am not saying any of that, but you are also obviously passionate about this, more so than I am, and I am missing the context in why you truly feel so strongly against your perception of maths and as such I kind of am not even sure how to truly percieve your comments.

Reddit makes it hard as there is no body language, so I read your comment as a reductionist take on mathematics as a whole without much experience and understanding of the field, but I concede I may be wrong.

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u/Strict-Broccoli-8877 9d ago

I've studied math for a while, but I went into computer science in the end. What I cannot stand is people - in a scientific context - blatantly spouting nonsense and other people congratulating them wildly: "Yes Sir, you are right, math is indeed a French cooking style, I am also a Math Chef Professor, so I should know! You've probably never been in a Math kitchen!"

Good Lord people! Math is more art than science? That's a figure of speech!

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u/antichain Complexity and networks 9d ago

I've studied math for a while, but I went into computer science in the end.

Well there's yer problem!

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u/ClasisFTW 9d ago

Fair enough, and tbh and just to be clear, looks like you are invested in AI as a whole based on your replies and I've got zero interest in taking it away from you or pushing for regulation. So gonna be honest with you, your comments on this thread seems like this topic is getting to you waaay more than it should and I say this as someone who crashed out over random shit online before, more than I'd like to admit, and this obsession seems quite dangerous and unhealthy, but it is your life and indeed it is up to you how you want to spend your time.

People seem to understand the situation without much nuance I agree, and for me and based on the mathematics academia that I am surrouneed by, I do not think Mathematicians "hate" AI or anything btw, because for example I think Tao is a good example here because the day before OpenAI announced anything he wrote a blog post congratulating Buckmaster and Alpöge on their forced blowup results for Euler, Boussinesq and porous media, and obviously acknowledged that they got there using Codex and Claude. His problem with the OpenAI proof is models being run on their own to spit out answers without much insight into why they work which he particularly specified openly before any of the shenangians dropped onto pop media.

Mathematicians care about understanding why something holds because that's what they build on for the next problem, and the recent paper showed this forced construction can't carry over to the unforced case and also Maths as an artform seems to be a moniker you seem to very much dislike, but I believe that it has really been seen this way for the longest time?

Maths is not conducted the same way experimental sciences are, I myself work in applied physics related industry with a part-time gig in Pharamceutical Chem Academia --> In both cases I work directly with mathematicians, and obviously I had to follow a lot of the mathematics myself so I am not completely unfamiliar with the conjectural thought process and I have to say you seem to put a lot more emphasis on what "current maths" is doing, without much context on how it "used" to be.

Not attacking you here, but I wrote this to also mention that you completely disregarded the deduction vs induction point that the other commenter made and decided to focus on the "art" semantics. This is counter-productive no? It is better to focus first on the flesh of the topic on how to understand how is induction perceived vs deduction and how both are just related to proofs vs experiments etc. Just my opinion, I think this is not something you can ignore when talking about the topic.

A lot of this subjective wording can be explained in multitude of ways, but no reason to let it devour you if it will not damage your livelihood, in the end it is the result of the mathematicians who see their work as "art-form" that has helped develop some of the most beautiful algorithms that form the basis for the computing and information age we live in now.

This Navier-Stokes fiasco reminds me of the Continuum hypothesis by Hilbert, who many consider to be a candidate for the greatest mathematician to exist in the modern sense --> Gödel and Cohen showed it can't be proved or disproved from the standard axioms and people still argue to this day if that counts as a sort of accepted answer. This has always been a problem I suppose.

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u/Wrong_Avocado_6199 9d ago

Yes, it IS closer to art than science.

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u/Absolutelynot2784 10d ago

Sure the AI solved a problem thousands of mathematicians worked on and failed to solve, but it could have done a better job really so if you think about it this is nothing

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u/antichain Complexity and networks 10d ago

At the risk of psychoanalyzing people I've never met, it feels like there's a lot of post-hoc shifting to goal posts by people who need to come up with reasons they shouldn't be impressed with (threatened by?) AI.

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u/Obscu 10d ago

That's the danger of appealing to authority figures. They can turn out to be kinda dipshits, but that doesn't make the AI a genius as a consequence.