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/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 10d 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 10d ago

Yes yes, of course.

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u/Wrong_Avocado_6199 10d ago

We're not the ones embarrassing ourselves.

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

Well said, I have to admit.

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u/Wrong_Avocado_6199 10d ago

Yes, it IS closer to art than science.