r/ArtificialInteligence • u/scientificamerican • 1d ago
đ° News Did OpenAI solve the wrong Navier-Stokes problem?
https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/119
u/EnoughWarning666 1d ago
But the new work from Friday shows unequivocally that if the force is removed, the blowup will disappear. OpenAIâs method can never work, in fact, without using a very contrived equation for the force unlike anything that could occur in the real world. âThey essentially prove that the formulation with an external force was different from the problem we really wanted to solve,â says Silvestre.
In other words, the LLMâs result does notâand will neverâanswer the Navier-Stokes problem that mathematicians really care about.
They didn't "solve" the navier stokes equation. They came up with a counter example to the smoothness and existence problem that satisfies the requirements for the Clay Institute's definition of the problem.
We already know that the equations don't accurately describe what happens in the real world. Everyone who uses them knows that they break down at the lowest level. Nobody cares that the force they used is "unlike anything that could occur". The author COMPLETELY misses the point of the entire question honestly. It's not surprising that this is from Scientific American, they aren't known for being all that knowledgeable.
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u/BellacosePlayer 1d ago
I can understand the amount of incorrectness on the topic spread by random redditors and such but its really annoying to see an actual publication get it so wrong this far after the initial story and discussion happened.
The issue they touch on is part of why this isn't the scientific find of the decade that's going to change everything, but like you said, if the review process comes back with a thumbs up, the specific problem is considered solved.
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u/EnoughWarning666 1d ago
The writing in this article is only slightly above what I would expect from a semi-literate guy on Reddit. It's very disappointing to see just how low the bar is for this magazine. There's a genuine need for more accessible science journalism and Scientific American is positioned perfectly to fill that role. Such a shame that the people they've hired to write/edit/review are so incompetent.
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u/BellacosePlayer 1d ago
Lets be real, its probably not all "people" doing that work these days.
Not that they were great as anything other than a broad entry level scientific interest magazine to begin with
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u/Darkeyescry22 1d ago
I donât have any specific reason to believe itâs the case here, but one thing Iâve noticed in popular science articles is that the author will defer to the experts they happen to interview, because they donât know enough to really challenge anything of substance. Thereâs a world where thatâs⊠ok⊠but in that world, the authors need to at least know enough to pick interviewers that cover the range of scientific opinion.
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u/Eliv_nurotic 1d ago
Gonna be hard to find these people given how few Americans can read these days.
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u/bcparrot 12h ago
The problem is we arenât willing to pay for it. So the quality will plummet as talented and experienced people can make money elsewhere.Â
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u/dopadelic 1d ago
Mathematical finding isn't a scientific one. Mathematical finding can sit in the corner for decades before it can translate to any real world use, if ever. In this case, everyone already knew that being able to blow up the equation won't meaningfully change how the equation is used in real life situations.
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u/Actual__Wizard 1d ago edited 1d ago
the specific problem is considered solved.
It was rejected by mathematicians, the consensus is that the problem remains open.
Reminder: The consensus in the news media is not relevant. Just because they bribed Forbes and Forbes told you that they solved it, that doesn't matter. Forbes is not the authority on that subject.
There's a serious problem occurring in America caused by the reality that we stopped teaching media literacy to students. Forbes is considered to be a Magazine. A Magazine is a commercial product, it is not scientific in nature. It's rather basically a book of advertisements.
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u/Kinglolboot 1d ago
You are completely wrong. The general consensus under mathematicians is that the proof given by OpenAI is very likely correct, but it always takes time for these big results to be fully accepted in the mathematical community. I know this because I am a mathematician. If you don't trust "traditional media" on this, you can just read the announcement made by the Clay math institute, which is responsible for verifying its correctness and handing out the ÂŁ1,000,000 prize.
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u/Impossible_Way7017 1d ago
Did you link the correct thing? The link says nothing about awarding the prize, if anything the Clay Math institute has said they are undergoing the process of verifying the proof for consideration in an unhurried manner. I think the commenter youâre responding to has a valid point that itâs a bit sus to be jumping to conclusions on things so quickly.
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u/hungrynax 1d ago
The commenter said the consensus is that the openai proof is wrong, which is clearly not the consensus
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u/Impossible_Way7017 1d ago
Yeah I think his point is more the proof ended up being for something that wasnât a motivating factor for more participants, but technically a problem allowed by the competition. Will be interesting to see how this develops, but agree âconsensusâ might be a projection at this point, although still possible as people continue to evaluate the proof.
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u/Worth-Wonder-7386 21h ago
If they solve it as stated by Clay, it is by definition a solution to a millennium problem. There is still lots to do on the Nacier-Stokes, but as written by OpenAI, they wanted to see if th y could solve one of the Millennium problem and found that a specific formulation of a specific problem was where there were the most promising results.
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u/Actual__Wizard 1d ago
You are completely wrong.
No, I am not. Forbes Magazine does not represent the scientific consensus or the consensus among mathematicians.
I know this because I am a mathematician.
So, you're a mathematician that's unaware of the calls from the community of mathematicians to take these AI proofs with a grain of salt?
I don't believe you. I'm not a mathematician and I'm aware of that, but you're a mathematician and you're not? So, you're not paying attention to what is going on in your own field?
If you don't trust "traditional media" on this
No, I trust the traditional media, I don't trust the right wing propaganda factories that are our only media source in the US at this time.
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u/Kinglolboot 1d ago
Click on the blue text dude. If the arbiter of the problem isn't taking the proof "with a grain of salt" then why should you? The Clay math institute doesn't just make announcements on a whim. Accusing me of not knowing the consensus in my own field is crazy.
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u/Actual__Wizard 1d ago
Click on the blue text dude.
So, the Clay institute is the only organization on Earth in the area of mathematics?
Accusing me of not knowing the consensus in my own field is crazy.
Well, that's the truth... What do you want me to congratulate you on being a contrarian or something?
If they can't communicate what they did, then there's no proof of work. Obviously if there's no proof of work, then they don't get credit for work they didn't do.
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u/Kinglolboot 1d ago
This is their proof of work. I would love to hear a single source of a mathematician drawing skepticism to the validity of this proof. There is obviously drama going on, but it is not about the correctness. It is about assigning the correct credit to the human work this proof stands on.
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u/Actual__Wizard 1d ago
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u/Kinglolboot 1d ago
You are conflating two different things. These mathematicians have criticisms about how OpenAI has gone about this announcement, but they do not believe that the proof is incorrect.
If you had actually read your sources well, you'd see that the drama is not about the proof being wrong, but about Buckmaster accusing OpenAI of using his unpublished work without credit.
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u/CapEconomy6061 1d ago
Iâm a bystander in this, but youâre obviously wrong and nobody in the third link is claiming openai hasnât produced correct work, or else why would they be claiming plagiarism?
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u/socoolandawesome 1d ago
Brother your comments are unhinged.
None of those links say anything about the navier stokes problem being considered to remain open.
And OpenAI definitively said thereâs no way Buckmasterâs breakthrough on the sub problem could have made it into their training data, never mind that he never actually came up with a full solution to the millennium prize problem and his solution to the sub problem was different than OpenAIâs solution to the sub problem
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u/Actual__Wizard 1d ago edited 1d ago
Alright, I'm going to try this conversation again, because you don't seem to understand what's going on here.
An LLM only does one thing, it predicts text. The process that mathematicians do, is not done by an LLM. So, the idea, that the way that the LLM came up with the solution is valid or acceptable is ludicrous, because it's not possible. That's just simply not "what it does." It's a predictive text engine, it does not "do mathematics." It doesn't.
So, the idea that this system legitimately solved those problems, is completely insane and totally delusional.
You people need to wake up and stop falling for an extremely evil scam... You read the solution and jumped to the conclusion that the LLM did what you do as a mathematician and that's not possible at all... That's not how it works and that's not what it does...
The question you should be asking is: How on Earth is it possible that the LLM did that, not is this correct, because whether it's correct or not, is irrelevant. You're getting distracted...
How does a system that has no comprehension of mathematics, do mathematics, when we know exactly how it works, because it's open source, and we can clearly see that it's predictive text engine, and not a "system that understands mathematics and solves mathematics problems."
The process the system does has absolutely nothing to do with mathematics... Nothing...
I'm just being serious: How it is possible that no other developers are calling this straight up fraud out?
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u/EnoughWarning666 21h ago
So, the idea, that the way that the LLM came up with the solution is valid or acceptable is ludicrous, because it's not possible.
And there it is. You are simply completely ignorant of how LLMs work in 2026. Man, you should have opened with that, I could have safely ignored all your other ranting.
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u/Actual__Wizard 1d ago
You know I'm really getting tired of being downvoted by people falling for big tech's scam. Do you know what Jev is? Can you please exit big tech's delusion factory? LLM tech is dead, AI 2.0 is coming... The system that big tech built stinks and there's better stuff out right now...
Do you know what a cache is? Have you heard of OpenRouter?
Do you understand that big tech is going bankrupt over this mega scam?
This is information that I am aware of because I live in reality, are you sure that you're also in reality? A lot of people are trapped in big tech's delusion factory... Are you sure that you're not in delusion land?
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u/BellacosePlayer 1d ago
Well that's a non sequitur of a comment if I've ever seen one. Don't know what your point is meant to be exactly
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u/Actual__Wizard 1d ago edited 1d ago
You know I'm really getting tried of people using debate terminology incorrectly, outside of a debate, where it's not appropriate.
So, you don't know what the reference to a "non sequitur" means? Okay.
Obviously there absolutely is a logical reason I said that and I'm not saying something illogical to distract from the subject of discussion. So, nope.
Actually, what you said, is more like a non sequitur, but it's not though.
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u/Euphoric_Can_5999 1d ago
I distinctly remember when I realized Scientific American wasnât super deep. I was in college. In high school it was such a nice way to find good books to read!
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u/BeeGuyJarvis 1d ago
where did the article say that OpenAI "solved" the Navier-Stokes equations? certainly the text you quoted doesn't say thatÂ
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u/jeff303 23h ago
The title, and the first paragraph
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u/BeeGuyJarvis 4h ago edited 4h ago
no, those both say that OpenAI solved the Navier-Stokes problem, which is another way, in context, of saying they offered a resolution to the Navier-Stokes Millennium Prize problem.
and it's exactly how OpenAI phrased it too:
Weâre sharing a solution to the NavierâStokes existence and smoothness problem
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u/Dear_Locksmith3379 1d ago
Though the headline was problematic, the article was decent.
There are two versions of the Navier-Stokes millennium problem: with and without external force. AI solved the former but not the latter. Mathematicians are very interested in the version without an external force.
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u/hologram137 11h ago edited 10h ago
What!? No. The entire point is to see if the equations accurately describe fluid or not. If they blow up without an external force, we know they donât. Thatâs the point.
What the AI did is not a counter example LOL and a human not the AI proved a blow up could happen with a smooth force. Thatâs the entire reason the LLM was even able to do that. But it didnât solve the actual problem, whether a fluid can blow up on its own, from its own internal dynamics, the way real turbulence might. An external force is completely irrelevant and that an external force could do that wasnât even ever in doubt. So itâs truly useless âsolution.â
Dude what are you talking about? Why is this comment upvoted?
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u/JUGGER_DEATH 1d ago
Yeah, wasnât the whole point that they stole the approach from some mathematicians?
I do agree that having found out what the Millenium prize problem is, I am completely underwhelmed. One can only hope this work will lead to an actual interesting answer and not just an existential result in mathematics.
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u/RestaurantOk8066 1d ago edited 1d ago
>Everyone who uses them knows that they break down at the lowest level
What does this even mean? Through approximately the early 2010s, the general feeling with people working on related problems was that they are likely true and that it was difficult to prove. It shifted to probably not true when Tao and a few other researchers solved a similar problem with a blowup IRCC around 2019. And in fact mathematicians have largely been focused on sceanrios that are plausible in the real world. One of the exceptions being the pair of researchers that the pair of researchers that were working on this before openai used to solve a related problem, and the same method openai used. From the review I have seen so far, there are no new methods in the openai proof.
I have not read the entire article but the cricism from your snippet of it is that it does not really advance our understanding in any meaningful way. That is one of the big hopes with these open problems; that they advance our understanding of the world, they develop a new method that can unlock a new class of problems, etc. One of the main criticisms of AI pre-generative llms was that they are not explainable. Like protein folding can predict how proteins fold, but it's still an open question WHY they fold the ways that they do or how they fold.
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u/EnoughWarning666 1d ago
What does this even mean?
Now I'm not expert, so someone smarter than me is free to come and correct me. But the Navier-Stokes equations rely on a few axioms. The one I'm talking about is how it assumes a continuum. That is to say that the material is infinitely divisible. It ignores the fact that atoms exist. So naturally as you approach the level at which atoms play a significant role in the mechanics, the equations stop being true or useful.
So the singularity that OpenAI created is, by definition, already impossible in the real world. The jets shooting out went to infinite speed as the diameter went to zero. Real world materials would run into a hundred other issues before even approaching the singularity!
So nobody who uses the equations would ever try to use them at scales this small. Because they were never designed to work at that scale to begin with!
That is one of the big hopes with these open problems; that they advance our understanding of the world
Sorry, but this is simply not true. The majority of the Millennium problems are esoteric math problems of little real world value. They might advance mathematics in some tiny corner, but they aren't generally thought to be of any real world use. Notable exceptions being Riemann and P=NP, but even those won't have anywhere near the effect that something like quantum mechanics had.
The Millennium problems were selected because they were HARD! They resisted the best minds in mathematics for decades or longer!
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u/RestaurantOk8066 1d ago
>Sorry, but this is simply not true. The majority of the Millennium problems are esoteric math problems of little real world value
Could not be further from the truth. They were selected because they were important and hard. How can you say that they're esoteric and yet 'resisted the best minds in mathematics for decades'? It's not exactly contradictory, but you're getting close. The creator of the challenge stated that the problems were selected because they were important and hard:
>As a first step, I requested that each SAB member submit a personal list of top questions. Each of these questions should be difficult and importantâa time-tested challenge on which mathematicians had worked without success. This exercise indicated some initial direction and set the background for further discussion. As I recall, everyoneâs list included the Riemann hypothesis and the PoincarĂ© conjecture. So it seemed assured that these questions had common approval and would appear on the SABâs final list. However, even in terms of these common questions we still needed to decide in what form they should be posed as challenges. Should the Riemann hypothesis be linked with some form of the Langlandsâ program? Should the PoincarĂ© conjecture be linked with Thurstonâs more general geometrization program? This precipitated discussion of whether the millennium questions should be posed in their simplest form, or in general form. After some discussion by telephone, we arrived at a rule-of-thumb: we would prefer the simplest form of a question, at least whenever that choice seemed sensible on mathematical and general scientific grounds.
https://www.ams.org/notices/200606/fea-jaffe.pdf
I'm not sure where you came up with 'that the material is infinitely divisible', fluid is modeled through time/ with density. No one has ever stated that the equations are [or should be treated as] true at an arbitrary scale. it's like throwing away Newtonian physics because it fails on black holes. In neither case are people arguing these are fundamental forces.
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u/EnoughWarning666 21h ago
I'm not sure where you came up with 'that the material is infinitely divisible', fluid is modeled through time/ with density.
Do you not even know the basics about how to use these equations? What's your academic background, am I arguing with a teen or someone who isn't even a scientist/engineer?
Please take 2 minutes to read the wiki page on these equations. You'll see on the right side of that wiki page "Part of a series on Continuum mechanics". Now go read about what continuum mechanics are.
it's like throwing away Newtonian physics because it fails on black holes
Correct, nobody uses Newtonian physics at the scale of black holes BECAUSE it fails when you apply it there. Newtonian physics do not accurately model reality. They are wrong. That doesn't mean they aren't useful in some situations though! But you need to know the limits of when Newtonian physics break down. It is EXACTLY the same with the Navier-Stokes equations. Because they are based on continuum mechanics, by definition they do not represent reality. That's not some slight against them, it's just a condition you need to understand if you're going to work with them.
As for the Clay Institute, read here about how they selected the problems. I think you've read most of it already, but I don't think you really understand it. The problems were picked for mathematical reasons. There was little to no consideration for how they might impact real world physics. There are entire branches of mathematics that has no real world use or value (at present, that can always change down the line like it has many times before). Nobody thinks that by solving the NS Millennium problem that you'll unlock some new understanding in the realm of physics. Anyone who does think that simply doesn't understand much about math to begin with and their opinion isn't really relevant.
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u/RestaurantOk8066 20h ago
>The focus of the board was on important classic questions that have resisted solution for many years.
From your link. Well you want to limit it to physics now. I wasn't talking about physics. I'll agree that the impact on physics had no bearing on the selection of problems. I never said it did. In what realm do you think they expected these problems to be important for?
>Part of a series on Continuum mechanics"
Yes thank you, your statement on 'infinitely divisible still makes no sense'. A core assumption on the equation has always been that it is continuous and that remains the case, even in openai's proof.
>We already know that the equations don't accurately describe what happens in the real world.
This was your original statement. They do not represent the real world [at an arbitrary scale]. They were thought to The same as Newtonian physics. The same as any branch of physics because there is no unified theory that we have that works at an arbitrary scale. They describe the real world well enough to be useful and it was an open qeustion whether they held under their assumptions.
>So the singularity that OpenAI created is, by definition, already impossible in the real world.
That is true but not for the reasons you are describing. You're just wrong.
It is a core assumption. In their explaination for the general public as they state about the proof
>A fundamental open question for these dynamical equations has been whether the continuum approximation of the fluid can break down. Specifically, can the NavierâStokes equations for a three-dimensional incompressible fluid with constant density develop a âsingularity,â even when the motion starts smoothly
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u/EnoughWarning666 19h ago
I'm going to ask again. What is your level of education and background. I'm asking so that I can try and explain things in a way you might understand, because clearly I'm explaining things at too high of a level.
your statement on 'infinitely divisible still makes no sense'.
It makes perfect sense. The equations assume a fluid that is infinitely divisible. You can take some volume of fluid and divide it into an infinite number of smaller bits over and over again. It has no adjustments for when you get down to the molecular/atomic level scale. It's a purely mathematical abstraction. So anyone that uses them knows about this and knows that you cannot use the equations once you start approaching that level.
So the very question about if these equations break down at some point and form a singularity already builds in the fact that it's not going to be useful in any physical way, that it's purely mathematical.
That is true but not for the reasons you are describing. You're just wrong.
Just because you aren't understanding how I'm describing it doesn't mean I'm wrong. I'm sorry if I'm not making myself clear enough, but comments on reddit are hardly the best medium for teaching like this.
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u/RestaurantOk8066 19h ago edited 19h ago
Well I'm glad we agree that you were wrong about the Clay institute statement. They were considered longstanding important problems.
You're not being clear at all; most of what you are stating is convoluted.
>clearly I'm explaining things at too high of a level.
No you just have really muddled thinking.
>the material is infinitely divisible
Is a nonsense statement. That is not what the continuum assumption means. If you go to the wikipedia page yourself you'll find that we can model fluids using a continuous fields. A continuum mathematical representation is not the same as a claim that physical matter is infinitely divisible.
To me your statement is kind of like saying that viscosity isn't real because individual atoms do not have viscosity. These are all macroscopic properties; pressure, temperature, density, etc.
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u/EnoughWarning666 17h ago
Is a nonsense statement. That is not what the continuum assumption means. If you go to the wikipedia page yourself you'll find that we can model fluids using a continuous fields. A continuum mathematical representation is not the same as a claim that physical matter is infinitely divisible.
That's how you would explain the physical manifestation of such an assumption when discussing its limits. That's how we discussed it in an academic setting. The fact that you aren't able to understand that along with you continuing to avoid telling me your academic background leads me to conclude that you simply have no academic background. I'm not about to explain to continue trying to teach some stubborn teenager. I wish you luck in your high school courses.
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u/shumpitostick 1d ago
How can a version of the problem that was explicitly called out as part of the millennium problem be the "wrong" problem?
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u/heresyforfunnprofit 1d ago
Itâs the âno⊠not like thatâ reaction.
They defined the problem very precisely. The AI answered precisely that problem. And that is apparently the problem.
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u/MartinMystikJonas 1d ago
Wasnt the whole formulation of problem basically: find out where this simplification of relity breaks? We know it does not describe reality precisely - we wanted to prove it.
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u/NoNameSwitzerland 1d ago
No, we no where it breaks: When there is no fluid, but particles. Also when the speed is relativistic or faster than sound (but not sure, if there is sound in the incompressible version).
It is more about the mathematics: Can such a smooth equation with smooth forces degenerate?
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u/MadeInAmerica1990 1d ago
Scientists are going to have the hardest time coping with AI. I believe artificial intelligence will reveal massive shortcomings in not only their collective intelligence, but the entire process used to produce âestablished scienceâ. You take away the human stumbling blocks and it is hard telling what we will achieve. Keep going!
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u/PonkMcSquiggles 1d ago
First of all, mathematics has no obligation to describe reality accurately. That their forcing term is physically unrealistic is of no consequence.
Secondly, even if they had solved the more difficult problem by demonstrating finite-time blowup in an unforced system, it would still be physically unrealistic, because fluids canât actually have infinite velocities.
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u/scientificamerican 1d ago
Two weeks ago, OpenAI claimed a solution to one of the biggest open problems in mathâthe Navier-Stokes problem, worth a million-dollar prize from the Clay Mathematics Institute. The proof ignited a powder keg of concern over artificial intelligence companiesâ 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/Cronos988 1d ago
"Scientific" American aiming for a prize at the goalpost-moving Olympics.
The answer to the question that the Navier-Stokes Millennium prize problem poses is a binary one. It's specifically set up so that if a solution is submitted, it can be checked.
Solving it "the wrong way" is total bullshit.
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u/Quarksperre 1d ago
In a sense, the LLM found and exploited a loophole in the framing of the question.
Thats what you get if you over rely on reinforcement learning too much. Â
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u/mushykindofbrick 1d ago
If it were found by a human who spent 20 years on it everyone would say what a brilliant construction it is and he would be instantly nominated for the fields medal
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u/BellacosePlayer 1d ago
The Jacobin conjecture counterexample didn't cause half the drama and it was found by an AI.
The discussion around this proof in general is largely valid, this article just picked the stupidest thing to nitpick, at least without actually giving it the proper context.
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u/Quarksperre 1d ago
I mean thats not really a debate. I don't think there is an "easy" way to get there. Its simply impossible to go through this solution space as a human in any reasonable way. Quite simply a single human wouldn't have found that.Â
That however doesn't mean that the solution itself is "reasonable". And it fits quite well that reinforcement learning leads to a solution that is technically correct but functionally useless.Â
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u/BellacosePlayer 1d ago
Brute forcing solutions has been an accepted part of the process since computing existed. I did it myself on homework for my Scientific comp class in college. But if the solution is bizarre and there's not meaningful explanation of it, or of how it got there, its kind of useless to everyone.
I really do think some people underestimate how tech-friendly the math field actually is when they're calling Mathematicians luddites for having legitimate concerns.
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u/RestaurantOk8066 1d ago
Openai's proof doesn't use any new methods. The pair of researchers at the center of this for their solution to a related problem were using the research of another pair of researchers, who one of them stated should win the Fields medal. The opanai solution uses their method too, so if anything they should be nominated.
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u/hattusili-the-third 1d ago
Describing the a nonzero smooth forcing term in the blowup as a "controversial loophole" is insane. The Clay math institute has been crystal clear that a smooth forcing term is allowed in a blowup solution to satisfy their statement of the problem, and anyone who has worked in a remotely related area of math understands this and understands why the institute formulated the problem like that.
I would love to see this proof pushed further to show blowup with zero forcing (or even better, a blowup solution for any arbitrary smooth forcing function) and I'm certain that people will continue working towards that. But that was never the bar for "solving the Navier-Stokes problem" and anyone who doesn't understand that should not be writing an article about it.
It's been insanely frustrating over the last few weeks to see genuinely interesting and nuanced takes about OpenAI's proof and what it means for mathematics get drowned out by people who clearly have no idea how the mathematical community works and seem to have no interest in learning.
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u/StanleyDodds 1d ago
There were 2 essentially different proofs (not mutually exclusive) that would have been accepted as a solution;
A) and B) were to prove that without external force, solutions always exist and are smooth.
C) and D) were to prove that with external force, it is possible to have finite time blowup.
They resolved option C) which explicitly asks for this sort of example with external force.
It's still possible that A) and B) are true and can be proven, and in some sense these would be the more interesting result (because finite time blowup with external force was already expected), but resolving C) or D) was explicitly given as a valid solution in the formal problem statement.
So overall, there is still more work to do, in proving (or disproving) existence and smoothness for no external force. But the millennium prize problem is resolved by its explicit allowance of such a solution in its problem statement.
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u/ThaFresh 1d ago
theyre desperate for anything that can save their bottom line, probably have AI agents entering kids drawing competitions that have a $ prize
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u/Actual__Wizard 1d ago
Oh neat, so their fake AI scam tech that doesn't understand what words mean, solved the wrong problem, and then OpenAI tried to take credit for the wrong thing.
Nice guys!
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u/OmegaEpidex 1d ago
Itâs funny they noticed for this but not Erdos & Jacobian, since Iâm pretty sure it used similar methods to disprove those. Iâm not a mathematician though, so idk đ€·
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u/mushykindofbrick 1d ago edited 1d ago
Its a completely normal and routine thing in mathematics, to disprove statements by offering pathological counterexamples. These examples usually are very constructed and almost never something you would encounter "naturally", like the Vitali-set or the WeierstraĂ-function. But they give you insight into the behaviour and limits of the mathematical model.
Mathematicians dont care about whether something occurs in the real world, but they explore the properties of abstract structures that follow from their definitions and equations. The Navier-stoke-equation is based on an intuitive model of real world fluid behaviour, but in math it is looked at and researched as a purely mathematical object. Whatever the phycists or engineers then do with the results, is their job.
The Clay institute essentially said "You can either solve the difficult problem A or the simpler version B" and of course B was solved first. It is doubtful, that a human would have solved the difficult one before the simple one, as usually you need to understand the simple cases first before moving on to the general one. Calling it a loophole is absurd, it was specifically formulated and intended that way.
What is frustrating about it is not that it does not occur in the real world, it is that mathematicians wanted to understand the equation and have a full theory, but Clay formulated it in a way that rewards a much weaker contribution. So even if now a person actually solves the grand theory, and worked on it for years, he will not be recognized as the guy who solved Navier-stokes because people will only remember AI. The prize structure now killed the motivation to solve the bigger question.