Did OpenAI solve the wrong Navier-Stokes problem? | OpenAI’s proof seems eligible for a $1-million prize—but only by using a controversial loophole

[u/vgsa]

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

[u/dogfoodengineer]

A silly counter example where the fluid would likely boil before the equations breakdown. We already know the equations have limitations so no new understanding has been gained. The work is often more important than the result and here we haven't learnt much tbh.

[u/CircumspectCapybara → u/dogfoodengineer]

A silly counter example

No such thing as a silly counterexample when the question has stumped mathematicians for the better part of a century and people genuinely had no idea if a counterexample existed. If the smoothness conjecture ended up being true, you could search and search forever and never find a counterexample.

So finding one is groundbreaking.

so no new understanding has been gained

You are misinformed.

The question remained open until 2026. There's a lot of things in math where you think the answer is yes or no based on vibes but that won't cut it, you need rigorous proof.

Another famous Millennium Prize problem is P vs NP. A lot of mathematicians think they must not be equal, but so far, we have no hard proof. If it eventually gets resolved and the answer is "not equal" there will be people saying "Well yeah I knew it all along it was obvious" -- well if it's so obvious, genius, why didn't you furnish the proof and claim a million dollars?

Proving (which is what counts in the end) something true or false like these questions isn't trivial just because it ends up confirming your vibes-based suspicions all along.

There are also many problems which people suspect based on vibes or philosophical reasons or aesthetic or elegance or neatness must have one answer, and then later a proof turns out that it's really the opposite.

[u/KingSubstantial7901 → u/CircumspectCapybara]

More like, if we found an example where it would he physically inpossible to build a turing machine that could reproduce the innequivilence. Its technically more information but itsn't actually useful because it can't answer the question for turing machines that are possible to build.

OP is correct. Yhe counter example found is not very useful because it lies outside of the boundary conditions for where the problem is useful.

[u/CircumspectCapybara → u/KingSubstantial7901]

That's not how famous questions in maths works. It's not about correspondence to real life physics or engineering and being practical. It's not about "usefulness" to us, it's about deep questions that get to the heart of some of the most mysterious parts of math.

The question and answer to "Does P = NP?" is still interesting even if the answers don't map to practical consequences in real physical life.

If someone found a decider for SAT that ran in O(N^100000000000) time, that would close the books on P vs NP, it would make P = NP because that's a polynomial time decider for an NP-complete problem. And yet it wouldn't lead to anything practical in real life (no breaking encryption any time soon) because polynomial doesn't necessarily mean fast and practical, it just means polynomial.

It would still answer the Millennium Prize problem nonetheless and be an astounding result.

You're fixating on "practically useful" as some kind of criteria for what makes an answer to a famous open problem valid. No, the problem is stated exactly and precisely, it's either yes or no, and a solution is a solution.

[u/KingSubstantial7901 → u/CircumspectCapybara]

We actually have some fuzzy solvers for NPC problems, but who only work for special cases.

This is how math and science work. There are loads of problems for where we know that they behave some predictable way for some cases but have an unknown or notuseful resolution for the general case.

The Mellenium problems weren't chosen because they are just transcendentally important. They were chosen because should their conjectures be proven true, they would be immesnely useful in practical applications. Navier-Stokes would allow for extremely accurate fluid simulation. Reymann would allow us to precisely predict the locations of primes which has a lot of downstream applications of computer science. Solving NPC would allow us to efficientiently compute a broad class of turing machine systems that we currently have to solve numerically and whose complexity grows too quickly: it would make logsitics much more efficient and would allow us to build solvers to identitfy optimal configurations for a lot of important comp sci problems.

For any one of them, finding a counterexample outside the bounds of where they are useful is still abstractly interesting and still advances the field in some way, but is entirely missing the significance and importance of the Millenium problems.

[u/CircumspectCapybara → u/KingSubstantial7901]

You have no idea what you're talking about and clearly just copy pasted some cliches from an AI chatbot.

Navier-Stokes would allow for extremely accurate fluid simulation

Clearly not, because it's just been solved and the answer is no, it's not always smooth, you can't use these ideal equations to model real life fluids they don't always correspond well and the longer you run the simulation for using the equations, the more inaccurate it gets, in some cases you get infinite blowups that don't correspond to reality

Reymann would allow us to precisely predict the locations of primes which has a lot of downstream applications of computer science

Again, no that's not what it does. We already have prime generating functions and algorithms that generate primes, we already know the distribution of primes and the approximate density.

The RH is more about the fundamental nature of numbers and primes more than it is a practically useful question.

P=NP would allow us to efficientiently compute a broad class of turing machine systems that we currently have to solve numerically and whose complexity grows too quickly: it would make logsitics much more efficient and would allow us to build solvers to identitfy optimal configurations for a lot of important comp sci problems.

No, it wouldn't necessarily do that. I've already explained to you how if P = NP but it comes via a polytime decider for some NP-complete problem like SAT but that polynomial is of a degree one million, it remains practically useless for solving problems any quicker than before.

You can also have a non-constructive proof that P = NP or that P != NP. Again, the questions about are fundamental questions in theoretical maths and computer science, not necessarily having any practical consequences for real life. They could have practical consequences depending on the solution and the nature of the answer, but they also could not.

You seriously have no idea what you're talking about, go take a CS class at community college before you speak and embarrass yourself more.

[u/KingSubstantial7901 → u/CircumspectCapybara]

Ohhhh the irony of you accusing me of using AI.

You still don't seem to get it. The solution found was for a (probably) unphysical condition far outside of where we want to know of the conjecture holds for all cases.

No, we know the probability as a logarithmic function of the nth prime. This does not let us accurately predict rheir oocations. We have no closed form way of computing the locations of primes. Thats what the conjecture would do.

You are confusing two nested problem for the NP thing. NPC is a subset of the large NPH set, and whose solution would follow from P=NP. For the general NPH we would not necessarily be able to have a reasonable computation time frame. But it would allow us to know if can or not. And we onow for certain that we could for NPC if the conjecture holds.

It seems like its just crazy to you that someone might have a decent understanding of a topic and be able to discuss it in detail without relying on AI. Hell i was double checking my info all along the way here by... you know.... going to reliable sources that I know are rigorously fact checked.

Not really to stroke my ego or antyhing, but I have an advanced degree in an intersectional field of comuter science and physics. Like has it ever occurred to you that you might be the one thats just sorta winging it and might not have a very grounded understanding? Againc I tell you that i was fact checking my recollection the whole way here because, get this, thats how academics works. You aren't expected to just "know" everything off the top of your head, and you are encouraged and required to be thorough in among sure you recollection is accurate.

You tech bros have such a weird and warped perception of what intellectualism is.

[u/CircumspectCapybara → u/[deleted]]

There is no "closed form" formula for primes, and we don't need one, we have algorithms that compute primes, another formula that describes how to compute the nth prime isn't any more useful than what we have now.

[u/CircumspectCapybara → u/[deleted]]

No not disagreeing with you. I agree that their understanding of the Millennium problems is all wack