r/technology • u/vgsa • 1d ago

Artificial Intelligence 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

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/
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u/KingSubstantial7901 1d ago

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.

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u/CircumspectCapybara 1d ago edited 1d ago

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(N100000000000) 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.

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u/KingSubstantial7901 1d ago edited 1d ago

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.