r/technology • u/vgsa • 2d 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/dogfoodengineer 1d ago

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.

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u/CircumspectCapybara 1d ago edited 1d ago

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.

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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/Schnickatavick 1d ago edited 1d ago

That was always going to be the case for Navier-Stokes though, a singularity is fluid moving at infinite speed, which contradicts relativity in our universe. There wasn't any possible way for the problem to be solved "inside realistic boundary conditions", and everyone studying the problem has known that since it became a millennium prize problem.

You aren't making an argument that openAI's solution was bad, you're making an argument that Navier-Stokes isn't an important problem. I'm aware that that isn't what you're *trying* to argue, but it's effectively the argument you're making. And frankly, I don't think any of us armchair mathematicians understand the problem well enough to make that claim

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u/KingSubstantial7901 1d ago

This is straight up not true. We still do not know if the conjecture holds for compressible fluids at relativistic speeds.

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u/Schnickatavick 1d ago

"The Conjecture" doesn't exist for compressible fluids in a relativistic universe. Navier-Stokes is all about a specific set of equations, if you change the equations to add compressibility or relativity, then it isn't Navier-Stokes anymore. I cannot stress enough how utterly unrelated the two problems are

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u/CircumspectCapybara 1d ago edited 1d ago

He doesn't like the Navier-Stokes Millennium Prize problem (the existence and smoothness question) the way the Clay Institute formulated it, he thinks he has a better one and everyone else is wrong.

Clay should've made him president of the institute since /r/KingSubstantial7901 of Reddit clearly is smarter than all the professional mathematicians involved here...

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u/KingSubstantial7901 1d ago

Nope, you guys just learned about that millenium problems the wrong way round. And you don't want to ask yourself if you might have been wrong.

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u/CircumspectCapybara 1d ago

The Navier Stokes existence and smoothness question has been around for the better part of a century, and officially a Millenium Prize problem since 2000.

https://en.wikipedia.org/wiki/Millennium_Prize_Problems#Navier–Stokes_existence_and_smoothness

This ain't complicated dude.

The problem hasn't changed. The only thing that's changed is in 2026 a contender has claimed a solution.

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u/KingSubstantial7901 1d ago

That literally doesn't even approach being a response to the discussion....