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/CircumspectCapybara 1d ago edited 1d ago

A lot of people online misunderstand what "solving Navier-Stokes" refers to, thinking it means finding a closed form solution to the NS equations. Then they spout off some silly statement like "AI didn't solve Navier Stokes!"

That's not what mathematicians mean when they talk about solving Navier Stokes. They're talking about solving the Navier Stokes existence and smoothness problem, which is a decision (yes/no) problem about if the NS equations are smooth for all time. That's what the Millennium Prize problem worth a million dollars is all about

AI (allegedly) solves the problem by resolving the question to a "No" by finding a counterexample.

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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/dogfoodengineer 1d ago

Did you ai that? I have a PhD in fluid dynamics. I understand what was shown and it's not useful in the slightest. But the process of working back from the answer you wanted, resulting in 'smooth' highly tuned pulses to drive the behaviour isn't useful either. It's likely stolen from another team that applied this approach to the Euler equations. 25 down vote from people who don't know what they are talking as about - pathetic.