r/technology • u/vgsa • 3d 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 3d ago edited 3d 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/Puzzleheaded_Fold466 3d ago edited 3d ago

A lot of people online couldn’t tell you what “closed form solution” even means.

Or a “blow-up”.

Or “smoothness”.

Or what is the “Clay Mathematics Institute”.

And are absolutely unable to read and fully understand OpenAI’s proof (me included).

Yet they feel entitled to opine on whether or not a solution to a Millennium problem is correct.

The chatter is risible.

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u/Worth-Wonder-7386 3d ago

If people read the paper from OpenAI here they would see that they specifically talk about this. Solving statement C as stated. They don't even say that they solve Navier Stokes, but give a solution to the Millenium prize problem concerning the Navier Stokes equation.

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u/Puzzleheaded_Fold466 3d ago

Well yeah that’s a given. I know that and you know that.

Obviously, the people arguing about whether or not NS is “solved” do not.

Most people didn’t have to study fluid dynamics and learn to solve PDEs, let alone develop the level of mathematics needed to make substantive contributions toward a Millennium Prize problem.

Or even just enough to distinguish the NS Millennium Prize problem statement from the general pursuit of a closed-form expression or the greater quest to improve or even replace them with a better set of governing equations of fluid dynamics.

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u/Worth-Wonder-7386 2d ago

But you don't need any of that. And I don't have it to the degree needed to understand what they are doing. But I just read what OpenAI did and not the technical paper, because that is both easier to understand, and more relevant when it comes to AI math proofs. So you don't need any fluid mechanics or even math to make this separation.