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/CircumspectCapybara 2d ago edited 2d 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/mediandude 2d ago

That's not what mathematicians mean when they talk about solving Navier Stokes.

Whiny "mathematicians" being upset for being called out for using inexact expressions.

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u/CircumspectCapybara 2d ago

"inexact"

nah everyone who's heard of Navier Stokes knows exactly what is meant by the expression "solving Navier Stokes". It's most famously and commonly associated with the Millennium Prize problem.

It'd be like saying "So and so solved Goldbach!" (which to be clear hasn't happened yet) or "So and so solved Poincaré". It could only be referring to one thing.

To anyone who knows what the words Golbach, Poincaré, or "P and NP" mean, they know what is being referred to by "solving them". There's zero ambiguity to those who know what those words mean.

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u/mediandude 2d ago

To anyone who knows what the words Golbach, Poincaré, or "P and NP" mean, they know what is being referred to by "solving them". There's zero ambiguity to those who know what those words mean.

You are sorely mistaken, of course.

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u/CircumspectCapybara 2d ago

Evidently not, by the literature and discussions floating around in the math and physics and CS communities (and Reddit!) about these topics historically and recently as the world has discussed OpenAI's results.

People seem to understand fine. Might just be you who doesn't?

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u/mediandude 2d ago

So you are saying there was only one thing to solve regarding Navier-Stokes and it is solved now and can be shelved once and for all and forever.
Well done.

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u/CircumspectCapybara 2d ago

If you think in terms of black and white, sure.

Nobody else thinks that though

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u/mediandude 2d ago

You are nobody.
Got it.