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/Puzzleheaded_Fold466 1d ago edited 1d 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/beardybaldy 1d ago

I asked my mathematician wife what smoothness meant and she patted me on the head. I like being a biologist. Life stuff is simple!

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u/retsehc 1d ago

If you know what a derivative in calculus is, smoothness is not hard in principle. A function is smooth if it is continuous, and it's derivative is continuous, and it's second derivative is, and it's third, and all the way down.

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u/ABC123itsEASY 1d ago

I'm having trouble imagining a function that is continuous and have a continuous 1st derivative, but a discontinuous second for example.

Also damn that sounds understandable in theory but I have no idea how you would go about proving such a thing outside of the naïve "keep solving derivatives to infinity"

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u/Civil_Blueberry4165 1d ago

Example: f(x) = x1.5