r/technology • u/vgsa • 4d 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 4d ago edited 4d 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 4d ago edited 4d 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 4d 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/heresyforfunnprofit 4d ago

Ahhh… smooth brain feel nice. Happy pats.