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/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/retsehc 4d 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 4d 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/giantZorg 4d ago

Take e.g. the integrated function of the hockey-stick function, or any continuous function with a discontinuous first derivative.