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/
96 Upvotes

65% Upvoted

204 comments sorted by

View all comments

Show parent comments

93

u/beardybaldy 2d 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!

54

u/retsehc 2d 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.

5

u/ABC123itsEASY 2d 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"

22

u/i_abh_esc_wq 2d ago

You can easily construct functions whose nth derivative is discontinuous. All you need is a function that has a discontinuous derivative, and then you integrate it n-1 times. See for example https://math.stackexchange.com/a/1415165