[sundarurfriend]

If the equations are only useful approximations anyway, why are edge case breakdowns so important or surprising like the article seems to indicate? If they are as imprecise as Newton's laws, why are mathematicians looking for "unfailing" precision from them?

Or is the article simply wrong in the initial few paragraphs?

[monochromatic]

The Clay problems are pure math problems. Any approximate application they have to the real world is just an accident.

[foota]

I think part of it is just mathematical interest, and maybe part of it is hope for more efficient or otherwise better approximations for fluid behavior.