Comment by dekhn

Mostly the parts I hear about. But I also communicate with mathematicians on a regular basis and I can see what they are working on, which is representative of the field. It's about 90% "cohomology of abstract Lie groups that morphize into string theory" and about 10% "practical thing that engineers can use to make my cell phone work better". (amusingly, although I literally made up that sentence, it turns out it's not far from something somebody worked on: "The cohomology of compact simple Lie groups and spin groups connects to string theory by providing the topological obstruction classes—specifically the first fractional Pontryagin class ...." OK, kind of emphasizing my point there.

No, the intuition and techniques that get developed to solve the NS conjecture have little or no bearing on the practical details of doing CFD. That's a common story/thread (and I hear the same story in quantitiative biology, my area of expertise), but often times, it's just a loose justification given to justify funding.