there's a dumb saying from free market idiots:

those that do do, those that can't teach.

or something along those lines.

it's probably an ayn rand quote, or something.

in math, the only structure that exists is the university; those that do have no option but to teach. there's no free market for abstract math; mathematicians just make it up as it comes to them, and put it aside for somebody else.

we pride ourselves in our platonic disinterest in application.

we openly make fun of engineers....

but i may suggest tracking down the works of alexander grothendieck for some alternative views from a distinguished mathematician.