One of the problems facing academic mathematicians is that they can't really tell anybody what they do. There was an example parody of an academic mathematician whose specialty was "Riemannian Hypersquares."
This hypothetical professor had a specialty so obscure that there might be fewer than ten people worldwide who would even understand his field of study, other mathematicians specializing in Riemannian Hypersquares.
These seven or eight mathematicians write papers that only the others in that group can understand and, for everybody else, the only explanation they can offer is, "It's very complicated, you wouldn't understand it." This is a cop-out.
If this is a cop-out for an academic weenie, then it is also a cop-out for a practicing industrial mathematician. Maybe I can't explain the subtleties of what I do, but I should be able to explain the problems I'm solving and the value I add to my employers and to others.
This is part of a bigger issue, the notion that what is easy to explain is usually what should be done. There is a close relationship between pedegogy and practice. This may reflect some deep and fundamental principle, but I think it is closer to the idea that what our minds learn best is usually what works best.