[BeetleB]

>I hear people say that about mathematicians, physicists and even philosophers, yet I've never come across any of them in my career. I suspect it's wishful thinking.

I think it's more common among physicists.

Branching over into computer science is common.

As is economics and engineering.

I rarely see a non-math PhD as a faculty in the math department. Same with physics. However, it is not at all unusual to see a math/physics PhD as a faculty member in another department.