But doesn't that highlight a fundamental difference between mathematics and programming, in that the majority of programmers out there are working on problems u

But doesn't that highlight a fundamental difference between mathematics and programming, in that the majority of programmers out there are working on problems using programming as a tool, whereas the majority of mathematicians work on maths itself? I don't mean to disparage either craft, mathematics is a wonderful thing, and of course the applications are enormous and vital to science and engineering, however the majority of work is not applied. Additionally there is some truth in this, in that the majority of working programmers are 9-5ers who have no passion for programming, whereas maths work is difficult to get into and not necessarily as well paid as other professions so those who work in it are necessarily more passionate.