As the joke goes
Programmer : chooses her variables always different, with a name as explicit as possible
Mathematician : chooses her variables from a handful of greek letters
Unfortunately, it doesn't generalize across specialties.
By comparison, the programmer chooses names explicitly based her own understanding and modeling of the problem, which may confuse others.
both approaches have their strengths and weaknesses.
I think you mean sub-sub-sub-subspecialty. I don't often read mathematics papers but when I do, it's infuriating how people think that [squiggle] has a universally understood meaning when in actual fact there are only a handful of people in the world (most of whom probably work in the same building as the author) who use [squiggle] to mean that.
Bear in mind, though, the papers are written for that same group. For good or for ill.
You mean, like p in statistics?