It only assumes that single characters are desirable variable names. Especially if (as in Lisp) one does not draw a conceptual distinction between variables and functions, it is common to see multi-letter variable names.

Here is a typical example of a modern research paper:

http://math.stanford.edu/~conrad/papers/locchar.pdf

Most variables are one letter, but notice, e.g., GL in the fifth line (the General Linear group, not G times L), ker in the seventh, etc.

One reason for brevity is that we like to write on paper and/or the chalkboard.

And to answer your last question, I think math does concern itself with readability. Many mathematicians are obsessive about making sure that their work is as readable as possible, although unfortunately this is not universal.

An important difference is that to operate with the term is much easier to use short names. If a term is adding in the right side of a equation, and you want to put it on the other side subtracting, you must copy all the equation (and Ctr-C Ctr-V doesn't work in paper.)

A typical program is written one, read a few times (perhaps years later) and executed many times.

A typical math calculation is typed once and read only a few times (a few minutes later) and discarded ("archived").

In the draft, I usually find myself replacing sin(x) and cos(x) by s and c, because it's only a little calculations and in the following 10 minutes I will remember what it means and there is no other s or c in sight and I get bored of writing all the letters.

> Perhaps it could be better put as 'Why doesn't maths concern itself with readability like programming does?'

Readability is a personal opinion in some ways. I guess I have grown up using mathematical symbols in Physics classes since middle school so those symbols didn't feel arcane to me when I hit my first real math classes.