People who enjoy the current state of mathematics will probably think the OP is trolling, but it's a reasonable question.
Perhaps it could be better put as 'Why doesn't maths concern itself with readability like programming does?'
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.
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.
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.
Notation has evolved since ancient Greece. Euclid, for example, is quite readable in translation, but he did not use modern shorthand. See for yourself:
http://aleph0.clarku.edu/~djoyce/java/elements/elements.html