x: "some real-valued variable"
n: "a countable quantity, usually a total"
i: "an index"
k: "some kind of constant", often an integer, whose value doesn't change, "c" is also used for this
e: almost never used as a variable, it's Euler's number
p: some kind of probability, or a prime number, along with p and q
t: some kind of parameter, often goes from [0,1] or (0,1)
z: complex numbers
I have a Master's in EE so I've studied this a bit.
So, while you might be used to that notation and in context it's clear that's far from universal. Further someone can be an expert in more than one area and incompatible notation slows down collaboration for little gain.
u, v: elements of vector spaces
G, H: groups
g, h: elements of groups or
g, h: homomorphisms, isomorphisms etc
e: group identity
K, F: fields
I: ideals
f: functions
(x): sequences
x_i: i-th element of a sequence
A, B: matrices
It all depends on the context it's used of course
But anyone who is serious about writing maintainable code today should be using an IDE where the benefits of susinctness are entirely relegated by intellisense-like tools.
Trading readability for conciseness is near the top of my list of "crimes against future maintainers."
So I had never thought about this in the context of mathematical symbols, but this makes total sense and I'm strongly in favor of relegating mathematical conciseness in favor of readability and specificity.
Compare the two following statements:
One from Euklid's elements (written 2.5k years ago):
"Given two straight lines constructed from the ends of a straight line and meeting in a point, there cannot be constructed from the ends of the same straight line, and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively, namely each equal to that from the same end."
And my attempt of translating the above, in what should effectively be Hilbert's notation (19th-20th century):
If there are two triangles ABC and ABD where AC=AD and BC=BD and C and D are on the same side of AB then C and D are the same point.
Which one was easier to parse in your mind?
As a bonus try rewriting this formula using longer variable names and tell me how legible it would look http://i.imgur.com/wCWkyNL.png (it's from a proof of one of Syllow's theorems https://en.wikipedia.org/wiki/Sylow_theorems )
Altough, judging by the old timey language of the book, it's possible the book predates Hilbert's axiomatization of Euclidean geometry and the proofs in it were good enough for the standards of its time.
In modern mathematics proof by picture generally means you've drawn / pointed out a single example, possibly wrongly or in a way that doesn't generalize, and because you've shown that one example holds you assume all possible examples hold. That, obviously, needs not be the case.
Of course, this mathematical convention carried over into programming as well, with i,j, and k serving as index variables.