All words are arbitrary collections of letters. map, filter, join, and split - for at least 2 of those, the most common meaning is so far removed from the programming meaning that they might as well be something shorter like 'mp'.
Nor all all words arbitrary collections of letters, most words have some form of alternating consonant vowel structure that makes them easy to speak and remember. Write a program that just arbitrarily combines letters and I doubt you'll get much out that looks like words; there are lots of patterns in how we create words, it isn't arbitrary. If you can't read your code aloud and sound reasonable then you've probably inappropriately abbreviated your identifiers.
Map is by far a better name than mp; there is no shortage of vowels; map is already a short identifier and a real word.
One doesn't just sit and speed-read math in a single pass. Nor poetry. Good programs have that kind of density and deserve the same consideration; they are not newspaper columns. The trouble with the shallow notion of readability that says "I should be able to random-access any line of code and understand it right away" is that it results in less intelligible whole programs, which is a net loss of readability and of other things as well.
I wish more good programmers understood this. The bad ones we can write off, but too many good ones have been schooled to focus overly on the line-of-code. If you have a million lines of code, it doesn't much matter how readable an individual line is; nobody's going to be able to read the whole thing. What we should be striving for is to produce an equally functional program with orders of magnitude less code (which would automatically be a more functional program). This requires a quite different notion of readability.
Math notation is horrendous by the way, too many implicit assumptions about the readers background knowledge. See what Gerry Sussman has to say about it. The great thing about code is it forces one to be explicit, which forces one to actually understand and learn.
This is heresy, but I actually think it might be better if it weren't a real word. I find I benefit from inventing names for functions or data abtractions. It helps to clear the mind of what those things might be.
Plus making map into mp or whatever makes it much more googleable. And don't get me started on Clojure having map and a Map.
By the way, there is a variant of "googleable" that I find to be a valuable property for names in a codebase, and that is "greppable". I try to make sure that the name of any important concept is a unique string in the program, so a simple grep will yield all the places it occurs. I'll even rename things that aren't as important, if their name includes this string, to preserve said uniqueness. (And no, the 'find usage' feature of IDEs doesn't come close to satisfying this need, since a concept can appear in many ways that don't yield to code analysis, such as comments.)