As a physics student, often I find when doing blackboard problems, the lecturer will struggle to find a good variable name for a variable e.g. "Oh, I cannot use B for this matrix, that's the magnetic field".
Even ignoring the many letters used for common physical concepts, it seems most of the usual Greek and Latin letters already have connotations that would make their usage for other purposes potentially confusing, for instance one would associate $p$ and $q$ with integer arguments, $i,j,k$ with indices or quaternians, $\delta$ and $\varepsilon$ with small values, $w$ with complex numbers and $A$ and $B$ with matrices, and so forth.
It then seems strange to me that there's been no effort to introduce additional alphabets into mathematics, two obvious ones, for their visual clarity, would be Norse runes or Japanese katakana.
The only example I can think of offhand of a non Greek or Latin character that has mainstream acceptance in mathematics would be the Hebrew character aleph ($\aleph$), though perhaps there are more.
My question then, is have there been any strong mainstream efforts, perhaps through using them in books, or from directly advocating them in lectures or articles, to introduce characters from other alphabets into mathematics? If there have been, why have they failed, and if there haven't been, why is it generally seen as unnecessary?
Thank you, and sorry if this isn't an appropriate question for math.stackexchange.com, reading the FAQ made it appear as if questions of this type were right on the borderline of acceptability.
Best Answer
To add to some of the letters and alphabets mentioned, in set theory, the Hebrew letters $\aleph$ and $\beth$ are used.
It is common to, as you mention, use specific variables letters for specific purposes. More obscure, foreign letters are probably seldom used simply because they have no need to be introduced. Mathematicians already they have two alphabets to choose variables from!
However, for things that have specific purposes, like constants or special functions, cannot be given the same variable letter without causing some confusion.