[ktt3ja]

> Do mathematical formulas have to use Greek letters rather than useful variable names like "distance" or "speed"?

I feel that using "useful variable names" like you describe would actually make it less useful because they overlap with common language and writing them out in say, formula, would make them too long (and thus less readable).

I find that for any common topics, there's a subset of "default" variable names that are used so often that when you see it, you pretty much instantly recognize what it's meant to represent anyway. Using Greek letters is no problem as you get used to it eventually, and they make things stand out more than simply using the 26-characters Latin alphabet.

[gchpaco]

Also depending on the discipline you're working in you can make very confident assumptions about what a random mathematical object is depending on which language it is typeset in. In the context of programming language type systems, for example, a Greek letter is almost always an ML style type variable (think Haskell type a -> b -> a stuff) whereas Roman type is almost always a ground object (int, bool, whatever). Vectors are boldface, groups are capitals, fields are blackboard bold, lowercase letters in a group context are almost certainly group elements... In some contexts you're actually reaching for new alphabets (e.g. the Hebrew letters that are used for infinite cardinals) to be even more distinctive.