[OkayPhysicist]

This same pattern comes up a lot, whether it be mathematical notation, programming language syntax, or scientific jargon. Some people crusade against them, while others (typically practicioners of the respective field) insist that these constructs are useful.

My hypothesis is that it's a bias from limited information. You have something with inherent complexity to it: math, music theory, physics, code, you name it. In order to represent those complexities, complex jargon gets formed. An outsider attempting to understand a given field is likely to have a (in these cases correct) assumption that the field is complex: if it wasn't, then they wouldn't be putting effort into understanding it.

In their effort to understand it, they eventually run into something they don't understand immediately or easily. They then assign the majority of their perceived complexity of the system to that first thing they got stuck on.

So instead of thinking "programming is hard" they think "reading/writing source code is hard". The practicioners of the field, with the benefit of hindsight, know that picking up the syntax/jargon/notation was in fact far easier than understanding the concepts they represent. But the outsider can only see the immediate challenge, which is the symbology.

[DarylZero]

The constructs are always useful, but rarely do they form a coherent whole, because they're formed by accretion. The "outsiders" are usually going to be right: throwing everything out and designing the language from scratch would allow for substantial improvements, regularization, etc. The insiders will however have adapted to the existing system and found its complexities easy enough to navigate. And that is why the USA does not use metric.

[DarylZero]

Also I just want to add... mathematicians have ⋅, ×, and ∗ to express multiplication, but decided that they also needed ADJACENCY OF CHARACTERS to express multiplication, and therefore mathematics is not allowed to use variable names longer than one letter.

Come the fuck on, mathematics.

[kmill]

It's fine, you just add a space. It's also used for function application, like "sin x".

I'd say single-letter variable names are mostly due to ease of handwriting when doing calculations (or for giving a chalkboard talk), and authors tend to just use what they've already come up with when writing things up. Mathematicians seem to be very tolerant of ambiguous parsing, so that can't explain all of it.

[sieste]

When reading a math proof it helps to spell out what the symbols stand for, instead of saying the symbol names, for example, instead of "E equals m c squared" say "energy equals mass times speed of light squared". This also greatly helps understanding. If you can't keep track because there are too many symbols, make a little lookup table.

[DarylZero]

You can point to "sin", but in practice math just doesn't use multi-char variable names. The trig functions are special cases. Doesn't mean you're allowed to name arbitrary vars like that.

[kmill]

What about ker, coker, im, hom, end, aut, lim, colim, Set, Top, Man, Mat, Vect, GL, SL, SO, Lie, Gr, Tor, Ext, tr, Rep, char, rank, Isom, ann, hull, Diff, ...? I'm just copying multiletter names out of my preamble.tex file here.

I get that these aren't variables, but it's really not so uncommon outside of trigonometry to have multi-letter names for things that appear in equations.