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I don't get the issue. It's just notation. You could "feel" the same way about the integral sign or fractions or about underused letters in your own alphabet.

When the greek letters are used, they usually give you a clear indication that they are "something different" from the things written. It's much either to understand that alpha, beta, gamma, delta are some counterpart to a, b, c, d than if you had to use i, j, k, l (for example).

Lowercase Xi is indeed always written horribly (like a tornado), but at least in my studies, everyone wrote it equally horribly and all in the same way.

For my first encounter with lowercase xi, I was sure the professor was taking advantage of his tenure and trying to pass off a scribble as a variable, and that was with my having made a point to familiarize myself with the Greek alphabet the previous semester. Somehow I don't remember him bothering to pronounce it!

Then there are the German algebraists who developed ring theory, for whom Greek letters were not sufficient -- they reached for their Fraktur. The correspondences for certain letters -- like A and S -- can be inscrutable to neophytes.

While I get why notation shouldn't matter, I do find it to be more tiring to read new notation where I don't already have an internal pronunciation.

Apparently set theorists weren't satisfied with Greek, Fraktur or blackboard bold, so they use (at least) aleph and beth from Hebrew.

I wish we used more Cyrillic characters in math, just to keep things varied.

Just notation? I don't see that it's a trivial matter, any more than good writing is trivial. I'm reminded of a recent HackerNews thread on Why is Maxwell's theory so hard to understand?

https://news.ycombinator.com/item?id=22812969

Drawing bottom up: "'S' (with a slightly flattened bottom), then a 'c', then a little hook"; sometimes find myself even muttering 's,c,hook' as I write one even today.

I take your point but there are downsides to restricting oneself to only Roman letters. In a few fields I've been a student of, there's a bias against introducing Greek letters. The downside is one does run out of letters. Eventually one needs Greek letters if one wants to not communicate in an amateurish manner -- either that, or one is forced to use multi-letter variables like "Eff", "Density", which are somewhat unwieldy, especially in complex expressions.

Also some Greek letters have such a strong conventional association with certain quantities that using Roman letters in their place can be more obfuscating, e.g. ρ = density, Δ = change, η = efficiency, θ = parameter, σ = standard deviation, μ = mean, τ = time constant, etc.

Notation is to some extent a function of a community's conventions.

While I'm with you on the Greek, bra/ket notation is one of the best anywhere in physics. Here [0] are some examples of why it generally looks simpler, and here's [1] a derivation which would be a nightmare to write without it.

0: https://physics.stackexchange.com/questions/488903/advantage... 1: https://physics.stackexchange.com/questions/533523/confusion...

> but also always horribly written by students/teachers, and made it even more incomprehensible.

Honest question: why does the horribly written matter at all? For all intents and purposes the symbol could be a smiley face or a little drawing of a tree. Indeed, in a freshman course you sometimes have at least one worksheet using trees,cars,stars, apples to make this point. As long as the smiley on page 1 and the smiley on page 3 look the same you are fine.

Same for mu, nu, kappa, rho. They could just be written as C1,C2,C3,C4, but it makes it much easier to read when you use the Greek letters, because you can be reasonably certain that for example rho has something to do with a density (while C4 tells you nothing).

Some (maybe most) people find it easier to remember and comprehend things they can vocalize, so using an inscrutable character, even consistently, can cause problems.

Greek letters have simpler vocalisations than "c4" or whatever, though?!

This relates to internal vocalisation, a subject on HN a couple of times recently, as I don't really do that (particularly for equations) then it was never an issue for me. Though at 15 I learnt the Greek alphabet as I was into physics, that probably helped.

People who need to vocalise to read, and don't bother learning (or coming up with) a vocalisation are going to find it very difficult.

I think it's mostly an artifact of mathematicians using a single letter for variables. (Which one could also argue against.)

Certain variables pick up a conventional meaning, and one quickly runs out of letters.

It's pretty common in physics to use subscripts to label variables, like m-sub-e for mass of an electron, say.

It's just that at some point you run out of letters, having some 35 glyphs more just comes in handy. Very much so if you have indices for different spaces.

Notation shouldn't be a problem if it's compact enough. Then the bra-ket one is foolproof and not too many physicists study functional analysis proper, so it makes sense to simply follow Dirac there.

To write the lowercase xi and zeta, I imagine that I am looping around the horizontal bars in the corresponding uppercase letters, and they tend to come out approximately right.

I remember a Greek-born colleague writing the uppercase Omega as just an underlined letter O. I suppose that shape is probably the idea behind the flourishes in the typeset Omega.

I found it disproportionately mindblowing realizing omega and omicron are literally "big o" and "little o."

Zeta takes some practice to make legible. Michael Covington's sheet on how to write Greek letters, while oriented towards linguists and language learners, is very clear and aesthetically appealing: http://www.covingtoninnovations.com/pens/#GREEK

I had one professor in university who called lowercase xi “squiggle” and wouldn’t make much effort to draw it properly. He would talk about, for example, “d squiggle d t,” and so on.

The advantage of a xi is that it looks nothing like an x so coordinate transformations (xi = f(x), tau = f(t)), are easier to keep track of.