TITLE: Are notations intended to look nice?
QUESTION [5 upvotes]: I was just wondering: when mathematicians come up with new concepts that requieres new notations, do they only look at how practical it is, or does asthetic also play a role? For example, I have seen both $\mathcal{O}_X$ and just $O_X$ as a notation for the structure sheaf of a ringed space here, and while I believe that very often "canonical reasons" are available to choose one notation over the other, are there examples of notations where the creator just thought it looked nice, and are there even examples where notations are more made to look nice than to be practical?
This raised the question wheter mathemacians care about beauty, which I would certainly answer with yes, but also what beauty is: rather an elegant argument internal in mathematic logic, or also the way it looks written down on paper?

REPLY [5 votes]: In the past, before computers, printing was mechanical,  and, due to the human effort and mechanical limitations inherent in typesetting, notation was far more limited. Math books didn’t sell a lot of copies even back then, so spending a lot of time typesetting them was not cost-effective.
To typeset $\mathbb R,$ you had to actually have a cache of physical $\mathbb R$ characters, at least one for every occurrence on a page.
This meant that a lot of niceties, like fonts to indicate types, were less likely to be used. So $\mathcal O_X$ was a nicety unlikely to be found in early texts. In those times, there were a few special symbols. To distinguish types, they might distinguish capital and lower case Roman letters, and capital and lower case Greek letters.
We still have “hidden notation/conventions.” For example, we tend to treat variables $n,m$ as integers, and $x,y$ as real. This is particularly noticeable in the limit notation:
$$\lim_{n\to\infty}\quad\text{versus} \quad\lim_{x\to\infty}$$
Most mathematicians know these  mean two different things, even though there is no “logical” reason for the change of letter to change the meaning. In theory, the notation should indicate the domain of the limit, but in reality, we usually don’t need it.
Computer typesetting makes it much easier to invent clearer notations. Not just fonts, but superscripts and subscripts are much easier. Something like:
$$\underbrace{1+1+\cdots +1}_{n\text{ times}}$$
was nearly impossible with physical typesetting.
As for aesthetics, that depends on what you mean. Clarity has a certain aesthetic nature, and some of us find simplicity and clarity an aesthetic of its own.
But notation is meant to communicate clearly, and usually briefly. Most notation is only “beautiful” in the mathematicians’ eyes, the way that proofs and definitions can be beautiful, by making ideas seem more transparent.
That said, there is a risk of too much notation. The tendency to use logic symbols $\forall,\exists,\lnot, \land,$ and $\lor$ outside the setting of logic can be unclear unless the statements are very brief. They are appropriate on blackboards during lectures, because the lecturer is trying to be brief and speaks their meaning, but in text, English is preferred.
How much notation we use is an aesthetic choice, and requires conscious efforts at clarity. An ugly page is hard to read.
An example of notation I hate, personally, is $\vec v.$ It works for small numbers of vectors, but with a lot of vectors, the arrows seem too noisy. If I need to distinguish vectors from scalars, I much prefer to use bold face, $\mathbf v.$

It is worth noting, one reason we use Greek letters so much is that most educated people in Europe were taught Latin and Greek. This also meant that printers, particularly academic printers, tended to have a set of Greek letter.