For example these equations look similar,
x^2+4x+5=0
y"+4y'+5=0
Even though one is a polynomial equation and the other is a differential equation, the common visual pattern suggests that the techniques needed to solve them may be similar.
On the other hand in programming there's no need to do this, all the math has already been worked out on paper, so it's better to use clear, distinct, easy to type variable names.
How important is form when I'm programming mathematics?
Not important.
Who in their right mind does math on a computer, math is implemented on a computer, but it's done by hand.
Maybe you think this becuase your used to writing math on computers that make writing that math ugly and obtuse?
Besides, having the math you've written by hand closely match the syntax you use on the computer can greatly reduce the cognitive burden of switching between code and paper.
Making your code performant, and doing a thorough numerical analysis, usually requires a significant rearrangement of your formulae.
Why would I use the variable name "probability_distribution_on_m" instead of "rho_m", when I know all along what rho_m means in the contexte of my code (the symbol use throughout the paper). Usually, I comment at the beginning and specify what the variables mean and to what they correspond in the paper. And if somebody needs to read my code, that person will need to understand the paper first. More descriptive variable names won't make the person understand the paper better.
Of course, when I am writing some non-scientific software, I will use descriptive variable names, because there is no complicated formula, no paper that sets the context of the code, and it makes sense in general to have descriptive variables for logic elements for a clear code.
What I do think is bad form would be naming it ρ_m.
Edit:
There are like 5 replies to this mentioning different ways of doing it (including memorizing 3 digit unicode values) none of which seem more intuitive than writing "mu".
\mu<tab>
I agree that we need better system-wide tools for arbitrary Unicode input. Font support and confusable glyphs are also issues. But I think these are solvable problems, and they will be good problems to have solved.
Also, Emacs has an input method which supports "\mu", and this convention is also used in Racket for things like λ.
Write for the convenience of the reader, not of the writer!
We're in the 21st century, all the tools we use should have reasonable Unicode support. The fact that we collectively keep on talking about typing non-ASCII characters as a real problem is a pretty depressing reflection of our shared computer infrastructure :(.
You just type \mu and then hit the tab button and you get μ. I actually switch over to my Julia REPL all the time when I’m emailing someone and want to type a greek character.
So you can see how this becomes a bit of a barrier to entry.
For new users, if they're not used to writing unicode characters and don't have an editor with nice support, then they don't have to write them.
The julia community has a pretty strong convention of giving both unicode and ascii versions of almost all functions. Some packages don't have this convention, but I'm not aware of any big important ones that don't follow it.
I use vim, and have a completions plugin (part of julia-vim mode), so that I can write \mu<tab> for any unicode name, which makes it as easy to type as "mu", but easier for me to read (as it matches my textbook expectation of the formula).
And LaTeX codes are not always obvious. For example it's \triangleleft but \leftarrow
The solutions to those problems is to use better fonts, terminals, and editors. Using Unicode characters is fine but some people do have legitimate problems with them.
Not all fonts are good fonts for an evey use use; heck, not all fonts make 0 and O or 1 and l and I clearly distinguishable.
> The solutions to those problems is to use better fonts, terminals, and editors
Exactly.
Typing certainly does add more friction between u and µ than a chalkboard would, though it is perhaps also notable that mathematicians seem to have felt that it's worth the effort, and have come up with a quite nice system for it in LaTeX -- and I would certainly not mind seeing more languages and editors add support for LaTeX completions the way the Julia ecosystem has.