Apologies in advance, but I don't have time to write this as clearly and effectively as I want to, but I felt I had to express an opinion here, and raise some points. Pascal misquoted: long letter, I lack the time to write a short one.A difference is that when you're reading someone else's code you're usually doing it to try to fix a problem in a specific part of the code, and specifically not trying to understand the full setting, the full architecture, and the grand idea(s).
I could give you an example of a proof, explained in detail, easy to follow every step, and at the end you still wouldn't have gained any understanding of the field, the area, the ideas, or the underlying reasons why things are true. You will have been helped in your small scale specific task in getting control of one tiny aspect, but without working on it for yourself, gaining the insights for yourself, doing the work for yourself, you won't get the bigger picture.
When I work with code, especially someone else's code, I almost invariably end up replacing the long, descriptive variable names with single letter names within the scope of a page. It's easier to read a short line than a long line that's trying to describe, again, the meaning and purpose of every variable. Being able to keep definitions and meanings of variables over a page or two of scope is trivial, especially when you have an IDE that can remind you if necessary. Personally, I don't use one, but I've seen them used to good effect.
When working intensively on a piece of code, keeping track of what "v" means comes naturally, it's repeated often enough that you have effectively used spaced repetition and have learned it. Having constantly to skim over the full_description_of_the_entire variable_encoded_in_the_name becomes a chore.
And no, I don't check back in the version with the single letter names, because others don't share my style, ability, or point of view, and they insist on having verbose code that reads like a novel. That's fine for fixing small errors in local code, but that's not what math is about.
I find it interesting that every mathematician I've discussed this with says that coding and math are fundamentally different activities. Almost every coder I know seems to think somehow they are the same, even though they haven't done any really advanced math.