I wish math notation becomes substitued with pseudocode. I can never figure out all the greek letters!
But more often than not I look at papers, where I know what they were doing and how and just have to ask myself: Why would you go through the work of translating what you did back into formulas, which bring exactly zero benefit and are harder to understand than the code you wrote?!
But come high school years, or in British sixth form studying for"A levels", I scored in the top decile for my class and for Applied Math, but the bottom dectile for Pure Math.
I think you can make a very good argument that math notation is not doing the potentially career changing job it could be doing, by not expanding the keys. Darn, even a key table index alongside would be night and day better. Edit - didn't remember the length of my comment after coming back to it after a break, so culled the excess. The punchline was that when we got a new young and enthusiastic Pure tutor, who was French, so he in true anger would explain to us in great eloquent depth, my marks equalized in two semesters.
There's surely something like a formal study of students to show if comprehension is the main reason math is hard?
2) I agree with the gist of your point, but I'm guessing you're being down-voted because you come off as sort of flippant. Anyhow, I've long thought that mathematics should have hover-text to help remove the mental overhead of translating the concise notation to meaningful interpretation. Obviously, using variables names like `velocity_of_thing` is much too verbose in mathematics (papers would 1000's of pages); however, β with hover-text "This is the velocity vector of the thing." would be super helpful IMO.
Both formats have their origins in Wolfram Mathematica.
If there's a way to add that sort of hover annotation in LaTeX, I'd gladly use that for my thesis.
That is not obvious to me. Perhaps in a purely mathematical paper with dozens of formulas, but that's not my field of study. In any paper I read of any discipline, I never came across any paper filled with enough formulas that it would make sense to compress at the cost of clarity.
I fully agree, though, on following conventions (that only conveys extra context) and using hover text to act as a quick lookup function. I actually looked for the latter in the past but couldn't find a way to do it in LaTeX.
Fair point, but with this approach, even simple formulae could really clutter up a page if the variable names are long and descriptive (imagine just a rational function!). Also, as with programming, folks might abbreviate (e.g., `vel_thg`) and then we're nearly back at square one.
But anyway that's programming. Papers are a little different of course, with limited space so usually there are no big code parts with declarations and comments. Which is also why I like blog posts: things are clickable and interactive. A PDF is super static and you can't expect a reader to click through to the code or to be able to zoom in.
[1] well, she claims not to be, but from my POV it's math even if she says it's a subfield.
Math is heavily optimized for peope already familiar with the topic at hand. In many cases, that's the only way you have a chance of understanding the paper at all. So long names would just be noise to the main audience of the paper.
If that's really true, you are getting bad advice.
All you're really doing is substituting something you're unfamiliar (or less familiar) with, common mathematics symbols, with something you specifically happen to be more familiar with (programming pseudocode).
It's really no different than someone looking at your pseudocode and saying "why can't they just write it in plain English?"
Ideally, you'd have both. The clean math notation AND pseudocode.