I feel like this isn't quite fair to math, most of these can apply to school math (when taught in a very bad way) but not even always there imo.

Its true that math notation generally doesn't give things very descriptive names, but most of the time, depending on where you are learning and what you are learning, symbols for variables/functions do hint at what the object is supposed to be E.g.: When working in linear algebra capital letters (especially A, B, C, D as well as M) are generally Matrices, v, w, u are usually vectors and V, W are vector spaces. Along with conventions that are largely independent of the specific math you are doing, like n, m, k usually being integers, i or j being indices, f and g being functions and x, y, z being unknowns.

Also math statements should be given comments too. But usually this function is served by the text around the equations or the commentary given along side them, so its not a direct part of the symbolic writing itself (unlike comments being a direct part of source code). And when a long symbolic expression isn't broken up or given much commentary that is usually an implicit sign that it should be easy/quick for the reader to understand/derive based on previously learned material.

Finally there's also the Problem with having to manipulate the symbols. In Code you just write it and then the computer has to deal with it (and it doesn't care how verbose you made a variable name). But in math you are generally expected to work with your symbolic expressions and manipulate them. And its very cumbersome to keep having to rewrite multi-letter names every time you manipulate an expression. Additionally math is still generally worked on in paper first, and then transferred into a digital/printed format second, so you can't just copy + paste or rely on auto completion to move long variable names around, like you might when coding.

Very well put.

You can't except learning the science of abstraction by making it concrete. Exampled are not more than examples and if one field required abstract theory, it is indeed the mathematics.

Functional programming is much more math oriented and I think works well here, as it likes to violate a lot of these rules as a rule. I think it's what makes it so challenging and so obvious for different folks.

but teaching math through “how you would implement it in code” seems really interesting.

This is near exactly how I handled learning advanced mathematics back in the late 80s and early 90s. This method takes the abstract and makes it practical, which is what many people really need in order to effectively learn.

I know this is just a simple example but sum() doesn't teach you about the concept of sums. It would have to be something like:

def sum_up(my_list):
    result = 0
    for item in my_list:
        result = result + item
    return result

Then you could run that through a debugger and see how the variables change at every step. That way you can develop an understanding of what's going on there.