> Expressions with all kinds of strange symbols, often variables introduced that are either completely undefined or defined ad hoc locations remote from the usage, integrals and sums with no subscripts / unclear scoping, etc etc.
This is what mathematical notation looks like if you are lacking some of the fundamental knowledge to read it. I know what that's like because I've been there. Learning mathematics like you would programming doesn't really work - because often you can't just look up something you don't understand (how can you Google a mathematical symbol when you don't even know it's name?).
Pretty much the only way to learn mathematics is from the ground up.
> and I even know people who will ignore all the text in a paper and just look for the equations
Mathematical notation is mostly a substitute for words and that's why those equations can be embedded in natural language and "read". Ignoring the words in a mathematical paper and just looking at the "funny symbols" doesn't make any sense. You're only seeing tiny glimpses of the actual reasoning and are probably missing most of it.
A mathematician may chose to write "B contains all elements of A, and A contains the element x.", or they may chose to write "A ⊆ B and x ∈ A". Same thing. Also note how the second example still had an english word in the middle of it. If that "and" was an "or" the sentence would have an entirely different meaning. Can't just ignore that stuff.
Sure you could replace that "and" with yet another symbol, and in something as simple as that nobody would really care, but in something more complex the mathematician would just be trying to produce an unreadable mess on purpose.