I'll try to clarify mine: yes, a plus sign vs. a capital sigma can be quickly explained. Let's imagine you're reading a short paper about, say, signal processing, and it says in a footnote or prefatory matter "we use tau for 2 pi". Also it uses the sum notation I brought up. Oh, and the exponential is different too: maybe one of these https://math.stackexchange.com/questions/30046/alternative-n... or maybe just the electrical-engineering angle symbol for exp(i theta).

Now you start reading the actual new material but even the fourier series looks all different and you're like "why is the author imposing this cognitive tax on me?" You can work through it, but why? The author must be a weirdo.

That'd be a reasonable reaction. But if notational trivia matter to those of us "with a freakish knack for manipulating abstract symbols" (http://worrydream.com/KillMath/) then they must also matter as a barrier to people who are more average in that regard. I agree if you're saying that something like sigma vs. plus sign is far down on the list of ways to improve mathematical communication -- even any notational reforms would not come first. (Though see http://cognitivemedium.com/ for some more thoughts on how computers doing what paper can't opens up new possibilities.) I also agree that learning must be active -- learning isn't just a matter of more efficiently pouring knowledge into a student's head. The difficulty can be roughly divided into accidental and essential; you must do well at engaging with the essential difficulty of the subject to engage well at all. But smoothing the accidental, trivial difficulties is not, in aggregate, trivial.