Without jargon, it would be roughly impossible to talk about compound mathematical structures. But I certainly agree that more exposition and a greater number of worked-out examples are a great help when trying to understand abstract math.

It would also be great to have papers written in a hyperlinked format (after so many years of the web...) so that when you click on a jargon term, you get something like a Wikipedia article about that concept with a few examples and some exposition. Wikipedia itself would be fine with me, though academics might want more official peer review (see Scholarpedia).