And beyond RorHar's well-stated point, there is a degree to which advanced articles should be allowed to be advanced.  I am a trained mathematician, but I don't pretend that I should be able to understand this article, even when it's well-written and entirely fleshed-out.  Class field theory is complicated stuff and people spend years trying to understand even its basics.  It's a bit presumptive to come here and pretend like anyone from off the street should be able to read this article once and understand it.  I don't think this is an elitist way to think about it.  Math is hard sometimes.  The most we can hope for is that the lede is sufficiently "blue" that one could work their way back through the links and try to get some context for understanding this necessarily specialized article.