This list sounds like new programmers complaining about the difficulty of language syntax - which largely vanish once you know enough that it melts into the background and poses no significant cognitive burden.  They are <i>valid</i> observations, but they miss the point that (generally speaking) mathematics is about communicating ideas <i>to other people who speak the language</i>.  Most high level mathematics involves both a great deal of implicit knowledge, and potentially introduces completely new ideas that may not be easily expressed with existing terminology.