I am in complete agreement. I've done a fair amount of teaching, which is to say I was employed to communicate information, such that someone else (from a fairly random selection sample) could and would remember it well enough to actually use the information productively.

I have done this so much that I feel poorly abou tleaving the last paragraph as it is, given that I know there is most certainly a way to find a more parsimonious way to express what I am saying, and I think that is the trust of why mathematical language (and the language in wikis, or APIs, for example) is succinct to the point of absurdity.

Everyone is striving for what's called maximum information density, communicating as much data with as few words as possible, and they do so in the jargon of their respective fields of interest. The problem is, those that are not specialized in that field cannot decipher the language well enough to gain anything of use from their efforts at being succinct. Quite the contrary, the field of potential interest becomes even less appealing for having appeared so mentally taxing to parse.

Reddit has this ELI5 idea, which I think stems from Denzel Washington's character in the movie "Philadelphia" (Mr. Washington plays an attorney defending an AIDS patient who has been unduly fired) saying "Explain it to me like I'm five years old", to get people to reduce their use of jargon and get to the heart of the matter.

Needless to say, the point I am making is that it is one of the great intangibles to be able to communicate one's self effectively, and in my experience is only done well when the communicator understands the level of interest and/or understanding of the communicatee, and can adjust their vocabulary "filter" accordingly.

I think math is particularly tough in this regard because of the amount of time that goes into understanding topics that might be complex for an untrained observer (like an Eigen value, for instance, which are critical for a basic understanding of linear regression).