If, as you say, "[a] natural language is rooted in the evolution of a culture’s conventions" and "math is formal, which means that formality is a social stance," then math must be a natural language.

You (and your strenuous example in particular) deal more with notation and not language per se. (See e.g. "language" of music versus its notation.)

Totally off topic, but is there something you don't hate? (Except your pet ideas of cosmic horror etc., that is.)