The motivation behind nearly all writing is to communicate. With the end goal to communicate well, you should consider both what you want to communicate, and to whom you plan to communicate it. This is no less valid for mathematical writing than for any other type of writing. The primary goal of mathematical writing is to assert, utilizing carefully developed logical conclusions, reality of a mathematical statement. Careful mathematical readers don't assume that your work is all around established; they should be persuaded. This is your first goal in mathematical writing.
I'd like to offer an autistic perspective to writing, if I may.
Once we decide to communicate with the world, many of us on the spectrum often take the world very "literally". We use writing to sort and organize our thoughts more easily, and not necessarily to communicate. Many of us do our thinking on paper, and that goes for working through math problems. Those of us with short term memory deficiencies, use writing to orient our lives in time and space. Words are abstract symbols that can be used by the wary for wayfinding in a hostile world..."danger...high threats, low threats, suspicious colours, hostile textures, safe place, safe people, safe noises".... Words provide us with a kind of abstract proprioception.