There are many different kinds of writing (expository, technical, persuasive, narrative, etc.), each with its own objectives, practices, and idiosyncracies. The purpose of mathematical writing is to convey some technical material to an audience, so it is crucial to (1) know your audience and (2) be clear and concise.
Know your audience. Know the reasons why your audience is reading your writing. Find out what information they already know and what they don't know.
Be clear and concise. Don't use flowery language. Put away that thesaurus! Never use synonyms for technical terms. Short and direct sentences often work best. Don't worry too much about the rhythm of your technical writing. Eliminate unnecessary words.
Idiosyncracies of mathematical writing: The personal pronoun "I" is rarely used in technical writing. If you don't like using passive voice, try using "we." Use mathematical symbols to enhance the clarity and precision of your writing, not to make your writing look cool. Punctuate all mathematical symbols appropriately, and think carefully about whether to display (set apart on a separate line) large groups of symbols (like equations).
books on mathematical and technical writing.