Final Perspectives

The purpose of this article is not to offer advice about how to write mathematics well. Such advice can be found in many places. However, I do have three pieces of very general advice, which inform the rest of the article. The first is to be clear about your intended readership; for example, if you want what you write to be understood by an undergraduate, then do not assume knowledge of any terminology that is not standardly taught in undergraduate mathematics courses. The second is to aim for this readership to be as wide as possible. If, with a small