The Grammar According to West
by Douglas B. West
Summary
I have been accumulating observations about writing mathematics for many years. These conclusions arose both from writing textbooks and from noting writing errors commonly made by my thesis students and in papers submitted to journals.
My first objective was to train my students, thereby reducing the time needed to edit their theses. As the document grew, I made it publicly available in the hope that others may find it useful. I have received a broad range of responses, mostly positive. If you don't find it useful (or if you object to it on principle), then please ignore it. I hope to make some writers of mathematics (especially students and non-native speakers of English) aware of issues they may not have considered; small changes can produce mathematical writing that is easier to read by wider audiences.
After an introductory explanation of why care in writing mathematics is needed, I discuss (1) mathematical style, (2) notation and terminology, (3) punctuation and English grammar as used in mathematical writing, and (4) English usage for non-native speakers. Some points are minor distinctions, but even these make mathematical writing clearer when used consistently. My intent is not to make writing rigid, but rather to make it transparent to avoid distracting the reader by ambiguities or awkwardness in the flow of the narrative.
I note that a number of other articles and even books have been published on writing mathematics; see some of these here. I list these just to make alternative viewpoints available, without judgment pro or con. One contrast to note is that my list below focuses on relatively specific items. I have not yet included much discussion of the general structure of an article; some of these references discuss that.
Index of specific items
Introduction and Motivation
Live mathematical conversations use many shortcuts that are inappropriate in precise mathematical writing. The context is known by all participants, and shortcuts evolve to save time. Furthermore, the speaker can immediately clarify ambiguity. Without immediate access to the author, written mathematics must use language more carefully. Also, mathematical concepts are abstract, without context from everyday experience, so the writing must be more consistent to make the meaning clear. Outside mathematics, imprecise writing can still be understood because the objects and concepts discussed are familiar.
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