A Guide to Writing Mathematics

A guide to Writing Mathematics is a 17-page guidebook by Kevin P. Lee on the topic of mathematical writing, presumably written for Lee's students.

Motivation

As you advance in mathematics, it becomes increasingly important to demonstrate understanding of your study — true mathematical writing is not to be confused with "showing your work."

Mathematics in grammar

Lee's position on mathematics' place within English grammar coincides with that of other authors [cite:@lee2010advice]: formulae occur as sentences, or as part of sentences. Lee goes on to inspect the grammatical structure interior to the formulae themselves, suggesting that certain figures serve as complete sentences, with the usual subject-verb-object structure, while others act as nouns. As an example of the former, take the equation "$1+1=2$," in which "$1+1$" is the subject, "$=$" is the verb, and "$2$" is the object.

Mathematical figures are to be punctuated as you would any other piece of writing.

Structuring your paper

Organisation is important.

• Start with an introduction.

  • Just as in traditional writing, it is greatly beneficial to lead with a "hook."

  • Provide an overview of the paper. What you'll do, possibly how you'll do it, and where it'll take you.