These notes are from the 2018 version of the course. A significantly expanded new version will be made available once the 2019 course starts. 🤓

In everyday and literary English, grammar gaffes are embarrassing and occasionally misleading. In maths writing—assuming you already speak English quite well—it is less a matter of blushes and missed connections, as it is a matter of getting the form right.

We have mentioned before how a creative vocabulary is a hindrance in maths, rather than a boon, and how statements should be put as plainly and clearly as possible, rather than with a flourish. We have talked about conventional phrase-patterns and punctuation. The language elements we have least touched upon are verbs, and they are the ones that allow us to manipulate mathematical objects and express their relationships.

Today we discuss the tense, mood, and voice of verbs in formal mathematical writing. In particular, we usually write using a simple tense, in the imperative or interrogative mood, and in a balanced mixture of the active and passive voice. Finally, we warn against the temptation to abuse the grammar rules.