Overview of how to write mathematical ideas clearly, precisely, and in a useful structure.
Mathematics is written so that ideas can be checked, reused, and understood by other people. A correct idea may still be hard to follow if it is written poorly. Good mathematical writing makes the structure visible.
This chapter introduces the basic craft of writing mathematics. It explains how to organize a mathematical text, how to state definitions and theorems, how to write proofs, and how to avoid common sources of confusion.
Mathematical writing should be precise, but it should also be readable. Symbols are useful when they reduce ambiguity. Words are useful when they explain purpose, context, and meaning. A good text uses both.
The goal is not decorative style. The goal is clear communication. A reader should know what is being defined, what is being claimed, what has been proved, and how each part connects to the next.