# Ten simple rules for mathematical writing

Mathematical writing is the type of writing where mathematics is used as a primary means for expression, deduction, or problem solving. It is fundamentally different from creative and expository writing for two main reasons:

- it involves the interplay of two languages (natural and math),
- it requires much slower reading (it expresses complex ideas that must often be read and pondered several times).

As a result, many of the rules and suggestions found in writing style manuals are inadequate and/or do not apply. We propose an approach to mathematical writing, based on a set of simple composition rules. These rules are outlined in a slide presentation from an April 2002 lecture at MIT (edited later), and focus on the structure of the entire document (the content and the interconnections of different parts):

*** Organize in segments**

*** Write segments linearly**

*** Consider a hierarchical development**

*** Use consistent notation and nomenclature**

*** State results consistently**

*** Don’t underexplain – don’t overexplain**

*** Tell them what you’ll tell them**

*** Use suggestive references**

*** Consider examples and counterexamples**

*** Use visualization when possible**

The lecture slides can be freely downloaded and used for personal or educational purposes.