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.