Ten Simple Rules for Mathematical Writing

Dimitri P. Bertsekas

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.

https://notebooklm.google.com/notebook/4729fd06-9ad5-4fc4-bc13-e44f680d13ca/audio

It can be used while viewing the slides

Ten Simple Rules Essay by ChatGPT