For the last three years, Princeton University Press has published annually a handy collection of previously published articles under the title *The Best Writing on Mathematics*. Edited again by Mircea Pitici, the 2012 volume is now available.

The widely varying articles in these collections are of interest not only for the information they contain but also as useful models of expository writing in mathematics. As you read a selection, it is worthwhile reflecting on what you like and don’t like about the article and the way the author has chosen to present the material.

You can start with the question of what drew you to a particular article to start with. Was it the topic, author, title, or something else? What does this say more generally about techniques for capturing a reader’s attention?

* How is the material organized? Is there an organizing principle that governs the order in which topics are presented?

* Does the opening paragraph set the stage effectively? If so, how does the author achieve such a result?

* What factors make the article compelling to read? In what ways (and at what points) may it fail to keep your attention?

* What roles do word choice and sentence structure play in keeping the reader interested?

* What audience is the author trying to reach? Is he or she successful?

Such observations can help inform your own writing as you strive to improve your ability to communicate mathematics to your chosen audience.

Of the 24 selections in *The Best Writing on Mathematics 2012*, six articles are from MAA publications:

“Mathematics Meets Photography: The Viewable Sphere” by David Swart and Bruce Torrence. *Math Horizons*, 19(September 2011), pp. 14-17 and 19(November 2011), pp. 24-27.

“Dancing Mathematics and the Mathematics of Dance” by sarah-marie belcastro and Karl Shaffer. *Math Horizons*, 18(April 2011), pp. 16-20.

“How to Be a Good Teacher Is an Undecidable Problem” by Erica Flapan. *College Mathematics Journal*, 42(November 2011), pp. 350-354.

“How Your Philosophy of Mathematics Impacts Your Teaching” by Bonnie Gold. *College Mathematics Journal*, 42(May 2011), pp. 174-182.

“Augustus De Morgan behind the Scenes” by Charlotte Simmons. *College Mathematics Journal*, 42(January 2011), pp. 33-40.

“Was Cantor Surprised?” by Fernando Q. Gouvêa. *American Mathematical Monthly* 118(March 2011), pp. 198-209.

The MAA annually presents awards for the best expository writing published in its three journals and in *Math Horizons*, MAA’s magazine for students. These prize-winning articles are all available on the MAA website. Like the selections in *The Best Writing on Mathematics*, they serve as illuminating examples of expository writing in mathematics and deserve scrutiny not only for the ways in which they succeed but also for the ways in which they could have been better.

There’s always room for improvement and lessons to be learned from the efforts of others to present mathematical material.