Bell curves are out. Fat tails are in. Thus reads the summary that aims to entice anyone scanning the table of contents of Steven Strogatz‘s The Joy of x: A Guided Tour of Math, from One to Infinity (Houghton Mifflin Harcourt, 2012) to read chapter 22, “The New Normal.” An expository masterpiece, from the one-sentence chapter descriptions in the table of contents to the extensive endnotes, The Joy of x has earned Strogatz the 2014 Euler Book Prize, awarded by the Mathematical Association of America at the 2014 Joint Mathematics Meetings in Baltimore. Named for prolific Swiss mathematician Leonhard Euler

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Danica McKellar is the recipient of the 2014 Joint Policy Board for Mathematics (JPBM) Communications Award. She is an actress (The Wonder Years, The West Wing), a published mathematician (while earning her bachelor’s degree in mathematics at UCLA), an advocate for mathematics education, and a New York Times best-selling author. McKellar’s books, blog, and public appearances have encouraged countless middle and high school students, especially girls, to become more interested in mathematics. Her books include Math Doesn’t Suck: How to Survive Middle School Math without Losing Your Mind or Breaking a Nail (2007), Kiss My Math: Showing Pre-Algebra Who’s Boss (2008), Hot

Read more →Would you consider use of the word “references” in the following sentence to be acceptable or unacceptable? The paper references several articles on global warming. How would you vote on the use of “referenced” in the sentence below? Yea or nay? During the press conference, the mayor referenced the recent floods. These two examples were among the dozens recently presented to a panel of about 200 writers, scholars, and critics. The editors of the American HeritageDictionary of the English Language poll the panel members annually on a broad range of usage questions. The effort is a reflection of the fact

Read more →Paul Zorn, St. Olaf College Part I: Introduction Part II: Mathematics in Literature Part III: What Is Mathematics? Part IV: Mathematical Language: Learning from Barbie Part V: Rule Books and Tour Guides: Two Live Questions Part VI: Lessons from History Part VII: Valuing Communication Mathematical communication is well done, and appropriately valued, by our associations and societies. The MAA, for instance, publishes no fewer than nine book series, all of them expository in one sense or another. MAA journals and e-publications have a similar focus. MAA journals are very popular. These include the Monthly, the Magazine, and the CMJ. See their respective

Read more →Paul Zorn, St. Olaf College Part I: Introduction Part II: Mathematics in Literature Part III: What Is Mathematics? Part IV: Mathematical Language: Learning from Barbie Part V: Rule Books and Tour Guides: Two Live Questions Part VI: Lessons from History Pedagogical writing is certainly hard work. But it’s an honorable profession, and has been so for a long time. I’d like to cite, as evidence, two historical examples in point: Augustus de Morgan, who wrote actual textbooks, and Abraham de Moivre, who wrote in what seems to me a notably pedagogical style. Consider first the British logician Augustus de Morgan (1806-71),

Read more →Paul Zorn, St. Olaf College Part I: Introduction Part II: Mathematics in Literature Part III: What Is Mathematics? Part IV: Mathematical Language: Learning from Barbie Part V: Rule Books and Tour Guides: Two Live Questions Next, I’d like to acknowledge two general questions that apply broadly in expository writing, but face textbook authors with particular force. First is what I call the rule book question. How would you help your kid excel at, say, soccer? Hand her a World Cup rule book to study? Or roll a ball out the back door and get out of the way? No sane

Read more →Paul Zorn, St. Olaf College Part I: Introduction Part II: Mathematics in Literature Part III: What Is Mathematics? Part IV: Mathematical Language: Learning from Barbie On, then, to mathematical communication with our students and in our classrooms. I’ll sometimes refer specifically to textbooks. But I think that the same general principles apply, mutatis mutandis, to the larger project of communicating mathematics to non-specialists. Or, as Thurston put it, attempting to convey ideas to people who don’t already know them. Communication with fellow specialists in a mathematical area seems to me to pose almost entirely different expository problems to those of

Read more →Paul Zorn, St. Olaf College Part I: Introduction Part II: Mathematics in Literature Part III: What Is Mathematics? OK, let’s get more serious and mainstream about mathematical communication as such, in service of mathematics itself. What, first of all, is this thing called mathematics that we’re hoping to communicate? Many people would mention patterns. For others, mathematics is just what mathematicians do. In any case, defining mathematics precisely, and non-recursively, is famously difficult. Perhaps it’s a moving target. The late William Thurston, who received a Steele Prize in 2012, had interesting things to say about this in a 1994 paper, “On Proof and

Read more →Paul Zorn, St. Olaf College Part I: Introduction Part II: Mathematics in Literature Before we get to the harder stuff, please indulge me in some random thoughts, from a defrocked English major, on mathematics and mathematicians in literature. Mathematics, mathematicians, and literature have non-empty intersection, as we all know. One might cite Flatland, various works of Lewis Carroll and John Updike, and Jorge Luis Borges‘s Library of Babel, which contains every possible book that can be written with the available font of symbols. (That’s infinitely many books, but at least it’s countable.) Mathematics plays interesting roles in all of these,

Read more →Paul Zorn, St. Olaf College Retiring MAA Presidential Address, Joint Mathematics Meetings, San Diego, January 11, 2013 Abstract: Mathematicians don’t just do mathematics. We communicate our subject too, by speaking, writing, teaching, illustrating, editing, explaining, and professing it, for expert and non-expert audiences alike. Words, pictures, equations, and other media may be well or poorly suited to the special purposes of mathematical exposition, and mathematical exposition may be good, bad, or indifferent, depending largely on its audience. But, as I will argue with examples, mathematical exposition is at its best real and valuable mathematics—and no less challenging or deserving of

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