The Best Writing on Mathematics 2010

There is a tremendous amount of wonderful expository work being done on mathematics, but I doubt that I am alone in finding insufficient time to explore it all. I must be deliberate about finding ways to get myself to read the things I want (writing book reviews helps), but I know that I am doomed to be forever overwhelmed. The articles outside of my immediate interests, those that explore the diversity and the broader discipline of mathematics, are the ones that most often lose out to other priorities.

A collection like editor Mircea Pitici’s Best Mathematical Writing on Mathematics can ease this frustration. All of the material is accessible to a broad mathematical audience and includes essays on the history, philosophy, education, and practice of mathematics. The book includes articles, columns, books, and presentations of various sorts, including the popular press and journals of mathematics and mathematics education. All of the material was published in 2009. Many sources are sufficiently obscure that some of these papers could have easily been overlooked by even the most voracious mathematical consumer.

There is considerable variety here. Among the thirty-five pieces (not counting a thorough introduction by Pitici and a nice forward by William Thurston), we get personal reflections like Freeman Dyson’s discussion of types of contributors to mathematics and physics in his AMS Einstein Lecture “Birds and Frogs,” educational commentary such as a criticism of the role of calculus texts in education from Ann Kajander and Miroslov Lovric, historical exposition such as Judith Grabiner’s exploration of Lagrange’s interest in proving Euclid’s parallel postulate, and some popular goodies like Steven Strogatz’s New York Times column on modeling romantic relationships with differential equations. One can always quibble about what should or should not have been chosen for inclusion (Pitici points out that many decisions were guided by reprinting restrictions), but the material is thoughtfully selected overall.

What the reader will not find is much deep mathematical content. Indeed, there is almost no mathematical notation to be found in the collection. The editor emphasizes in the introduction that this is the best writing on mathematics, not in mathematics. Advanced topics such as information-based complexity and circle packing do appear, but they are usually broad invitations or narratives of mathematicians’ journeys through these topics and not detailed expositions. Everything in the book is meant to be accessible to an undergraduate.

The articles are grouped into vaguely titled sections (Mathematics Alive, Mathematicians and the Practice of Mathematics, Mathematics and Its Applications, Mathematics Education, History and Philosophy of Mathematics, and Mathematics in the Media), but most do not fit squarely under any one of these categories and so the assignment of essay to section is largely arbitrary. That’s not really a complaint so much as a concession to the nature of the compilation. Original citations are found in the table of contents; short biographies of the authors can be found at the end of the book. (I’ll nitpick briefly and suggest these data be presented right along with the articles.)

This is the kind of book with which mathematics students would do well to have a chance encounter — something that would do well lying around a math lounge. It is not the book one recommends for a student to learn how to mimic good writing for an impending thesis nor to learn any real new mathematics, but rather it offers a glimpse into how we mathematicians think and talk about our discipline — and why many of us are so passionate about it. The book is well-suited for college libraries; even though it compiles material published elsewhere, the sources are uncommon.

This is the first in what is intended as an annual publication and I am grateful for it, since I almost certainly would have missed most of these articles. I found the content variously engaging, informative, inspiring, silly, and annoying (identifying which is which is left as an exercise for the reader), but I feel enriched for having read all of them. It is a recommended collection for anyone with an interest in the practice of mathematics at pretty much any level.

Bill Wood is a mathematician, board game enthusiast, lousy disc golf player, and impending faculty member at the University of Northern Iowa.