Paul Zorn, St. Olaf College
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 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 websites for download information.
Mathematical exposition is the main focus of MAA publications, but MAA has no monopoly on this important area. One notable example from the AMS is the What’s Happening in the Mathematical Sciences series, now in its eighth iteration and pushing 15 years old. This tightly edited and punchy series describes recent developments in mathematics and its applications for general mathematical audiences.
The AMS’s Mathematical Moments series of one-page posters on mathematical topics, aimed at students, is another notable and, to my eye, successful expository effort. It’s successful to my ear, too. I post these Moments outside my office door and hear students discussing them.
MAA and AMS are not alone. SIAM News, too, is full of sharply written and well-edited exposition, forthright commentary, and, yes, news about industrial and applied mathematics.
Commercial and university publishers also do good work in communicating expository mathematics. The A K Peters series, now part of CRC Press, is one notable and long-running example of fine, beautiful, stylish, and well-edited mathematics.
The Best Writing on Mathematics series is another example, from Princeton University Press. This annual anthology, now in its third year, assembles a remarkably eclectic selection of good writing on mathematical topics from all over, ranging from the mathematics of dance and photography to the philosophy of mathematical discovery and invention.
As an MAA guy I’m proud on behalf of that Association to report that no fewer than 6 of the 24 articles in the 2012 edition appeared first in MAA publications, including the Monthly, Math Horizons, and the College Mathematics Journal. One of my favorites is a historical piece (“Augustus De Morgan Behind the Scenes”) by Charlotte Simmons, on Augustus de Morgan, from the College Mathematics Journal.
Our societies also recognize good exposition with prestigious awards, including the Allendoerfer, Beckenbach, Chauvenet, Euler, Evans, Halmos-Ford, JPBM Communications, Pólya, and Steele prizes.
Finally, to the mildly polemical part of my talk.
I propose that mathematical exposition be considered—not just by us, as mathematicians, but also by departments, colleges, universities, and the like—as a fully respectable mathematical activity.
I hasten to add that I think I’m preaching, here and now, mainly to the choir. Our societies, as the previous examples amply demonstrate, already respect and reward and promote good mathematical exposition, in at least some of its forms, just as they should.
But good mathematical exposition should be rewardable in what I referred to earlier as academic currency: tenure, promotion, and other forms of professional advancement. If societies like ours have a role to play here, it could be in advocating more strongly for broader and more accommodating professional reward systems for scholarly activity.
Given that I’ve spent much of my own mathematical career creating, editing, and promoting mathematical exposition, this may sound like special pleading. In fact, I have no personal axe to grind. My day-job institution, St. Olaf College, has what seems to me an exemplary policy on scholarly activity, defining it broadly, but emphasizing peer review to assure high standards and accountability. I find the example of Lynn Steen, now retired but formerly my departmental colleague and also a predecessor as MAA President (in 1985 and 1986), inspiring in this respect.
Like other forms of mathematical activity, mathematical exposition may be good, bad, or indifferent, depending significantly on its audience. (The quality of other forms of mathematical activity, come to think of it, also depends significantly on its audience.)
Mathematical exposition at its best is real and valuable mathematics. Mathematics is a big tent. Its vitality and growth depend on contributions from many directions. Telling its story takes everyone’s best efforts.
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For a report on Paul Zorn’s address, see the article by Claudia Clark.