A Primer of Mathematical Writing

This is the second edition of a classic that first appeared twenty years ago. Most of the changes to writing since that time have had to do with the technology of publishing, and this book reflects that thoroughly.

The scope of the book is much broader than one might imagine. In addition to writing research papers, Krantz discusses writing review papers, articles for a broad audience, textbooks, grant proposals, letters of recommendation, editorials, book reviews, and email. About one-quarter of the book is devoted to the general art of writing. Here Krantz focuses on the errors he sees most commonly, referring the reader to Strunk and White’s classic The Elements of Style.

The remainder of the book focuses more on academic writing, and on mathematics in particular. For the latter Krantz recommends Higham’s Handbook of Writing for the Mathematical Sciences. Indeed, many topics treated in Krantz’s book are treated in more detail elsewhere, and Krantz provides four pages of references.

One apparent omission is a discussion of the formal style manual, such as The Chicago Manual of Style. Such books define a set of conventional answers to all the many issues that Krantz and others offer opinions on or leave to good judgment. Anyone hoping to publish is likely to have such a manual enforced on them, and be expected to adhere religiously to it — a process that takes some skill, work, and practice. Too many graduate students are shocked to learn about this when they submit their dissertation to the thesis office, and some mention might have been helpful here. Absent such a definitive guide, many writing choices are a matter of opinion, and many will disagree with details in Krantz’s advice — or anyone else’s.

The book’s faults are few. Though it does ask writers to consider the needs of readers whose native language is not English, it also includes too many attempts to be funny, which may backfire with that audience. The typeface is a bit wispy for your elderly reviewer. The eleven page index may prove helpful, but the nine page table of contents seems to violate the advice to waste no words.

This book is must reading for graduate students in mathematics and for current mathematicians whose writing could use a little help. Highly recommended.

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After a few years in industry, Robert W. Hayden (bob@statland.org) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He contributed the chapter on evaluating introductory statistics textbooks to the MAA’s Teaching Statistics.