Customer Reviews

How to Write Mathematics

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This short booklet contains four essays about how to write mathematics papers and books. The essays by Steenrod and Halmos, two prominent figures of 20th century mathematics, stand out for their common sense, depth and lucidity. They bring forth essential strategic issues, such as the need to maintain a clear separation between the formal and informal parts of mathematical papers, as well as useful tactical issues such as choosing notation. In my opinion, the essays transcend the field of mathematics, and the principles that they delineate are applicable to all areas of scientific writing.

While information on how to write mathematics right is always of value, this book is not a strong example of the right way to show how to write it. The weakness is that there are very few {write way, wrong way} examples, which is the best way to learn. The explanations are generally textual in form, which when you consider that mathematics is based on the use of compact symbols, is not an effective manner of explanation. I found the book "Writing Mathematics Well: A Manual for Authors" by Leonard Gillman to be much clearer in explaining how to write mathematics.

The various authors of "How to Write Mathematics" set out to describe their own personal writing styles, beginning with an admission that there is a lack of consensus on this topic. Indeed, the book closes with a couple of pages by the last author critiquing the advice of the first. On including detailed proofs in your publications, for example, you will find one author prescribing and another proscribing the practice.

The essays were written independently and this shows in the overlap and the contradictions. Whereas I have been highly critical of multi-author books in the past, the approach seems to work in this collection. Recalling my own efforts in writing a book on a topic within another field, I found myself agreeing or disagreeing with the authors on the various points. I was relieved to note that as early as at least three decades ago, authors before me shared identical conflicts with editors and copyreaders.

Based on my limited experience in writing, I had developed a number of half-formed rules of thumb. Given the recommendations of writers more experienced than I as so boldly presented, I am likely to be more aggressive in applying these rules. I would recommend this book to those authors with at least a few writing efforts under their belts. Given the specific nature of the examples in the essays, however, it is likely that only mathematicians will fully appreciate this book.

Paul Halmos gives wonderful advice on how to write in mathematics. Get it.