An Introduction to the History of Mathematics, 6th edition, Howard Eves, 1990, xviii+775 pp., $142, ISBN 0-03-029558-0. Brooks/Cole [Thomson Learning, Inc.], Pacific Grove, CA 93950 http://www.thomsonedu.com
What do you want from your history of mathematics course? Not enough new teachers of the subject ask this question, and fewer still know that most authors will tell you what they are presenting. Howard Eves gives you his opinion in the introduction to his classic text: "In the belief that a college course in the history of mathematics should be primarily a mathematics [his italics] course, an effort has been made to inject a considerable amount of genuine mathematics into this book. It is hoped that a student using this book will learn much mathematics, as well as history."
This text does indeed introduce the reader to the history of mathematics, but it is not overly historical in the sense that newer texts [those of Katz and Suzuki, for example] are. For the most part the notation is modern, as are the explanations. For the novice teacher, this works very well; with more experience one might like to see the mathematics as it was actually done at the time. All the usual topics are here. In fact, one could argue that they are the usual topics because Eves made them so! The book itself is a wonderful read. The emphasis, however, is on biography and anecdotes, not as much on mathematics. Oh, but what anecdotes! After all, this is the man who wrote the wonderful In Mathematical Circles series of books. It is the stories and trivia that will stick with the reader. For future mathematics teachers, this is definitely not a bad thing, as these stories can be used to motivate and entertain students in the mathematics classroom. The book also contains illustrations, maps, pictures of mathematicians, and pages of famous works. These not only enhance the readability of the text but can also be used by future mathematics teachers in their classrooms.
Mathematics is not done in isolation and Eves’ text recognizes that. Throughout the text we find relationships between mathematicians and their times and the new “Cultural Connections” contribute to this emphasis. "Cultural Connections" are new to this edition and are written by the author’s son, historian Jamie Eves. In these brief essays the younger Eves gives an overview of the history of each time period, including social and political topics. This places this text in the middle ground between books that pay little attention to background history and the relationship of mathematics to the broader culture and books [like those of Calinger and Cooke] that excel in this area.
What most people love about Eves’ book [and this reviewer is no exception] are the "problem studies" and "essay topics" at the end of each chapter. While the problem studies are not always directly connected with the history contained in the chapter, they do fit the time period. These problems are non-trivial, but they allow the student to investigate for him/herself some interesting mathematics. They can also be done in the classroom. This is where Eves does "inject a considerable amount of genuine mathematics into this book." The problem studies and essay topics are a great help to the beginning history of mathematics instructor who wishes to assign projects to students but has yet to develop a collection of her own. These are also useful for other mathematics courses where the instructor wishes to interject some history into the course. One can find an appropriate problem study for most any course in the standard undergraduate curriculum. Instructors should be warned, however, that the book does include a fairly complete set of answers to the problem studies.
If you are teaching a history of mathematics course for the first time, you should give serious consideration to this text. You can feel comfortable in the knowledge that hundreds of your colleagues have taught successful courses using the book. If you have taught history of mathematics before, likely you have seen this book, but if not, get it and read it. You will use the anecdotes forever. If you do not teach history of mathematics, but want to enliven your class with ready-made historical projects, look no further.
Gary S. Stoudt, Professor of Mathematics, Indiana University of Pennsylvania