This book grew out of a few casual hallway conversations in the Colby College Mathematics Department about two years ago. but its roots are much deeper and older than that. For many years we have been interested in the history of mathematics, both for its own sake and as an aid in teaching mathematical concepts to a wide range of audiences. One of us has used it as a major ingredient in several college mathematics texts for liberal arts students and as an important part of his contributions to an NCTM Standards-based high school mathematics series. The other has done considerable background research in the field, has participated in the Mathematical Association of America's Institute for the History of Mathematics and its use in Teaching, and teaches a course in the history of mathematics at Colby. We are convinced that knowing the history of a mathematical concept or technique leads to a deeper, richer understanding of the concept or technique itself.
Unfortunately for teachers and other people with some interest in mathematical history but relatively little time to pursue it, most books on the subject are dauntingly large. If you want some historical background as you prepare to teach quadratic equations or negative numbers, or if you are just curious about the history of π or the metric system or zero, where would you look? The indexes of most history books will point you to a disjointed scattering of pages, leaving to you the task of piecing together a coherent picture. A topical search on the Internet is likely to inundate you with information, some reliable, some spurious, with little guidance as to which is which.
We decided to write a book with your needs in mind. The main part of this book is a collection of twenty-five short historical sketches about some common ideas of basic mathematics. These sketches illustrate the origins of an idea, process, or topic, sometimes connecting seemingly distinct things that share common historical roots. They are preceded by a brief panorama of the history of mathematics, from its earliest days to the present. This provides a skeletal framework of important people and events that shaped the mathematics we know today, and it supplies a unifying context for the separate, self-contained sketches. Of course, the choice of sketch topics was quite subjective; we were guided partly by our own interests and partly by our sense of what might interest teachers and students of mathematics. If you would like to suggest a sketch topic for the next edition of this book, we invite you to submit it to Oxton House Publishers, either by mail to the address on the copyright page of this book or by e-mail to one of the authors.
We have made every effort to reflect accurately the historical facts as they are known today. Nevertheless, history is far from an exact science, and incomplete or conflicting sources often lead to conflicting judgments of fact among scholars. Some stories about mathematical people and events have evolved over many years, creating a body of "folklore" with very little hard documentary evidence to support it. Despite their potential to annoy historical scholars, many of these stories — like folk tales in every culture — are valuable, either as allegories or as mnemonic "hooks'" to help you (or your students) remember a mathematical idea. Rather than ignore such anecdotes entirely and lose their value, we have opted to include some of the more interesting ones, along with appropriate cautions against taking them too literally.
To help you track down more information about any topic that interests you, the section entitled "What to Read Next" is an annotated list for further reading. It includes some pointers to reference works, but its heart is a short "ought-to-read" list of books that we think anyone interested in the history of mathematics probably would enjoy.
A note about notation: In recent years, some history books have been using B.C.E. ("before the common era") and C.E. ("the common era") in place of the more traditional B.C. and A.D., respectively. Depending on which historian one consults, this is either (a) the notation of the future for historical literature, or (b) a passing ''politically correct" fad. Without taking a position on this question, we have opted for the notation that we believe to be more familiar to most of our potential readers.
Acknowledgments
We are indebted to many colleagues from near and far for sharing their knowledge and for their forbearance in responding to our sometimes peculiar questions. In particular, we thank mathematics education consultant Sharon Fadden in Vermont, Jim Kearns of Lynn-field High School in Massachusetts, and Bryan Morgan of Oxford Hills Comprehensive High School in Maine for reading and commenting on earlier versions of the book. Special thanks also to Georgia Tobin for creating the TEX symbols for Egyptian and Babylonian numerals, and to Michael Vulis for converting them to PostScript format; to Robert Washburn of Southern Connecticut State University for providing some of the material in Sketch 6; and to Eleanor Robson, who generously gave us permission to use one of her drawings of Old Babylonian tablets (on page 63).
We are deeply grateful that one of us was able to participate for two summers in the MAA's Institute for the History of Mathematics and its use in Teaching. IHMT helped to transform a lifelong interest in the history of mathematics into a solid base of knowledge on which it was easy to build. Special thanks to IHMT organizers Fred Rickey, Victor Katz, and Steven Schot, to the Mathematical Association of America, its sponsoring organization, and to all the IHMT colleagues — an interesting, varied, knowledgeable, and helpful bunch of people. Many of them answered questions and made useful suggestions while this book was being written, earning still more of our gratitude in the process.
Our debt to the many historians of mathematics whose work we read and used as we were writing this book is enormous. Were it not for the giants on whose shoulders we attempted to stand, we couldn't possibly have done the job. We have tried, in bibliographical notes scattered throughout the book and in the ''What to Read Next" section, to point our readers towards some of their work.
We also would like to thank Don Albers, Martin Davis, David Fowler, Julio Gonzalez Cabillon, Victor Hill, Heinz Lüneburg, Kim Plofker, Eleanor Robson, Gary Stoudt, Rebekka Struik, and the members of the Historia Mathematica group for their answers to our questions. Of course, any mistakes that remain are our own.