This is an extraordinary book for anyone interested in the history of mathematics. The author notes in the preface that reading historical mathematics can be fascinating, challenging, enriching, and endlessly rewarding. He then proceeds to illustrate how to analyze and get the most out of original source material.
The idea for this short but insightful book originated from the author’s experiences while teaching the history of mathematics at Oxford University. Most historians of mathematics will be cognizant of many of the author’s observations and comments; however, the way that this author presents them is exceptional. After finishing this book, readers will be better prepared to ask thoughtful questions to better scrutinize historical writings and to appreciate and understand the significance of secondary and tertiary sources.
The book is partitioned into five chapters. The first (What Does It Say?) includes an excellent description on how to examine and evaluate a piece of historical writing. Using two historical passages, the author illustrates how to decipher and glean information from the material. A number of relevant questions that might be asked while perusing such material are included. The importance of comparing modern versions to the originals is highlighted. With respect to translations, the author aptly remarks that a good rendition will turn the words into English but leave alone the mathematics and notation used. Readers are urged not to just read what authors write but to observe how they say it in order to learn about how they think while writing it. The chapter ends with several short exercises intended to hone readers’ skill on the lessons learned.
The second chapter (How Was It Written?) begins with a delightful piece of mathematical writing. The reader is asked to determine the identity of the author as well as where and when the piece was written. After a short pause, the author shows readers how to sharpen their skills in order to analyze the passage in order to obtain the answers to his queries. Other questions that might be asked are discussed. There is also valuable information on how to obtain original source material in libraries and on the web and good suggestion on what sources would be good to begin working with.
In the third chapter (Pen and Ink), the durability, prestige, and dissemination of written material is discussed. In the fourth chapter (Readers) there is information on how to determine the intended audience for the source, the expected mathematical knowledge of the readers, and why it is necessary to check the mathematics. There are questions to ask in order to better determine what the author was thinking when the material was written. The chapter concludes with several examples for readers to practice their skills. The last chapter (What to Read, and Why), illustrates the importance of reading significant historical mathematics and how one might determine whether a piece of mathematics is noteworthy. There are suggestions for teachers on what sources may be apropos for a history of mathematics course where reading historical writing is required.
Another goal of the book is to help the readers see modern mathematics afresh, to learn more about mathematics, and to get a different perspective on familiar ideas. Readers are encouraged to go to source books or originals to engage with our predecessors and learn from them not just what that wrote but how they wrote that way and why.
Two of the things that endeared me to the book were summaries that were set out in boxes to remind readers of the key techniques discussed and the pauses for the reader to think and comprehend, which were aptly illustrated with the symbol on the left. The book may be directed at those interested in the history of mathematics, but the valuable lessons that can be learned in this book apply to reading original sources in other disciplines as well.
Jim Tattersall is Professor of Mathematics at Providence College, in Providence, RI.