[This is the first volume of a set of five entitled Pioneers of Mathematics; this review covers all five books. –Ed.]
This delightful five-volume set of mathematical biographies is a must for any high school or college mathematics teacher. Intended for a high school students or the interested general reader, these books can be enjoyed by anyone who wishes to learn a little about some of the most influential names in mathematics and how through their work they impacted mathematics specifically and society in general.
Bradley launches the series with Thales of Miletus (ca. 625 – ca. 547 B.C.E.) and concludes with youngster Sarah Flannery (1982– ). Each of the five volumes presents short biographies of ten mathematicians, so we get a look at fifty of the most influential and diverse mathematicians and practitioners of mathematics.
The volumes are arranged chronologically as follows:
(See the table of contents for a list of subjects by volume.) Each biography is ten to twelve pages long and covers both the life and work of the subject, with special attention paid to their most influential publications. The selection of subjects is culturally broad and diverse.
In selecting only 50 subjects, some favorites are missed, most notably Descartes, while others are included that are not usually among the top names, such as Benjamin Banneker. As the list of books shows, much more attention is given to recent (still living) mathematicians, including several women. These last two points are sound pedagogically, in that motivation comes by providing students with a means to identify with the study of mathematics. How better to do that then to show that mathematics was not invented by long-dead well-off white males?
The exposition is clear and easy to read, without being to simplistic or too heavy-handed. Each chapter stands alone and contains suggestions for further reading. Each volume contains a glossary of terms, and extended reading list as well as a list of the major mathematical organizations in the US. The biographies do not include references. However, given the audience and intended use of this work, this can be forgiven. On the other hand, one can argue that it is never too soon to lead by example and show good scholarship.
For the “long dead” subjects, much of the material presented consists of the most common biographies found in other sources. This means that some (not too many) of the "urban legends" about them are presented. The appropriateness using these legends, however, has been debated in the history of mathematics community of late. Proponents of their use cite, for example, the number of people who chose mathematics as a field in part because of reading E.T. Bell’s largely fanciful Men of Mathematics. But even those who favor their use believe students should be told that they are probably not quite true.
Since more modern mathematics is inherently more difficult, the difficulty of the mathematics increases with each volume. Volumes one and two are accessible to high school students. Volume three is more appropriate for a college math major. The last two volumes can be read by anyone, however, given that the topics and theorems mentioned would only be familiar to someone with an advanced degree. That fact might these two volumes become frustrating for a general reader.
Volume four includes biographies of several computer pioneers, and thus would be of interest to anyone with a computer leaning. Volume five contains biographies of John Conway and Stephen Hawking that would be of interest to and accessible to anyone. Volume five also contains biographies of mathematicians who work heavily in industry (Yau, Chung, Daubechies) that would be of interest to many students. By ending with such a young mathematician as Sarah Flannery, Bradley leaves the message that mathematics knows no boundaries: race, sex or age.
The greatest strength of the five Pioneers in Mathematics volumes is the breadth and diversity of the subjects selected. Any reader will find names they are familiar with as well as names they know little or nothing about. Though the mathematics in the latter volumes is more advanced, Bradley does an excellent job of simply stating the most general ideas of the topics and focusing on how the subject impacted that area of study. However, in presenting the lives and work of several of the more recent subjects whose work is on the cutting edge of math and science, the author can only list subjects and publications, which becomes repetitious, as well as irrelevant for the non-specialist.
Overall, this series of 50 biographies of mathematicians leaves the reader with a clear impression of the impact each subject had on the field of mathematics and the wider field of science in general. I thoroughly enjoyed these gems, and would recommend them to anyone, teachers and students especially, who want to get a good feel for the people behind the mathematics, past and present.
Amy Shell-Gellasch is a Faculty Fellow at Pacific Lutheran University in Tacoma, WA. She is actively involved with the MAA and its History of Mathematics SIGMAA as chairperson to several committees. She enjoys researching and promoting the use of history in the teaching of mathematics through editing books and organizing meetings. She received her bachelor’s degree from the University of Michigan in 1989, her master’s degree from Oakland University in Rochester, Michigan in 1995, and her doctor of arts degree from the University of Illinois at Chicago in 2000.
The Birth of Mathematics: Ancient Times to 1300
The Age of Genius: 1300 to 1800
The Foundations of Mathematics: 1800 to 1900
Modern Mathematics: 1900 to 1950