A History of Mathematics

A History of Mathematics, Jeff Suzuki, 2002, xiii+815 pp., $125, ISBN-13 9780130190741.  Prentice Hall, Upper Saddle River, NJ 07458     http://vig.prenhall.com/home

This text “had me at hello.”  In the author’s introduction, Professor Suzuki explains “…the best way to understand history is to experience it.  To understand why mathematics developed the way it did, why certain discoveries were made and others missed, and why a mathematician chose a particular line of investigation, we should use the tools they used, see the mathematics as they saw it, and above all think about mathematics as they did.”

He delivers on the latter counts.  The text uses the language and notation of the original works being studied.  Suzuki does often include a running commentary in modern notation for the faint of heart, however.  There are many quotes from translations of original sources throughout the text, although I would have liked to have seen better referencing throughout the text in order to facilitate further study.  Where the author does not deliver is in the area of “why?”  The text has very little in the way of historical background and motivation, although most chapters do have a brief section of some historical introduction.  This is also not a book that emphasizes “cultural connections.”   This is a mathematics book, which, in fairness, the author points out in his introduction.

This text covers the usual ground for an undergraduate history of mathematics course.  All of the content is in the standard undergraduate curriculum.  The text serves as a nice introduction to the mathematical content students may not have seen at the time of taking a history of mathematics course.  The author begins with the mathematics of Egypt, Mesopotamia, the Greek world, China, India, and the Islamic world before moving on to Medieval and Renaissance Europe.  From there the text is divided into chapters based on famous men or subject matter: The Era of Newton and Leibniz, Analysis, Algebra, Geometry, and so on.  In choosing this text you can rest assured that the standard topics in an undergraduate history of mathematics course will be covered.  There are also some nice touches, with coverage of application of areas, early mathematical induction, and some extra material from Viète, and Hudde’s rules, for example.

Many instructors choose a text for exercises, and Suzuki’s text would be a good choice.  Exercises appear at the end of each section rather than each chapter, and typically involve using historical techniques to solve problems or solving actual problems from historical works.  There are also many examples throughout the text to give the reader guidance.  On an aesthetic note, the font is clear and crisp, as are the wonderful diagrams.  The text has fewer images than many history of mathematics books out there, but it does contain some nice images.

Professor Suzuki has written a solid history of mathematics text, one that I have used with success in my classes.  It covers the topics I need, at a level that is just right—not too difficult, yet still challenging.  It gives a flavor of the mathematics of each era, and shows students how the mathematics developed.  I can make up for the few places mentioned above where the text is lacking with outside readings and other materials.  Next time you are considering a text, give this one a good look.

Gary S. Stoudt, Professor of Mathematics, Indiana University of Pennsylvania