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9 November 2001

A History of Math for the Masses

Jan Gullberg. Mathematics From the Birth of Numbers. Technical illustrations by Pär Gullberg. W. W. Norton & Co., 1997. 1093 pages.
ISBN0-393-04002-X

Reviewed by Sheldon Greaves

 

 

In my previous review I took a look at Georges Ifrah's The Universal History of Numbers. This week's review covers a book that makes an excellent supplement to Ifrah's text, and is a fascinating study in its own right.

Mathematics From the Birth of Numbers by Jan Gullberg is a playful yet well-crafted trip through the historical development of mathematical methods and discoveries. As with Ifrah's book, Jan Gullberg, who died the year after this book was published, was not a professional mathematician. Although Gullberg was trained as a surgeon, he falls squarely into the ranks of the amateurs.

If you don't know a great deal about math, this book will help you gain a greater appreciation of the kinds of discoveries and insights that have pushed the frontiers of mathematical thinking. If you have studied math (or remember much of what you studied), this book will serve admirably as a refresher although it is not really written as a pedagogical text. It serves better as a reference or just something that is very fun to read.

Gullberg's text is peppered with little cartoons, rhymes, limericks and other whimsical asides. These give his book a gentle and charming humor that lightens an otherwise daunting subject. He also includes illustrations from some of the great mathematical treatises of the past 400 years. Gullberg is someone who is clearly on intimate terms with the historical literature of mathematics. When he describes the works of great mathemeticians, one gets the distinct impression that he has actually read their works in their original forms. Since Gullberg, like many well-educated Europeans (he was a native of Sweden) is comfortable in a number of languages, he may well have done just that in preparing to write this book.

The early sections on numbers and counting are interesting, but are nowhere near as comprehensive as Ifrah's study. However, where Gullberg really shines is when he gets into concepts like powers and logs, combinatorics, symbolic logic, set theory, functions, geometry, trigonometry, vectors, calculus, probability theory, differential equations, and many other topics. The scope of this book is very impressive. Even if you have been steeped in mathematical thought, chances are if you spend some time with this book, you'll learn something new.