Read This!

The MAA Online book review column

Briefly Noted

February 2000

Readers of the College Mathematics Journal don't need me to explain this book to them, and will probably run and buy a copy for themselves without my say-so. For the rest of you, here's the scoop. For several years now, Ed Barbeau has been editing a regular column in the CMJ called "Fallacies, Flaws, and Flimflam." The column collects interesting examples of mistakes, fallacies, and other mathematical howlers. Some come from students, some from publications, others from contributors who have invented their own swindles and fallacies. This book (which acquired a "Mathematical" in the title to accomodate readers unfamiliar with the column) is a kind of "Best of FFF." It collects over 150 articles from the column, organized by topic into sections ranging from "Numbers" to "Advanced Undergraduate Mathematics," with some "Parting Shots" thrown in for good measure. There are some wild errors and some quite subtle ones, some things we recognize from many past student productions, others that are quite original, errors that reveal a creative mind at work. Collected together, they make a book of the sort one reads compulsively from cover to cover. I suspect it can be very useful in our teaching, since some of these creative mistakes would make great discussion starters. At times it's also a little daunting, because the author doesn't always explain what's wrong, leaving the reader with an interesting problem to think about. Other problems are discussed more carefully. For example, many articles give examples of arguments that "look right" and give the right answer, but are in fact incorrect; in these articles, the author often goes on to analyze under what circumstances this method will yield a correct answer. Mathematical Fallacies, Flaws, and Flimflam is definitely worth your time. (Fernando Q. Gouvêa)

In the early 1800s, the United States Military Academy at West Point was one of the only (perhaps it was the only) American colleges to pay serious attention to mathematics as an academic discipline and to make an effort to be up to date with what was then going on in Europe, particularly in France. Part of this effort was dedicated to building up a good mathematical library, which included a selection of the best books then current in Europe. Over the years, the library was augmented with many books, including many books written by West Point professors, who were encouraged to produce textbooks for their students (some of these were translations or adaptations of French books, but many were original works). As a result, the library at the Military Academy today contains an impressive collection of valuable sources for historians of mathematics. This book is a lovingly-prepared catalog of the materials at the USMA library that would be of interest to historians. A long introduction tells the story of the teaching of mathematics at USMA and of the building and preservation of its library. The catalog itself follows, and several valuable appendices round out the book. The first reproduces a catalog of the USMA library dating back to 1803. The second, which perhaps will be the most popular feature of the whole book, contains 30 photographs of title pages, frontspieces, and pages which contains annotations or other items of interest. Appendix 3 lists all the portraits of mathematicians to be found in books in the collection, and appendix 4 lists frontspieces found in many of the books. I suspect that few readers will want their own copy of this one, but this useful resource for historians would make a great addition to any mathematics library. (Fernando Q. Gouvêa)

Measuring the Universe is a pleasantly readable book that chronicles the human attempt to measure and make sense of the universe. It addresses the question of how it is possible to measure something indirectly. It begins with Eratosthenes and his attempt in the third century BC to measure the circumference of the Earth, and continues through to the relatively recent ideas of Stephen Hawking for measuring the size and age of the universe. The book was enjoyable to read when I turned off my mathematical curiosity. It is very historical in nature, describing not only the leaps in thought at various times in the past, but also the social and political landscape of the times when the various insights occurred or became accepted. I particularly enjoyed the discussion about the Copernican revolution. Yet I often wanted to see some of the math behind the different calculations. I wanted to see the math Eratosthenes used to calculate the circumference of the Earth, the old methods of calculating longitude and parallax, and the different methods to calculate distances to stars and galaxies.

The further I read the more I wanted to see some math in the book--not fuzzy generalizations for the math phobic, but real math and labeled diagrams and problems with real numbers worked out or with enough detail so that I could work them out myself. Then, on page 270, a formula appears at the top of the page in bold print. It is the formula for omega, the mass density of the universe. Yes! Some math and an explanation of each term in the formula! Reading further on the page, though, my heart sank on seeing the following series of statements referring to the formula:

At the risk of sending a great many readers running for cover, here . . . is the formula for omega. Consider it a souvenir, something a patient reader is owed for having made it so far with this book. We will not proceed to solve it.
This series of statements seems to say that the author believes that mathematics is just too hard for most people to understand or enjoy. I realized then that the entire book has been written from this point of view. The history seemed good but I wanted more mathematics and less fuzzy arguments. This is not really a book for historically-minded mathematicians, and I think it is not for the math phobic either. I feel it reinforces the idea that avoidance of math at all costs is an admirable quality. (Mary Shepherd)

Publication Data

Edward J. Barbeau,

Mathematical Fallacies, Flaws, and Flimflam. Mathematical Association of America, 2000. Softcover, 152pp., $23.95 ($19.00 to MAA members). ISBN 0-88385-529-1.

Joe Albree, David C. Arney, and V. Frederick Rickey, A Station Favorable to the Pursuits of Science: Primary Materials in the History of Mathematics at the United States Military Academy. History of Mathematics, vol. 18, American Mathematical Society and London Mathematical Society, 2000. Hardcover, xii + 272pp., $59.00. ISBN 0-8218-2059-1.

Kitty Ferguson, Measuring the Universe. Walker and Company, 1999. Hardcover, 342 pages, $27.00. ISBN 0-8027-1351-3.

Fernando Gouvêa (fqgouvea@colby.edu) is Associate Professor of Mathematics at Colby College in Waterville, Maine. His special interests include number theory, history of mathematics, science fiction, and Christian theology.

Mary Shepherd (shephemd@potsdam.edu) is Assistant Professor at SUNY College at Potsdam in Potsdam, New York. Her special interests include differential geometry and music.

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Read This! is the MAA Online book review column. Contributions are welcome; contact the editor if you'd like to be one of our reviewers. Books for review should be sent to the editor: Fernando Gouvêa, Dept. of Math&CS, Colby College, Waterville, ME 04901. Publishers, please check our reviews information page.

Copyright © 2000 The Mathematical Association of America

MAA Online is edited by Fernando Q. Gouvêa (fqgouvea@colby.edu).
Last modified: Wed Feb 02 21:30:51 -0500 2000