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Five-Minute Mathematics

Ehrhard Behrends
American Mathematical Society
Publication Date: 
Number of Pages: 
[Reviewed by
David Richeson
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Politics, crime, sports, obituaries, celebrity gossip, the funnies — this is the standard fare in our newspapers. What about mathematics? A statistic here, a graph there, sure, but real mathematics? Our mathematics? We may find a brief mention of Fermat's last theorem or the Poincaré conjecture, but that is the extent of it. Wouldn't it be great to have a regular column devoted to the beauty and power of mathematics — the traveling salesman problem, nonstandard analysis, P = NP, the Banach-Tarski paradox, Russell's paradox, and so on? It would never happen, right?

It did. In 2003 and 2004 Ehrhard Behrends wrote 100 weekly columns called Fünf Minuten Mathematik (Five-Minute Mathematics) for the German newspaper Die Welt. In 2006 these columns were revised and expanded, images were added, and it became a book of the same title. Now the book has been translated to English and is available through the American Mathematical Society (AMS).

The book has remarkable breadth. It covers probability theory, number theory, the history of mathematics, finance, computer science, topology, music, famous numbers, and on and on. The book jumps from topic to topic in no particular order. While some subjects are common and easy to explain, some are shockingly abstract — the book contains columns devoted to the empty set, axiomatic systems, mathematical equality, and proofs by induction (Did I mention that these were in a newspaper?!).

Of course every mathematician will undoubtedly spot her or his favorite missing topic. (How could he omit the Euler's polyhedron formula and the Platonic solids?) But overall Behrends does a remarkably good job of choosing a wide variety of interesting topics.

Behrends does not dumb down the material, he does not apologize for mathematical jargon, he is not afraid of formulas, and most importantly he is truthful about the mathematics. Occasionally he aims too high (such as explaining the Monty Hall problem using Bayes' theorem) or too low (informing the reader that π is pronounced "pie"), but most of the time he finds the right balance between rigor and readability. In fact, I often found myself thinking, "that's a great way to explain this," or "that's a clever analogy to use."

The question I asked myself as I read this book was: who is the audience? It is not me, exactly. While I enjoyed reading the book very much, the topics were all familiar to me. These are the cool mathematical tidbits that we naturally acquire as a member of the profession. They are the intriguing facts that we share with our mathematically interested, if not mathematically trained, friends. It is this group who would love Five-Minute Mathematics — math-loving high school students, mathematics enthusiasts, and undergraduate mathematics majors. (I am somewhat surprised that the AMS is publishing this book, as their books are not typically aimed at this crowd. I hope the book reaches its intended audience.)

This book is sure to be enjoyed by everyone who loves mathematics. With chapters 3–5 pages long, it is the perfect book to read before bedtime, on the beach, or on the train or bus while commuting to work or school.

While we may never see this again — a newspaper column devoted to pure mathematics — we may rejoice that it happened once.

Dave Richeson is an associate professor of mathematics at Dickinson College. He is the author of the forthcoming book Euler's Gem: The Polyhedron Formula and the Birth of Topology (Fall 2008).