The moment of proof: mathematical epiphanies

Donald C. Benson9780195117219, 0195117212

When Archimedes, while bathing, suddenly hit upon the principle of buoyancy, he ran wildly through the streets of Syracuse, stark naked, crying “eureka!” In The Moment of Proof, Donald Benson attempts to convey to general readers the feeling of eureka–the joy of discovery–that mathematicians feel when they first encounter an elegant proof.
This is not an introduction to mathematics so much as an introduction to the pleasures of mathematical thinking. And indeed the delights of this book are many and varied. The book is packed with intriguing conundrums–Loyd’s Fifteen Puzzle, the Petersburg Paradox, the Chaos Game, the Monty Hall Problem, the Prisoners’ Dilemma–as well as many mathematical curiosities. We learn how to perform the arithmetical proof called “casting out nines” and are introduced to Russian peasant multiplication, a bizarre way to multiply numbers that actually works. The book shows us how to calculate the number of ways a chef can combine ten or fewer spices to flavor his soup (1,024) and how many people we would have to gather in a room to have a 50-50 chance of two having the same birthday (23 people). But most important, Benson takes us step by step through these many mathematical wonders, so that we arrive at the solution much the way a working scientist would–and with much the same feeling of surprise.
Every fan of mathematical puzzles will be enthralled by The Moment of Proof. Indeed, anyone interested in mathematics or in scientific discovery in general will want to own this book.

Amazon.com Review The world described by mathematics might seem strange and daunting, but it is our world nonetheless. If you’ve ever experienced the pleasure of a sudden flash of mathematical insight–even while balancing your checkbook–then you know how miraculous a few digits and an equal sign can become at just the right time. Mathematician Donald C. Benson is intimately familiar with this phenomenon, and he has written The Moment of Proof: Mathematical Epiphanies to remind us that math can be as much fun as mountain climbing (and, of course, just as challenging). Part textbook, part puzzle book, it rewards our hard work with a steady flow of wide-eyed moments of clarity as we see how simple and elegant even the most frightening problem can be.
Benson covers classic problems like the sliding-tile and birthday-matching puzzles, but also delves into abstractions: counting, sorting, and “interesting numbers” all jump into his spotlight. This is fascinating enough, but his explanations of Russian peasant math and the secrets of the abacus have just the right mix of concreteness and abstraction to please anyone but the terminally mathphobic. Benson does expect quite a bit from his readers; paper and pencil are essential for complete understanding. But with each new epiphany, each new glimpse into the workings of the world, the effort invested in The Moment of Proof is returned, with interest. –Rob Lightner