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The noble idea that advanced mathematics can be made comprehensible to laypeople is tested in this sometimes engaging but ultimately unsatisfying effort. Mathematician and NPR commentator Devlin (The Math Gene) bravely asserts that only "a good highschool knowledge of mathematics" is needed to understand these seven unsolved problems (each with a milliondollar price on its head from the Clay Mathematics Institute), but in truth a Ph.D. would find these thickets of equations daunting. Devlin does a good job with introductory material; his treatment of topology, elementary calculus and simple theorems about prime numbers, for example, are lucid and often fun. But when he works his way up to the eponymous problems he confronts the fact that they are too abstract, too encrusted with jargon, and just too hard. He finally throws in the towel on the Birch and SinnertonDyer Conjecture ("Don't feel bad if you find yourself getting lost... the level of abstraction is simply too great for the nonexpert"), while the chapter on the Hodge Conjecture is so baffling that the second page finds him morosely conceding that "the wise strategy might be to give up." Nor does Devlin make a compelling case for the realworld importance of many of these problems, rarely going beyond vague assurances that solving them "would almost certainly involve new ideas that will... have other uses." Sadly, this quixotic book ends up proving that highlevel mathematics is beyond the reach of all but the experts.
Copyright 2002 Reed Business Information, Inc.
Adult/High SchoolIn May, 2000, the Clay Mathematics Institute posted a milliondollar prize to anyone able to solve any of what it considered the seven most important mathematical problems of the 21st century. They were chosen not for theoretical beauty alone, but because many of them deal with concepts in fields like physics, computer science, and engineering, and exist because practitioners in those fields are already using theoretical or practical design solutions that have not been mathematically proven. Devlin, "The Math Guy" from NPR's Weekend Edition, does a good job explaining the background of the problems and why theoretical mathematics as a discipline should matter to a general audience. Each problem has a chapter of its own and is given a treatment that, where applicable, extends back to the ancient Greeks. A passing knowledge of mathematics is important for taking in Devlin's work but a major in the subject is not, and this book should satisfy anyone looking for a layman's guide to modern theoretical mathematics. Or hoping to win a million dollars.
Sheryl Fowler, Chantilly Regional Library, VA
Copyright 2003 Reed Business Information, Inc.