Impossible? : surprising solutions to counterintuitive conundrums /

Readers familiar with Havil's Nonplussed! (CH, Oct'07, 45-0924) will know what to expect from Impossible?. Havil (Winchester College, UK) once again explores a variety of mathematical results and problems that at first appear to be self-contradictory, or stated in such a way that no solution could exist. In each case, he then either sketches a proof of why the result is not contradictory, or explains the solution to the seemingly unsolvable problem. As with Nonplussed!, this book relies heavily on results from probability, though more than half the chapters describe results and problems in other branches of mathematics. The presentation is fresh and fun. Some of the results, like the Banach-Tarski paradox and Braess's paradox, were the most enjoyable as they demonstrated that delicious sense of mystery that mathematics sometimes elicits. Like a magician revealing secrets, Havil maintains this sense through most chapters, dropping the punch line at just the right moment. This reviewer had hoped that the book would be written in such a way that general readers would understand most of the problems and results. "Impossible?" Perhaps not. Though Havil relies on postcalculus mathematics in many chapters, he does achieve this in a surprising number of instances. Summing Up: Highly recommended. Upper-division undergraduates through professionals. J. T. Noonan Mount Vernon Nazarene University