As the title suggests, Wells expects readers to do more than passively absorb the information he presents in this insightful survey of fundamental mathematical concepts. Dozens of illustrative brainteasers challenge readers to flex their own mathematical muscles as they read about the feats of the discipline's superstars, from Euclid to Euler. (It may console readers defeated by the harder puzzles to learn that giants such as Descartes, Leibniz, and Gauss have published erroneous work and that some centuries-old conundrums continue to vex and confound the best contemporary mathematicians.) But besides introducing us to fascinating personalities, Wells explains how a mathematician probes for a solution or constructs a proof, why a mathematician cannot use the same tools as a scientist, and why humans still outperform computers in perceiving hidden geometric relationships. For the nonmathematican looking for a helpful and entertaining guidebook to the wondrous world of numbers, here it is.