The Irrationals: A Story of the Numbers You Can't Count On
by Julian Havil
Princeton University Press: 2012 ($29.95)
The insides of this book are as clever and compelling as the subtitle on the cover. Havil, a retired former master at Winchester College in England, where he taught math for decades, takes readers on a history of irrational numbers—numbers, like √2 or π, whose decimal expansion “is neither finite nor recurring.” We start in ancient Greece with Pythagoras, whose thinking most likely helped to set the path toward the discovery of irrational numbers, and continue to the present day, pausing to ponder such questions as, Is the decimal expansion of an irrational number random?