The Irrationals

An entertaining and enlightening history of irrational numbers, from ancient Greece to the twenty-first century.

The ancient Greeks discovered them, but it wasn’t until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define – and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

‘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 v2 or p, 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?’‘ Anna Kuchment, Scientific American

‘The Irrationals is a true mathematician’s and historian’s delight.’ Robert Schaefer, New York Journal of Books

Author Biography

Julian Havil is the author of Gamma: Exploring Euler’s Constant, Nonplussed!: Mathematical Proof of Implausible Ideas, Impossible?: Surprising Solutions to Counterintuitive Conundrums, and John Napier: Life, Logarithms, and Legacy (all Princeton). He is a retired former master at Winchester College, England, where he taught mathematics for more than three decades.