Infinity is an awfully big subject, as Peter Pan might have said. Indeed there is not just one infinity, but infinitely many of them. Grappling with infinity is one of the main themes of mathematics, physics, astronomy, religion, and philosophy. ‘The infinite! No other question has ever moved so profoundly the spirit of man,’ said the German mathematician David Hilbert. It has even driven men mad.

John Barrow has written over a dozen expositions of cosmology and mathematics, including The Book of Nothing (Pantheon Books, 2001). He has here produced a popular and informative book for the interested layman, surveying infinity and its mind-boggling phenomena.

Any book on infinity must begin by distinguishing the notions of potential