The Art of the Infinite: The Pleasures of Mathematics

The Art of the Infinite: The Pleasures of Mathematics

The Art of the Infinite: The Pleasures of Mathematics

The Art of the Infinite: The Pleasures of Mathematics


Robert Kaplan's The Nothing That Is: A Natural History of Zero was an international best-seller, translated into ten languages. The Times called it "elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf" and The Philadelphia Inquirer praised it as "absolutely scintillating." In this delightful new book, Robert Kaplan, writing together with his wife Ellen Kaplan, once again takes us on a witty, literate, and accessible tour of the world of mathematics. Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved that infinity can come in different sizes, the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics. The Kaplans guide us through the "Republic of Numbers," where we meet both its upstanding citizens and more shadowy dwellers; and we travel across the plane of geometry into the unlikely realm where parallel lines meet. Along the way, deft character studies of great mathematicians (and equally colorful lesser ones) illustrate the opposed yet intertwined modes of mathematical thinking: the intutionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it. "Less than All," wrote William Blake, "cannot satisfy Man." The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination.


Things occupy space—but how many of them there are (or could be) belongs to time, as we tick them off to a walking rhythm that projects ongoing numbering into the future. Yet if you take off the face of a clock you won't find time there, only human contrivance. Those numbers, circling round, make time almost palpable—as if they aroused a sixth sense attuned to its presence, since it slips by the usual five (although aromas often do call up time past). Can we get behind numbers to find what it is they measure? Can we come to grips with the numbers themselves to know what they are and where they came from? Did we discover or invent them—or do they somehow lie in a profound crevice between the world and the mind?

Humans aren't the exclusive owners of the smaller numbers, at least. a monkey named Rosencrantz counts happily up to eight. Dolphins and ferrets, parrots and pigeons can tell three from five, if asked politely. Certainly our kind delights in counting from a very early age:

One potato, two potato, three potato, four; Five potato, six potato, seven potato, more!

Not that the children who play these counting-out games always get it right:

Wunnery tooery tickery seven Alibi crackaby ten eleven Pin pan musky Dan Tweedle-um twoddle-um twenty-wan Eerie orie ourie You are out!

This is as fascinating as it is wild, because whatever the misconceptions about the sequence of counting numbers (alibi and crackaby may . . .

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