An infinitely entertaining and informative journey into mathematical thinking

Robert Kaplan's The Nothing That Is: A Natural History of Zero was an international best-seller, translated into eight 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.

Using the art of the middle distance, that which is close enough for humans to draw by hand, the authors, who founded the all-inclusive educational experience they call The Math Circle, approach the concept of infinity through a variety of human minds. They describe the usual suspects (Pythagorus, Descartes, Leibniz) and many who would escape notice in a less-comprehensive work. They work through the mathematics in accessible text and illustrations, pulling in illuminations from an unexpected array of sources, including children's nursery rhymes and fiction of past ages.
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"Robert and Ellen Kaplan clearly relish the chance to expound the beauty of their subject, in prose that performs some glorious turns. They mix weighty but approachable maths with imagery and allusion, beginning with number and heading persuasively into the unknown. As the awesome presence of those infinite infinities finally takes hold, the mind reels and hairs stand on end. This is mathematics for the soul--just the way it should be."--New Scientist

"Anyone interested in a serious introduction to mathematics will delight in this volume. The Kaplans' background in languages and linguistics inclines them to a depth of literary allusion that few writers in any technical field can match. Robert Kaplan's prior book, 'The Nothing That Is: A Natural History of Zero,' remains, for my money, the best popular mathematics book ever written."--Margaret Wertheim, Los Angeles Times Book Review

"Guides the reader through some extremely difficult mathematical ideas in ways that are both imaginative and diverting. Mathematics is often said to be the science of the infinite; the Kaplans want us to appreciate mathematics as the art of the infinite, an art which involves invention, narrative and an inexhaustible pursuit of variations on themes."--London Review of Books

"Very enjoyable reading.... Related in a cheerful conversational tone with frequent allusions to, and quotations from, many other fields of knowledge, including literature, history, and philosophy.... This volume should appeal to a broad spectrum of readers interested in learning more about the beauty of mathematics."--Library Journal

"This is a mathematics with a plot and characters, as well as diagrams and formulas. These accounts vary from tragic to laugh-out-loud funny. Those who love math won't want to miss this one, and those who would like to love it but never have should give the book a try."--School Library Journal

In this delightful new book, Kaplan and his wife, Ellen, once again take readers 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.

Includes bibliographical references (p. 315-316) and index.

Robert and Ellen Kaplan are the founders of The Math Circle, a school, open to anyone of any age, that teaches the enjoyment of mathematics. They have been invited to lecture on mathematics teaching and the Math Circle to organizations such as the American Mathematical Society and universities in Spain and Switzerland. They live in Cambridge, Massachusetts.