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The Art of the Infinite: The Pleasures of Mathematicsby Robert Kaplan
Synopses & Reviews
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.
Book News Annotation:
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.
Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
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.
About the Author
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.
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