The Art of the Infinite The Pleasures of Mathematics

by Kaplan, Robert; Kaplan, Ellen

• ISBN13: 9780195147438
• ISBN10: 019514743X
• Format: Hardcover
• Copyright: 2003-04-03
• Publisher: Oxford University Press

Summary

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.

Author Biography

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.

Table of Contents

Acknowledgments	p. ix
An Invitation	p. 1
Time and the Mind	p. 3
How Do We Hold These Truths?	p. 29
Designs on a Locked Chest	p. 56
Interlude: The Infinite and the Indefinite	p. 75
Skipping Stones	p. 77
Euclid Alone	p. 100
Interlude: Longing and the Infinite	p. 131
The Eagle of Algebra	p. 133
Into the Highlands	p. 167
Interlude: The Infinite and the Unknown	p. 200
Back of Beyond	p. 202
The Abyss	p. 228
Appendix	p. 263
Bibliography	p. 315
Index	p. 317
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