The Art of the Infinite: The Pleasures of Mathematics

by Robert Kaplan, Ellen Kaplan

Overview

A witty, conversational, and accessible tour of math's profoundest mysteries.

Mathematical symbols, for mathematicians, store worlds of meaning, leap continents and centuries. But we need not master symbols to grasp the magnificent abstractions they represent, and to which all art aspires. Through language, anyone can come to delight in the works of mathematical art, which are among our kind's greatest glories.

Taking the concept of infinity, in its countless guises, as a starting point and a helpful touchstone, the founders of Harvard's pioneering Math Circle program Robert and Ellen Kaplan guide us through the “Republic of Numbers,” where we meet both its upstanding citizens and its more shadowy dwellers, explore realms where only the imagination can go, and grapple with math's most profound uncertainties, including the question of truth itself-do we discover mathematical principles, or invent them?

Product Details

ISBN-13:	9781608198887
Publisher:	Bloomsbury Publishing
Publication date:	07/01/2014
Sold by:	Barnes & Noble
Format:	eBook
Pages:	416
File size:	30 MB
Note:	This product may take a few minutes to download.

About the Author

Robert and Ellen Kaplan have taught subjects ranging from Sanskrit through mathematics to philosophy and history and founded The Math Circle. Robert Kaplan is the author of the bestselling The Nothing That Is: A Natural History of Zero. Ellen Kaplan is coauthor of Chances Are . . . and Bozo Sapiens, written with their son Michael. Together, Robert and Ellen are the authors of Out of the Labyrinth. Their website is www.themathcircle.org.
Robert Kaplan has taught mathematics to people from six to sixty, at leading independent schools and most recently at Harvard University. He is the author of the best-selling The Nothing That Is: A Natural History of Zero, which has been translated into 10 languages, and, with his wife, Ellen, the co-author of The Art of the Infinite.
Ellen Kaplan has taught mathematics to people from six to sixty, at leading independent schools and most recently at Harvard University. With her husband, Robert, she wrote The Art of the Infinite. Ellen is also co-author of Chances Are: Adventures in Probability and Bozo Sapiens: Why to Err is Human, co-written with her son, Michael Kaplan.

Table of Contents

Acknowledgments ix

An Invitation 1

Chapter 1 Time and the Mind 5

Chapter 2 How Do We Hold These Truths? 37

Chapter 3 Designs on a Locked Chest 71

Interlude: The Infinite and the Indefinite 93

Chapter 4 Skipping Stones 95

Chapter 5 Euclid Alone 123

Interlude: Longing and the Infinite 165

Chapter 6 The Eagle of Algebra 167

Chapter 7 Into the Highlands 209

Interlude: The Infinite and the Unknown 249

Chapter 8 Back of Beyond 251

Interlude: The Infinite There-But the Finite Here 283

Chapter 9 The Abyss 287

Appendix 329

Bibliography 391

Index 393

Editorial Reviews

Robert Kaplan can make even nullity interesting. His The Nothing That Is: A Natural History of Zero confounded the numerically challenged and became an international bestseller. In The Art of the Infinite, he and his wife, Ellen, extend that success to the nth degree, providing a elegant, often playful excursion into the mathematics of infinity. They explain that in the Republic of Numbers, the attempt to grasp the ungraspable is an essential activity.

In The Art of the Infinite, Robert and Ellen Kaplan take us on a grand tour, leading us from the terra firma of the simple counting numbers (one, two, three, four and so on) through the discovery of the rationals, the irrationals, the negatives and the complex numbers that combine the ordinary, or real, numbers and the imaginaries to generate a two dimensional number-space known as the complex plane. It is here that the famous Mandelbrot set lives, that enigmatic emblem of chaos theory. — Margaret Wertheim

The Los Angeles Times

While Kaplan (The Nothing That Is: A Natural History of Zero) and his wife intend this volume to delight the numerophobic into seeing the beauty in math, the "art" they describe is hidden in a thicket of dry proofs. And yet they've written a lovely and erudite history of the subject in spite of that, one that will absorb anyone who already fancies numbers and all their possibilities. Hand-drawn diagrams accompany dense explanatory prose in this exploration of infinity, as the authors chart mathematical discoveries and great thinkers throughout history. Frequent references to luminaries from the humanities (Shakespeare, Baudelaire, Gaudi, Robert Graves) would earn this book comfortable shelving in a liberal arts library if the math weren't so devilishly hard to grasp. (A typical passage compares the way great changes happen in mathematics with the way important figures enter the action in Proust.) The authors acknowledge that even math basics can be tricky: that the product of two negatives is a positive, for instance, is a puzzle that the Kaplans say "put too many people off math forever, convinced that its dicta were arbitrary or spiteful." The authors write that "[m]athematics is permanent revolution," and indeed, some may find their heads spinning. Nevertheless, a patient reader who loves thinking about thinking will be rewarded by the book's end; by the final pages, he or she will have personally experienced, via these diagrams and problems, many of the great discoveries in mathematics. Graphs and illustrations throughout. (Apr.) Copyright 2003 Reed Business Information.

Publishers Weekly

The Kaplans are founders of the Math Circle, a school that teaches the enjoyment of mathematics, and Robert is the author of The Nothing That Is: A Natural History of Zero. In this new book, the authors cover some of the elements of such areas as plane geometry, algebra, and trigonometry. The contents are chosen and arranged so as to lead into a concluding discussion of Georg Cantor's remarkable discoveries/inventions concerning the nature of infinity. All of this is related in a cheerful conversational tone with frequent allusions to, and quotations from, many other fields of knowledge, including literature, history, and philosophy. At times, a meander through a different discipline distracts from the main argument, but overall the Kaplans' approach makes for very enjoyable reading. This volume should appeal to a broad spectrum of readers interested in learning more about the beauty of mathematics. Recommended for all public and academic libraries.-Jack W. Weigel, Ann Arbor, MI Copyright 2003 Reed Business Information.

Library Journal

Adult/High School-This exploration of mathematics and its history involves plot and characters as well as numbers; the stories of the thinkers who were challenged by its mysteries and discovered its principles range from tragic to laugh-out-loud funny. Copyright 2004 Reed Business Information.

School Library Journal

"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

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