The Art of the Infinite: The Pleasures of Mathematics

The Art of the Infinite: The Pleasures of Mathematics

4.0 1
by Robert Kaplan, Ellen Kaplan, Ellen Kaplan
     
 

ISBN-10: 0195176065

ISBN-13: 9780195176063

Pub. Date: 10/01/2004

Publisher: Oxford University Press

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

Overview

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 Infiniteshows 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.

Product Details

ISBN-13:
9780195176063
Publisher:
Oxford University Press
Publication date:
10/01/2004
Edition description:
New Edition
Pages:
336
Sales rank:
822,110
Product dimensions:
8.90(w) x 5.50(h) x 0.90(d)

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

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The Art of the Infinite: The Pleasures of Mathematics 4 out of 5 based on 0 ratings. 1 reviews.
Guest More than 1 year ago
This book trys to present math to the millions and does a pretty good job. It is simple and sometimes witty but often the literary allusions intrude and the text bogs down in pages of relentless math--lovely if you like it and horrid if you don´t. If you already know alot of math you will still probably find the discussions of general math, geometry, projective geometry, and infinite series to be a nice refresher. If you don´t know any and don´t have a natural talent for it, you will find it very dense or impossible. Being somewhere in the middle I skimmed thru most of it and slowed down when it got interesting. If you have only a little time I would suggest the last chapter ´The Abyss` about Georg Cantor and transfinite arithmetic. At points they wax philosophical and ask the perennial question: is math is out there in the world or in here in our heads. Why not ask this about art or music or literature or computer programs or philosophy itself? In a very general way math must come from the same place that words and ideas and images come from---our brain evolved to make them and they must in many ways(every way?) reflect the structure of our brains, which reside in our dna which was shaped by natural selection which was shaped by the geology of the earth and the structure of our universe which comes from particle physics which comes from the laws of nature which are just there.