The moment of proof: mathematical epiphanies

341 Pages·1999·15.16 MB·English

by  Donald C. Benson

The Moment of Proof
The Moment of Proof
Mathematical Epiphanies
Donald C. Benson
OXFORD
UNIVERSITY PRESS
OXFORD
UNIVERSITY PRESS
Oxford New York
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Copyright © 1999 by Oxford University Press
First published by Oxford University Press, Inc., 1999
First issued as an Oxford University Press paperback, 2000
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Oxford is a registered trademark of Oxford University Press
All rights reserved. No part of this publication may be reproduced,
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electronic, mechanical, photocopying, recording, or otherwise,
without the prior permission of Oxford University Press.
Figure 15.9 on page 226 courtesy of B. B. Mandelbrot, The Fractal Geometry tif Nature (W.H. Freeman, 1982).
Library of Congress Cataloging-in-Publication Data
Benson, Donald
The moment of proof: mathematical epiphanies / by Donald Benson
p. cm. Includes bibliographical references and index.
ISBN 0-19-511721-2 (Cloth)
ISBN 0-19-513919-4 (Pbk.)
1. Proof theory—Popular works. I.Title.
QA9.54.B46 1999
511.3—dc21 97-52139
10 987654 3 21
Printed in the United States of America
on acid-free paper
Contents
Acknowledgments, vii
Introduction, I
I RECALLING
/ Reflections, 5
2 Hand in Hand, 13
3 Further Progression, 23
II COUNTING
4 Interesting Numbers, 41
5 Tenpins, and Counting, 57
6 Order and Reorder, ji
7 Outcast, 89
8 The Power of Two, 101
9 Divide and Conquer, 123
10 Set and Match, 137
11 Chance Encounter, 149
III BALANCING
12 Cutouts, 167
13 Seesaw, Marjorie Daw, 185
14 Two Pearls, 797
IV NUMBERING
75 New Numbers for Old, 209
16 Prime News, 227
77 The Unknown Division, 237
18 Secret Messages, 259
V WINNING
79 Be Wise, Optimize, 277
20 The Play's the Thing, 293
Notes, 311
References, 319
Index, 323
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Acknowledgments
I would like to acknowledge the loving encouragement and assistance of my dear wife Dorothy.
Without her help, this book would never have been written. I wish to thank her especially for reading and
rereading the manuscript and making suggestions and criticisms from the point of view of a mathematical
novice as well as for her many invaluable stylistic insights.
I would like to thank Ned Black for reading the entire manuscript and offering many valuable
suggestions.
I would also like to acknowledge the assistance and encouragement of Kirk Jensen at Oxford Uni-
versity Press and the helpful suggestions of Henry Alder, Eric Benson, and Sherman Stein.
This book, apart from the frontmatter, was typeset by the author using IffljiX..
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The Moment of Proof
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