Mathematical Encounters of the Second Kind
A number of years ago, Harriet Sheridan, then Dean of Brown University, organized a series oflectures in which individual faculty members described how it came about that they entered their various fields. I was invited to participate in this series and f
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For Gail Corbett
Philip J. Davis
Mathematical Encounters ofthe Second Kind
BIRKHAUSER
Boston. Basel. Berlin
Philip J. Davis Division of Applied Mathematics Brown University Providence, RI 02912
Library of Congress Cataloging-in-Publication Data Davis, Philip J., 1923Mathematical encounters of the second kind / Philip J. Davis. p. cm. ISBN-l3: 978-1-4612-7547-3
e-ISBN-13: 978-1-4612-2462-4
DOl: 10.1007/978-1-4612-2462-4
(hardcover: alk. paper) 1. Mathematics. 2 .. Mathematicians. I. Title. QAlO.5.D38 1996 96-22131 510--dc20 CIP Printed on acid-free paper
Birkhiiuser © 1997 Birkhiiuser Boston Softcover reprint of the hardcover 1st edition 1997
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Copyright is not claimed for works of U.S. Government employees. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use of specific clients is granted by Birkhiiuser Boston for libraries and other users registered with the Copyright Clearance Center (Ccq, provided that the base fee of $6.00 per copy, plus $0.20 per page is paid directly to CCC, 222 Rosewood Drive, Danvers, MA 01923, U.S.A. Special requests should be addressed directly to Birkhiiuser Boston, 675 Massachusetts Avenue, Cambridge, MA 02139, U.S.A
Designed and typeset by Martin Stock, Cambridge, MA Cover design by Joseph Sherman, Dutton and Sherman Design, Hamden, CT Original drawing (Carpenter p. 56) by Marguerite Dorian, Providence, RI
9 8 765 432 1
CONTENTS Preface I
II
VI
:wayofeons 'Theorem
I
Caryenter andt6e :wayofeon :AscriPtion
55
III
'The :.Man cw60 ~egan J{is Lectures wit6 ":Wame~"
IV
'The 'Rot6sc6i(d1 'Knew
Acknowledgments Bibliography
297
295
159
137
PREFACE A number of years ago, Harriet Sheridan, then Dean of Brown University, organized a series oflectures in which individual faculty members described how it came about that they entered their various fields. I was invited to participate in this series and found in the invitation an opportunity to recall events going back to my early teens. The lecture was well received and its reception encouraged me to work up an expanded version. My manuscript lay dormant all these years. In the meanwhile, sufficiently many other mathematical experiences and encounters accumulated to make this little book. My 1981 lecture is the basis of the first piece: "Napoleon's Theorem." Although there is a connection between the first piece and the second, the four pieces here are essentially independent. The second piece, "Carpenter and the Napoleon Ascription," has as its object a full description of a certain type of scholar-storyteller (of whom I have known and admired several). It is a pastiche, containing a salad bar selection blended together by my own imagination. This piece purports, as a secondary goal, to present a solution to a certain unsolved historical problem raised in t
