The Mathematical Experience, Study Edition PDF
Preview The Mathematical Experience, Study Edition
Modern Birkhäuser Classics Many of the original research and survey monographs, as well as textbooks, in pure and applied mathematics published by Birkhäuser in recent decades have been groundbreaking and have come to be regarded as foundational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain accessible to new genera- tions of students, scholars, and researchers. The Mathematical Experience, Study Edition Philip J. Davis Reuben Hersh Elena Anne Marchisotto Reprint of the 1995 Edition Philip J. Davis Reuben Hersh Division of Applied Mathematics Department of Mathematics Brown University and Statistics Providence, RI 02912 University of New Mexico USA Albuquerque, NM 87131 [email protected] USA [email protected] Elena Anne Marchisotto Department of Mathematics California State University, Northridge Northridge, CA 91330 [email protected] Originally published as a hardcover edition under the same title by Birkhäuser Boston, ISBN 978-0-8176-3739-2, ©1995 ISBN978-0-8176-8294-1 e-ISBN978-0-8176-8295-8 DOI10.1007/978-0-8176-8295-8 Springer New York Dordrecht Heidelberg London LibraryofCongressControlNumber: 2011939204 ©SpringerScience+B usinessMedia,LLC2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printedonacid-freepaper www.birkhauser-science.com J. Philip Davis Reuben Hersh Elena Anne Marchisotto With an Introduction by Gian-Carlo Rota The Mathematical Experience Study Edition Birkhauser Boston • Basel • Berlin Philip J. Davis Reuben Hersh Division of Applied Mathematics Department of Mathematics Brown University and Statistics Providence, RI 02912 University of New Mexico Albuquerque, NM 87131 Elena Anne Marchisotto Department of Mathematics California State University, Northridge Northridge, CA 913308313 Library of Congress Cataloging-in-Publication Data Davis, Philip J., 1923- The mathematical experience I Philip J. Davis, Reuben Hersh, Elena Anne Marchisotto : with an introduction by Gian-Carlo Rota. --Study ed. p. em. Includes bibliographical references and index. ISBN 0-8176-3739-7 (h : acid-free).--ISBN 3-7643-3739-7 (h acid-free) I. Mathematics--Philosophy. 2. Mathematics--History. 3. Mathematics--Study and teaching. I. Hersh, Reuben, 1927- 11. Marchisotto, Elena. III. Title. QA8.4.D37 1995 95-20875 51 O--dc20 CIP Printed on acid-free paper }J © 1981 , First Edition, Birkhiiuser Birkhiiuser ® Published 1995. Study Edition Birkhiiuser 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 (CCC), 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. ISBN 0-8176-3739-7 ISBN 3-7643-3739-7 First edition was designed by Mike Fender, Cambridge, MA and set in Baskerville and I.T.C. Caslon Light 223 by Progressive Typographers, York, P A Text for Study Edition was typeset by Martin Stock, Cambridge, MA Printed and bound by Quinn-Woodbine, Woodbine, NJ Printed in the U.S.A. 9 8 7 6 5 4 3 2 1 For my parents, Mildred and Philip Hersh * * * * For my brother, Hyman R. Davis Contents Preface Xlll Preface to the Study Edition XV Acknowledgements xvii Introduction XXI Overture 1 I. The Mathematical Landscape What is Mathematics? 6 Where is Mathematics 8 The Mathematical Community 9 The Tools of the Trade 13 How Much Mathematics is Now Known? 17 Ulam's Dilemma 20 How Much Mathematics Can There Be? 24 Appendix A-Brief Chronological Table to 1910 26 Appendix B-The Classification of Mathematics 1868 and 1979 Compared 29 Assignments and Problem Sets 31 2. Varieties of Mathematical Experience The Current Individual and Collective Consciousness 36 The Ideal Mathematician 38 A Physicist Looks at Mathematics 48 I. R. Shafarevitch and the New Neoplatonism 56 Unorthodoxies 59 The Individual and the Culture 64 Assignments and Problem Sets 70 3. Outer Issues Why Mathematics Works: A Conventionalist Answer 76 Mathematical Models 85 lX
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