The Mathematical Experience, Study Edition

522 Pages·2012·101.13 MB·English

by  Philip J. Davis

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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

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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
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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