Indiscrete Thoughts PDF
Preview Indiscrete Thoughts
Job #:111367 Author Name: Rota Title of Book: Indiscrete Thoughts ISBN #: 9780817647803 Modern Birkh~user Classics Many of the original research and survey monographs in pure and applied mathematics published by Birkh~user in recent decades have been groundbreaking and have come to be regarded as foun- dational 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 ac- cessible to new generations of students, scholars, and researchers. oT Arthur yramhtaz5 htiw noitceffa dna edutitarg Indiscrete Thoughts Gian-Carlo Rota Fabrizio Palombi Editor Reprint of the 1997 Edition Birkh~iuser Boston (cid:12)9 Basel (cid:12)9 Berlin Gian-Carlo Rota (Deceased) Fabrizio Palombi (Editor) Department of Mathematics Department of Philosophy and Philosophy University of Torino MIT Torino, Italy Cambridge, MA 02139 U.S.A. Originally published as a monograph ISBN-13:978-0-8176-4780-3 e-ISBN-13:978-0-8176-4781-0 DOI: 10.1007/978-0-8176-4781-0 Library of Congress Control Number: 2007940673 Mathematics Subject Classification (2000): 01A05 (cid:14)9 BirkMuser Boston All rights reserved. This work may not be translated or copied in whole or in part without the writ- ten permission of the publisher (Birkh~iuser Boston, c/o 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 de- veloped 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. Cover design by Alex Gerasev. Printed on acid-free paper. 987654321 www. birkhauser corn olraC-naiG Rota etercsidnI sthguohT oizirbaF ibmolaP 'EDITOR 'BIRKH)[USER "BOSTON (cid:12)9 'BASEL (cid:12)9 'BERLIN rotidE Gian-Carlo Rota Department of Mathematics Fabrizio Palombi Massachusetts Institute of Technology Department of Philosophy Cambridge, MA 02139 University of Torino USA Torino, Italy yrarbiL of Congress noitacilbuP-ni-gnigolataC Data Rota, Gian-Carlo, 1932- Indiscrete thoughts / by Gian-Carlo Rota : edited by Fabrizio Palombi. p. cm. Includes bibliographical references and index. ISBN 0-8176-3866-0 (alk. paper). -- ISBN 3-7643-3866-0 (alk. paper) 1. Mathematics. 2. Sciences. 3. Philosophy. I. Palombi, Fabrizio, 1965- II. Title QA7.R65 1996 95-52782 510--dc20 CIP Printed on acid-free paper (cid:14)9 1997 Birkh~iuser Boston; resu~hkriB ~| 1998 second printing Copyright is not claimed fowro rks of U.S. Government employees. All rights reserved. No part of this publication may be reproduced, stored in retrieval a system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without priorp ermission of the copyright owner. Permission to photocopy for internal or personal use of specific clients is granted by resui~hkriB Boston for libraries and other users registered with the Copyright Clearance Cen(tCeCrC ), provided that the bafseee 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 resui~hkriB Boston, 675 Massachusetts Avenue, Cambridge, MA 02139, U.S.A. ISBN 0-8176-3866-0 ISBN 3-7643-3866-0 Cover design by Joseph Sherman, Dutton & Sherman Design, Hamden, CT Typesetting by Hamilton Printing Company, Rensselaer, NY Printed in the U.S.A. 98765432 Contents Foreword by Reuben Hersh .................................... ix Foreword by Robert Sokolowski ............................... ~i Introduction by Gian-Carlo Rota .............................. xJx Part I. Persons and Places I. Fine Hall in its Golden Age ................................. 3 Remembrances of Princeton in the Early Fifties Alonzo Church ..................................... 4 William Feller ...................................... 7 Emil Artin ......................................... 12 Solomon Lefschetz ................................. 16 II. Light Shadows .......................................... 21 Yale in the Early Fifties Jack Schwartz ...................................... 21 From Princeton to Yale .............................. 22 Josiah Wil!ard Gibbs ................................ 24 Yale in the Fifties ................................... 26 Mathematics at Yale ................................ 28 Abstraction in Mathematics .......................... 30 Linear Operators: The Past .......................... 32 Linear Operators: The Present ....................... 34 Linear Operators: The Future ........................ 35 Working with Jack Schwartz ......................... 36 w .~. Contents .~o III. Combinatorics, Representation Theory and Invariant Theory .................................... 39 The Story of a M~nage t2 Trois Cambridge 02138 in the Early Fifties .................. 39 Alfred Young ...................................... 41 Problem Solvers and Theorizers ...................... 45 Hermann Grassmann and Exterior Algebra ............ 46 Definition and Description in Mathematics ............ 48 Bottom Lines ...................................... 51 .VI The Barrier of Meaning .................................. 55 .V Stan Ulam .............................................. 60 VI. The Lost Car6 .......................................... 63 Part II. Philosophy: A Minority View VII. The Pernicious Influence of Mathematics Upon Philosophy .. 89 VIII. Philosophy and Computer Science ...................... 104 IX. The Phenomenology of Mathematical Truth ............... 108 X. The Phenomenology of Mathematical Beauty .............. 121 XI. The Phenomenology of Mathematical Proof ............... 134 XII. Syntax, Semantics, and the Problem of the Identity of Mathematical Items .................................. 151 XIII. The Barber of SeviUe or the Useless Precaution ........... 158 XIV. Kant and Husserl ..................................... 162 XV. Fundierung as a Logical Concept ......................... 172 XVI. The Primacy of Identity ............................... 182 XVII. Three Senses of'A is B" in Heidegger ................... 188 (cid:12)9 o~ Contents o~o vii Part III Readings and Comments XVIII. Ten Lessons I Wish I Had Been Taught ................. 195 XIX. Ten Lessons for the Survival of a Mathematics Department . 204 XX. A Mathematician's Gossip .............................. 209 XXI. Book Reviews ........................................ 235 Paul Halmos: a Life ............................... 235 The Leading Line of Schaum's Outlines .............. 237 Professor Neanderthal's World ...................... 242 Uses and Misuses of Numbers ....................... 245 On Reading Collected Papers ....................... 248 Matroids ......................................... 250 Short Book Reviews ............................... 252 End Notes ............................................... 259 Epilogue by Fabrizio Palombi ................................. 265 Index .................................................... 273
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