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Claudio Bartocci Renato Betti Angelo Guerraggio Roberto Lucchetti l

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Editors

Mathematical Lives Protagonists of the Twentieth Century From Hilbert to Wiles Translated by Kim Williams

Editors Claudio Bartocci Universita` di Genova Dipto. Matematica Via Dodecaneso 35 16146 Genova Italy [email protected]

Renato Betti Politecnico di Milano Dipto. Matematica Piazza Leonardo da Vinci 32 20133 Milano Italy [email protected]

Angelo Guerraggio Universita` Bocconi Centro PRISTEM Via Sraffa 11 20136 Milano Italy [email protected]

Roberto Lucchetti Politecnico di Milano Dipto. Matematica Piazza Leonardo da Vinci 32 20133 Milano Italy [email protected]

Translator: Kim Williams Corso Regina Margherita, 72 10153 - Turin (Torino) Italy http://www.kimwilliamsbooks.com [email protected]

Translation from the Italian language edition: Vite matematiche, edited by C. Bartocci, R. Betti, A. Guerraggio, R. Lucchetti, copyright # 2007 Springer-Verlag Italia, Springer is part of Springer Science þ Business Media, All Rights Reserved The drawings are included with kind permission of Maria Poggi (Queneau, p. 134) and Geraldine D0 Alessandris (for all remaining drawings). Mathematical classification MSC: 01A60, 01A70, 01A80, 03A10, 08-03, 91-03

ISBN 978-3-642-13605-4 e-ISBN 978-3-642-13606-1 DOI 10.1007/978-3-642-13606-1 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010935446 # Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Mathematical knowledge is increasing at a dizzy rate. In the course of the last 50 years more theorems have been proven that in the preceding thousand years of human history: to give an idea of the order of magnitude, every year in specialized journals alone tens of thousands of research articles are published, and just as many more are made available on the Internet. Even given that the great part of these results are understandable and interesting only to specialists, others represent fundamental intellectual conquests, solving irksome problems or famous conjectures, est

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