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MYSTIC, GEOMETER, and INTUITIONIST This Page Intentionally Left Blank MYSTIC, GEOMETER, and INTUITIONIST MYSTIC, GEOMETER, AND INTUITIONIST This page intentionally left blank MYSTIC, GEOMETER, AND INTUITIONIST The Life of L. E. J. Brouwer 1881–1966 Volume 2 Hope and Disillusion DIRK VAN DALEN Department of Philosophy Utrecht University CLARENDON PRESS • OXFORD 2005 3 Great Clarendon Street, Oxford OX26DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York c Dirk van Dalen, 2005 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2005 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, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloguing in Publication Data Data available ISBN 0–19–851620–7 978-0-19-851620-0 Typeset by SPI Publishers Services, Pondicherry, India Printed in Great Britain on acid-free paper by Biddles Ltd., King’s Lynn, Norfock 10987654321 DEDICATION Dedicated to the Mathematical Research Institute at Oberwolfach– the organiza- tion and all members of staff– in appreciation of its major role in re-establishing mathematics in a free Europe, its role in promoting international co-operation, and for its generosity and encouragement, from which the present book also benefited This page intentionally left blank PREFACE Faire abstraction du monde d’objects (ce qui est necessaire´ pour travailler dans les mathematiques´ intuitionistes) n’est possi- ble qu’en eprouvant´ la vie comme un reve.ˆ Brouwer. In the twenties Brouwer had reached the undisputed status of master topologist and mysterious revolutionary. He had given topology a new lease of life; his inno- vations and his almost magical intuition determined to a large extent the course of topological research in the first half of the century. It had surprised the professional world that this genius had turned his back on traditional mathematics and started a thorough revision of the foundations of his subject. In volume 1 we have sketched the basic ideas and principles of his intuitionism; in this volume we will concentrate largely on the reception (and rejection) of his programme. Looking dispassionately at the turbulent years that followed after 1920, we can but conclude that Brouwer did not seek the conflict. His papers were technical and almost dull; if there was any provocation at all, it was in the subject matter, not in surreptitious attacks. It has been Brouwer’s misfortune that his name usually came up in conjuction with Hilbert’s. In itself that was nothing to be ashamed of; after all, David Hilbert was the man who succeeded Poincare´ as the unchallenged master of mathematics. Unfortunately a comparison between Brouwer and Hilbert was not particularly instructive or clarifying. It is difficult to find two mathematical geniuses of such totally opposite character. The Dutchman was the artistic, unfettered scientist, with an unbridled lust for travelling and friendships, while at the same time practicing meditation and entertaining austere moral and political convictions. A man who felt at home in salons as well as in the company of esoteric revivalists, who could be totally absorbed in mathematics, but who could equally well leave the subject alone; who had a reputation for defending lost causes, and who refused to sacrifice the moral issue to personal comfort. The great Gottinger¨ was a strong single-minded specialist, who devoted his life to the cultivation of mathematics and physics. A man whose mind never left mathe- matics alone, who nimbly jumped from one area to another to perform miracles. A man with just two goals in life: mathematics and Gottingen,¨ goals that were largely attained by his sheer mathematical intellect and his talent for leadership. The fol- lowing chapters will show that a conflict between the two was not a predetermined matter. One may well conjecture that without the First World War, there would not have been a conflict. As the reader will see, the Grundlagenstreit greatly exas- perated Hilbert, and the exchange of the twenties was not always kept within the confines of scholarly courtesy, but without the political complications there would not have been the fateful act that brought Einstein to the exclamation ‘I would never have thought that Hilbert was capable of such emotional outbursts.’ viii PREFACE Both men would have coexisted peacefully with now and then a scientific exchange on foundational matters. Hilbert’s Programme would have been killed by Godel,¨ so to speak, before a serious conflict could have erupted. The documents used in the present volume come mostly from sources men- tioned in volume 1. There is, however, a certain amount of new material from var- ious archives, to mention the major sources: the archives of Bieberbach, Courant, Doetsch, Hilbert, Hk de Vries, St.John’s College Cambridge, Heidelberg Univer- sity, Nationaal Archief Den Haag. Since the publication of the first volume a number of relevant historical studies have appeared; the following old and new texts have been useful in pro- viding information on various topics: [Blauwendraat 2004], [Georgiadou 2004], [Groot 1946], [Hesseling 2003], [Hubner¨ 2002], [Johnson 1979, Johnson 1981], [Knegtmans 1998], [Maas 2001], [Menger 1979, Menger 1994], [Urysohn1951], [Schroeder-Gudehus 1966], [Segal 1986], [Siegmund-Schultze 2001]. The references in this volume to Brouwer’s publications do not match the list of volume 1. The correspondence of Brouwer will in due time be published, the work is car- ried out as part of the Brouwer project in Utrecht. A similar project for Brouwer’s unpublished manuscripts is envisaged. To the long list of those who supported me with information and advice, I am happy to add the names of S.M.P. Brouwer-Euwe, Felix Browder, T. Corkery, Jonathan Harrison, Hans Huebner, C.B.J. Jonkers, Hans Ewald Keszler, R. van der Laan-van Heemert, M.S.van Leeuwen-Boomkamp, Eckart Menzler-Trott, Agnes van Noort, Volker Remmert, Bert Schweizer, Paul van Ulsen. I hardly need repeat what I said about the cooperation with my wife in volume I, she was again in every respect my partner in this joint project. Over the years my indebtedness to the Mathematical Institute at Oberwolfach has been accumulating. I started by attending the annual meetings on geometry, these were followed by meetings on logic, but gradually the institute became a friendly retreat where I could concentrate on the biography of Brouwer, away from the distraction called university. Like many before and after me, I came to appre- ciate the institute as the ideal place for exchange of ideas, research, and reflection. I am most grateful to the Oberwolfach establishment and the ever supportive staff members, who managed to turn the institute into a mathematician’s home away from home. Utrecht, June 2005 CONTENTS 12 The Fathers of Dimension 441 12.1 The two Russians 441 12.2 The definition of dimension 444 12.3 The Viennese connection 467 12.4 The scientific legacy of Urysohn 470 13 Progress, recognition, and frictions 481 13.1 The first skirmishes in the foundational conflict 481 13.2 Consolidation and entrenchment 493 13.3 The Riemann volume 503 13.4 International relations 508 13.5 The Dutch topological school 514 14 From Berlin to Vienna 538 14.1 More intuitionism 538 14.2 Feelings of crisis and German science 540 14.3 The Berlin lectures 544 14.4 The Vienna lectures 561 14.5 Other activities 569 15 The three Battles 573 15.1 The Grundlagenstreit 573 15.2 The Bologna conference 587 15.3 The war of the frogs and the mice 599 15.4 The endings of the Grundlagenstreit 636 15.5 The Menger conflict 643 16 The Thirties 672 16.1 Freudenthal arrives 673 16.2 Intuitionistic logic 676 16.3 The Sodalitas affair 678 16.4 Gottingen’s¨ fate under the Nazi’s 693 16.5 Bieberbach’s conversion 695 16.6 Compositio Mathematica 703 16.7 Gottingen¨ reconsidered? 710 16.8 Dutch affairs 715 17 War and Occupation 738 17.1 Occupied Holland 738 17.2 Weitzenbock’s¨ choice 740 x CONTENTS 17.3 Freudenthal dismissed 742 17.4 University—resistance or survival 746 17.5 Freudenthal’s fortunes 751 17.6 The declaration of loyalty 759 17.7 The Brouwer family in wartime 770 17.8 Weitzenbock¨ in uniform 774 18 Postwar Events 777 18.1 Purging the university 777 18.2 Faculty politics 799 18.3 Back to research 814 18.4 The loss of Compositio Mathematica 833 18.5 Rearguard actions 846 19 The restless Emeritus 860 19.1 The traveller 860 19.2 The pharmacy 887 19.3 The last years 895 19.4 Epilogue 907 20 Appendix 913 20.1 Dissertations under supervision of Brouwer 913 20.2 Correspondence and Archives 913 20.3 Chronology 917 References 920 Index 935 12 THE FATHERS OF DIMENSION 12.1 The two Russians For the next, and final, episode in Brouwer’s topological career we have to go back to 1923.
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