The World as a Mathematical Game John von Neumann and Twentieth Cent
Galileo and Newton’s work towards the mathematisation of the physical world; Leibniz’s universal logical calculus; the Enlightenment’s mathématique sociale. John von Neumann inherited all these aims and philosophical intuitions, together with an idea that
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Science Networks . Historical Studies Founded by Erwin Hiebert and Hans Wußing Volume 38 Edited by Eberhard Knobloch, Helge Kragh and Erhard Scholz
Editorial Board: K. Andersen, Aarhus D. Buchwald, Pasadena H.J.M. Bos, Utrecht U. Bottazzini, Roma J.Z. Buchwald, Cambridge, Mass. K. Chemla, Paris S.S. Demidov, Moskva E.A. Fellmann, Basel M. Folkerts, München P. Galison, Cambridge, Mass. I. Grattan-Guinness, London J. Gray, Milton Keynes
R. Halleux, Liège S. Hildebrandt, Bonn Ch. Meinel, Regensburg J. Peiffer, Paris W. Purkert, Bonn D. Rowe, Mainz A.I. Sabra, Cambridge, Mass. Ch. Sasaki, Tokyo R.H. Stuewer, Minneapolis H. Wußing, Leipzig V.P. Vizgin, Moskva
Giorgio Israel Ana Millán Gasca
The World as a Mathematical Game John von Neumann and Twentieth Century Science
Birkhäuser Basel · Boston · Berlin
Authors: Giorgio Israel Dipartimento di Matematica Università di Roma “La Sapienza” P.le A. Moro, 5 00185 Roma Italy e-mail: [email protected]
Ana Millán Gasca Dipartimento di Matematica Università Roma Tre Largo S. Leonardo Murialdo, 1 00146 Roma Italy e-mail: [email protected]
Translated from the Italian by Ian McGilvray
2000 Mathematical Subject Classification: 01A60, 01A70, 03-03, 68-03, 93-03
Library of Congress Control Number: 2008941508 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
ISBN 978-3-7643-9895-8 Birkhäuser Verlag AG, Basel - Boston - Berlin 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2009 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TCF ∞ Cover illustration: with the friendly permission by Marina von Neumann Whitman Printed in Germany ISBN 978-3-7643-9895-8
e-ISBN 978-3-7643-9896-5
987654321
www.birkhauser.ch
Contents Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
1
2
3
4
J´anos Neumann’s Early Years 1.1 A Jewish family in early twentieth century Budapest . . 1.2 A young talent in Hungarian mathematics belle e´ poque . 1.3 Lights and shadows. The von Neumann generation . . . 1.4 Student years in Germany . . . . . . . . . . . . . . . .
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1 2 7 13
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19 22
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25
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31 39
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49
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53 57 60
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67
Von Neumann in the United States 4.1 Princeton and the American mathematical community i
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