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Mathematical Events of the Twentieth Century

Russian mathematics (later Soviet mathematics, and Russian mathematics once again) occupies a special place in twentieth-century mathematics. In addition to its well-known achievements, Russian mathematics established a unique style of research based on the existence of prominent mathematical schools. These schools were headed by recognized leaders, who became famous due to their talents and outstanding contributions to science. | Mathematical Events of the Twentieth Century Mathematical Events of the Twentieth Century Edited by A. A. Bolibruch Yu. S. Osipov and Ya. G. Sinai 1 Springer PHASIS f A. A. Bolibruch Ya. G. Sinai Yu. S. Osipov Academy of Sciences Leninsky Pr. 14 117901 Moscow Russia e-mail osipov@ras.ru University of Princeton Department of Mathematics Washington Road 08544-1000 Princeton USA e-mail sinai@math.princeton.edu Editorial Board V. I. Arnold A. A. Bolibruch Vice-Chair A. M. Vershik Yu. I. Manin Yu. S. Osipov Chair Ya. G. Sinai Vice-Chair V. M. Tikhomirov L. D. Faddeev V. B. Philippov Secretary Originally published in Russian as Matematicheskie sobytiya XX veka by PhASIS Moscow Russia 2003 ISBN 5-7036-0074-X . Library of Congress Control Number 2005931922 Mathematics Subject Classification 2000 01A60 ISBN-10 3-540-23235-4 Springer Berlin Heidelberg New York ISBN-13 978-3-540-23235-3 Springer Berlin Heidelberg New York 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. Springer is a part of Springer Science Business Media springeronline.com Springer-Verlag Berlin Heidelberg and PHASIS Moscow 2006 Printed in Germany 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. Set for publishing by PHASIS using a special LTeX macro package Cover design Erich .