The Mathematics of Sonya Kovalevskaya
This book is the result of a decision taken in 1980 to begin studying the history of mathematics in the nineteenth century. I hoped by doing it to learn some thing of value about Kovalevskaya herself and about the mathematical world she inhabited. Having
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Kovalevskaya's certificate of election as a corresponding member of the Imperial Academy of Sciences, dated 29 December 1889 (10 January 1890). The certificate reads: The Imperial Academy of Sciences, by the authority of its supreme mandate of 8 January 1836, has elected Sophia Vasilievna Kovalevskaya, professor of the University of Stockholm, a corresponding member in the section of mathematical sciences. (Courtesy of the Institut Mittag-Leffler.)
Roger Cooke
The Mathematics of Sonya Kovalevskaya
With 21 Figures
I]
Springer-Verlag
New York Berlin Heidelberg Tokyo
Roger Cooke
Department of Mathematics University of Vermont Burlington, Vermont 05405 U.S.A.
Library of Congress Cataloging in Publication Data Cooke, Roger, The mathematics of Sonya Kovalevskaya. Bibliography: p. Includes index. l. Mathematical analysis-History. 2. Kovalevskaia, S. V. (Sof'ia Vasil' evna) , 1850-189l. 3. Mathematicians-Soviet Union-Biography. I. Title. QA300.C65 1984 515' .09 84-10599 ©1984 by Springer-Verlag New York Inc. Softcover reprint of the hardcover 1st edition 1984
All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag, 175 Fifth Avenue, New York, New York 10010, U.S.A. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Typeset by Interactive Composition Corporation, Pleasant Hill, California.
987 654 3 2 1 ISBN-13: 978-1-4612-9766-6 e-ISBN-13: 978-1-4612-5274-0 DOl: 10.1007/978-1-4612-5274-0
To Cathie, who keeps me in touch with what is most important, To Katya, Andrew, and Hilary, who bring us joy every day, To my father, who gave me an education beyond books and classrooms, and In loving memory of my mother
Letter from Kovalevskaya communicating her discovery of the Kovalevskaya case of a rotating rigid body. The letter was in Mittag-Leffler's possession and is possibly to him, though she usually addressed him less formally at the time the letter was written. (Courtesy of the Institut Mittag-Leffler. )
Preface This book is the result of a decision taken in 1980 to begin studying the history of mathematics in the nineteenth century. I hoped by doing it to learn something of value about Kovalevskaya herself and about the mathematical world she inhabited. Having been trained as a mathematician, I also hoped to learn something about the proper approach to the history of the subject. The decision to begin the
