In 1915 Emmy Noether was invited by Klein and Hilbert to Göttingen to assist them in understanding the law of conservation of energy in Einstein’s new general theory of relativity. She succeeded brilliantly. In the Invariante Variationsprobleme, published in 1918, she proved a fundamental theorem linking invariance properties and conservation laws in any theory formulated in terms of a variational principle, and she stated a second theorem which put a conjecture of Hilbert in perspective and furnished a proof of a much more general result.
This book will be of interest to historians of science, to teachers of mathematics, mechanics and physics, and to mathematicians and mathematical physicists. Also by Yvette Kosmann-Schwarzbach: Groups and Symmetries: From Finite Groups to Lie Groups, © 2010 Springer, ISBN: 978-0-387-78865-4.
Sources and Studies in the History of Mathematics and Physical Sciences Managing Editor J.Z. Buchwald Associate Editors J.L. Berggren and J. L¨utzen Advisory Board C. Fraser, T. Sauer, A. Shapiro For other titles published in this series, go to http://www.springer.com/series/4142 Emmy Noether (1882–1935) (photograph courtesy of the Emmy Noether Foundation, Bar Ilan University) Yvette Kosmann-Schwarzbach The Noether Theorems Invariance and Conservation Laws in the Twentieth Century Translated by Bertram E. Schwarzbach 123 Yvette Kosmann-Schwarzbach Centre de Mathématiques Laurent Schwartz École Polytechnique 91128 Palaiseau France
[email protected] Bertram E. Schwarzbach (Translator) e-ISBN 978-0-387-87868-3 ISBN 978-0-387-87867-6 DOI 10.1007/978-0-387-87868-3 Springer New York Dordrecht Heidelberg London Mathematics Subject Classification (2010): 01-02, 22-03, 22E70, 49-03, 49S05, 70-03, 70H03, 70H33, 83-03 © Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identi ed as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) In memory of Yseult d′′ r who liked science as well as history Preface What follows thus depends upon a combination of the methods of the formal calculus of variations and of Lie's theory of groups. Emmy Noether, 1918