On the Hypotheses Which Lie at the Bases of Geometry
This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided
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Jürgen Jost Editor
Bernhard Riemann On the Hypotheses Which Lie at the Bases of Geometry
Bernhard Riemann On the Hypotheses Which Lie at the Bases of Geometry
Classic Texts in the Sciences Series Editors Olaf Breidbach () Jürgen Jost Classic Texts in the Sciences offers essential readings for anyone interested in the origin and roots of our present-day culture. Considering the fact that the sciences have significantly shaped our contemporary world view, this series not only provides the original texts but also extensive historical as well as scientific commentary, linking the classic texts to current developments. Classic Texts in the Sciences presents classic texts and their authors not only for specialists but for anyone interested in the background and the various facets of our civilization.
More information about this series at http://www.springer.com/series/11828
Jürgen Jost Editor
Bernhard Riemann On the Hypotheses Which Lie at the Bases of Geometry
Editor JRurgen Jost Max Planck Institute for Mathematics in the Sciences Leipzig, Germany
ISSN 2365-9963 Classic Texts in the Sciences ISBN 978-3-319-26040-2 DOI 10.1007/978-3-319-26042-6
ISSN 2365-9971 (electronic) ISBN 978-3-319-26042-6 (eBook)
Library of Congress Control Number: 2016936876 Mathematics Subject Classification (2010): 51-03, 53-03, 53B20, 53Z05, 00A30, 01A55, 83-03 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser The registered company is Springer International Publishing AG Switzerland (www.birkhauser-science.com)
Preface
This could be the plot of a novel: The main character is a shy, sickly, young mathematician, living in poor conditions at a German university in the middle of the nineteenth century. He does not succeed in establishing a closer contact with the greatest mathematical luminary of his time. He is working toward his habilitation degree (a prer
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