Mathematics As A Tool: Tracing New Roles Of Mathematics In The Sciences

Boston Studies in the Philosophy and History of Science  327 Johannes Lenhard Martin Carrier Editors Mathematics as a Tool Tracing New Roles of Mathematics in the Sciences Boston Studies in the Philosophy and History of Science Volume 327 Editors Alisa Bokulich, Boston University Robert S. Cohen, Boston University Jürgen Renn, Max Planck Institute for the History of Science Kostas Gavroglu, University of Athens Managing Editor Lindy Divarci, Max Planck Institute for the History of Science Editorial Board Theodore Arabatzis, University of Athens Heather E. Douglas, University of Waterloo Jean Gayon, Université Paris 1 Thomas F. Glick, Boston University Hubert Goenner, University of Goettingen John Heilbron, University of California, Berkeley Diana Kormos-Buchwald, California Institute of Technology Christoph Lehner, Max Planck Institute for the History of Science Peter McLaughlin, Universität Heidelberg Agustí Nieto-Galan, Universitat Autònoma de Barcelona Nuccio Ordine, Universitá della Calabria Sylvan S. Schweber, Harvard University Ana Simões, Universidade de Lisboa John J. Stachel, Boston University Baichun Zhang, Chinese Academy of Science More information about this series at http://www.springer.com/series/5710 Johannes Lenhard • Martin Carrier Editors Mathematics as a Tool Tracing New Roles of Mathematics in the Sciences 123 Editors Johannes Lenhard Department of Philosophy Bielefeld University Bielefeld, Germany Martin Carrier Department of Philosophy Bielefeld University Bielefeld, Germany ISSN 0068-0346 ISSN 2214-7942 (electronic) Boston Studies in the Philosophy and History of Science ISBN 978-3-319-54468-7 ISBN 978-3-319-54469-4 (eBook) DOI 10.1007/978-3-319-54469-4 Library of Congress Control Number: 2017936971 © Springer International Publishing AG 2017 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Dedicated to Ann Johnson (1965–2016) This volume owes much to Ann. It synthesizes the work of the cooperation group “Mathematics as a Tool” that gathered over several years at the Center for Interdisciplinary Research (ZiF), Bielefeld. The core group consisted of P. Blanchard, M. Carrier, J. Jost, and J. Lenhard. They partly acted as authors; most of the chapters are by scholars who were involved in workshops or other events organized by the ZiF group. Ann, who sadly passed away shortly before the book came out, was more than a brilliant participant in a work