Mathematics, Substance and Surmise Views on the Meaning and Ontology
The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds
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Mathematics, Substance and Surmise Views on the Meaning and Ontology of Mathematics
Mathematics, Substance and Surmise
Ernest Davis • Philip J. Davis Editors
Mathematics, Substance and Surmise Views on the Meaning and Ontology of Mathematics
123
Editors Ernest Davis Department of Computer Science New York University New York, NY, USA
Philip J. Davis Department of Applied Mathematics Brown University Providence, RI, USA
ISBN 978-3-319-21472-6 ISBN 978-3-319-21473-3 (eBook) DOI 10.1007/978-3-319-21473-3 Library of Congress Control Number: 2015954083 Mathematics Subject Classification (2010): 01Axx, 00A30, 03-02, 11-04, 11Y-XX, 40-04, 65-04, 68W30, 97Mxx, 03XX, 97C30. Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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 Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com)
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ernest Davis
1
Hardy, Littlewood and polymath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ursula Martin and Alison Pease
9
Experimental computation as an ontological game changer: The impact of modern mathematical computation tools on the ontology of mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . David H. Bailey and Jonathan M. Borwein
25
Mathematical products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Philip J. Davis
69
How should robots think about space? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ernest Davis
75
Mathematics and its applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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