E-Book Overview
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 of assertions do mathematical statements make? How do people think and speak about mathematics? How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change again in the future? The authors include mathematicians, philosophers, computer scientists, cognitive psychologists, sociologists, educators and mathematical historians; each brings their own expertise and insights to the discussion.
Contributors to this volume:
Jeremy Avigad
Jody Azzouni
David H. Bailey
David Berlinski
Jonathan M. Borwein
Ernest Davis
Philip J. Davis
Donald Gillies
Jeremy Gray
Jesper Lützen
Ursula Martin
Kay O’Halloran
Alison Pease
Steven Piantadosi
Lance Rips
Micah T. Ross
Nathalie Sinclair
John Stillwell
Hellen Verran
E-Book Content
Ernest Davis Philip J. Davis Editors 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. . . . . . . . . . . . . . . . . . . . .