Simplicity: Ideals of Practice in Mathematics and the Arts
To find "criteria of simplicity" was the goal of David Hilbert's recently discovered twenty-fourth problem on his renowned list of open problems given at the 1900 International Congress of Mathematicians in Paris. At the same time, simplicity and economy
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Simplicity Ideals of Practice in Mathematics and the Arts Roman Kossak · Philip Ording Editors
Mathematics, Culture, and the Arts Series editors Jed Z. Buchwald Jeremy Gray Marjorie Senechal
The series Mathematics in Culture and the Arts will publish books on all aspects of the relationships between mathematics and the mathematical sciences and their roles in culture, art, architecture, literature, and music. This new book series will be a major resource for researchers, educators, scientifically minded artists, and students alike.
More information about this series at http://www.springer.com/series/13129
Roman Kossak • Philip Ording Editors
Simplicity: Ideals of Practice in Mathematics and the Arts
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Editors Roman Kossak Department of Mathematics The Graduate Center City University of New York New York, NY, USA
Philip Ording Department of Mathematics Sarah Lawrence College Bronxville, NY, USA
ISSN 2520-8578 ISSN 2520-8586 (electronic) Mathematics, Culture, and the Arts ISBN 978-3-319-53383-4 ISBN 978-3-319-53385-8 (eBook) DOI 10.1007/978-3-319-53385-8 Library of Congress Control Number: 2017935487 © 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
The 24th problem in my Paris lecture was to be: Criteria of simplicity, or proof of the greatest simplicity of certain proofs. Develop a theory of the method of proof in mathematics in general. Under a given set of conditions there can be but one simplest proof. Quite generally, if there are two proofs for a theorem, you must keep going until you have derived each from the other, or until it becomes quite evident what variant conditions (and
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