Open Problems in Mathematics
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which
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Open Problems in Mathematics
Open Problems in Mathematics
John Forbes Nash, Jr. • Michael Th. Rassias Editors
Open Problems in Mathematics
123
Editors John Forbes Nash, Jr. (Deceased) Department of Mathematics Princeton University Princeton, NJ, USA
Michael Th. Rassias Department of Mathematics Princeton University Princeton, NJ, USA ETH-Zürich Department of Mathematics Zürich, Switzerland
ISBN 978-3-319-32160-8 ISBN 978-3-319-32162-2 (eBook) DOI 10.1007/978-3-319-32162-2 Library of Congress Control Number: 2016941333 © 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 Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Preface John Forbes Nash, Jr. and Michael Th. Rassias
Learn from yesterday, live for today, hope for tomorrow. The important thing is not to stop questioning. – Albert Einstein (1879–1955) It has become clear to the modern working mathematician that no single researcher, regardless of his knowledge, experience, and talent, is capable anymore of overviewing the major open problems and trends of mathematics in its entirety. The breadth and diversity of mathematics during the last century has witnessed an unprecedented expansion. In 1900, when David Hilbert began his celebrated lecture delivered before the International Congress of Mathematicians in Paris, he stoically said: Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?
Perhaps Hilbert was among the last great mathematicians who could talk about mathematics as a whole, pr
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