Thomas Sonar The History of the Priority Di pute between Newton and Leibniz Mathematics in History and Culture Thomas Sonar TheR History of the Priority Di pute between Newton and Leibniz Mathematics in History and Culture With an Epilogue by Eberhard Knobloch Thomas Sonar Technische Universität Braunschweig Braunschweig Germany Translated by Thomas Sonar, Braunschweig, Germany; Keith William Morton, Oxford, UK; Patricia Morton, Oxford, UK Editor: Project Group “History of Mathematics” of Hildesheim University H.W. Alten, K.-J. Förster, K.-H. Schlote, H. Wesemüller-Kock ISBN 978-3-319-72561-1 ISBN 978-3-319-72563-5 (eBook) https://doi.org/10.1007/978-3-319-72563-5 Library of Congress Control Number: 2018934415 Originally published in German in the series “Vom Zählstein zum Computer” under the title: “Die Geschichte des Prioritätsstreits zwischen Leibniz und Newton. Geschichte - Kulturen – Menschen” (ISBN 978-3-662-48861-4) Springer-Verlag Berlin Heidelberg 2016 ISBN 978-3-662-48862-1 (ebook) © Springer International Publishing AG, part of Springer Nature 2018 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. Graphic on the cover: © Helmut Schwigon Printed on acid-free paper This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer International Publishing AG part of Springer Nature The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland The two warriors immortalised in the University Museum of Oxford [Photos Sonar] Dedicated to Keith William (Bill) Morton, mentor, teacher, and friend in Oxford, and to his wonderful wife Patricia (Pat) Morton. ‘The world, surely, has not another place like Oxford: it is a despair to see such a place and ever have to leave it.’ Nathaniel Hawthorne, 1856. [Morris 1978, p. x] About the Author Thomas Sonar was born 1958 in Sehnde next to Hannover. After studying Me- chanical Engineering at the University of Applied Sciences (‘Fachhochschule’) Hannover he became a laboratory engineer in the Laboratory for Control The- ory of the same University for a short time, and founded an engineering office. He then studied mathematics at the University of Hannover (now Leibniz Uni- versity), after which he worked from 1987 until 1989 at the German Aerospace Establishment DLR (then DFVLR) in Brunswick for the orbital glider project HERMES as a scientific assistant. Next he went to the University of Stuttgart to work as a PhD student under Prof Dr Wolfgang Wendland while spending some time studying under Prof Keith William Morton, at the Oxford Com- puting Laboratory. His PhD thesis was defended in 1991 and Thomas Sonar went to Göttingen to work as a mathematician (‘Hausmathematiker’) at the Institute for Theoretical Fluid Mechanics of the DLR; there he developed and coded the first version of the TAU-code for the numerical computation of compressible fluid fields, which is now widely used. In 1995 the postdoc- toral lecture qualification for mathematics was obtained from the TU (then TH) Darmstadt on the basis of a habilitation treatise. From 1996 until 1999 Thomas Sonar was full professor of Applied Mathematics at the University of Hamburg and is professor for Technical and Industrial Mathematics at the Technical University of Brunswick since 1999 where he is currently the head of a work group on partial differential equations. In 2003 he declined an of- fer of a professorship at the Technical University of Kaiserslautern connected with a leading position in the Fraunhofer Institute for Industrial Mathematics VII VIII About the Author ITWM. In the same year Sonar founded the centre of continuing education for mathematics teachers (‘Mathelok’) at the TU Brunswick which stays active with regular events for pupils also. Early in his career Thomas Sonar developed an interest in the history of mathematics, publishing in particular on the history of navigation and of logarithms in early modern England, and conducted the widely noticed exhi- bitions in the ‘Gauss year’ 2005 and in the ‘Euler year’ 2007 in Brunswick. Further publications concern Euler’s analysis, his mechanics and fluid mechan- ics, the history of mathematical tables, William Gilbert’s magnetic theory, the history of ballistics, the mathematician Richard Dedekind, and the death of Gottfried Wilhelm Leibniz. In 2001 Sonar published a book on Henry Briggs’ early mathematical works after intense research in Merton College, Oxford. In 2011 his book 3000 Jahre Analysis (3000 years of analysis) was published in this series and in December 2014 he edited the correspondence of Richard Dedekind and Heinrich Weber. Altogether Thomas Sonar has published ap- proximately 150 articles and 14 books – partly together with colleagues. He has established a regular lecture on the history of mathematics at the TU Brunswick and has for many years held a lectureship on this topic at the Uni- versity of Hamburg. Many of his publications also concern the presentation of mathematics and the history of mathematics to a wider public and the improvement of the teaching of mathematics at secondary schools. Thomas Sonar is member of the Gesellschaft für Bildung und Wissen e.V. (So- ciety for Education and Knowledge), the Braunschweiger Wissenschaftliche Gesellschaft (Brunswick Scientific Society), a corresponding member of the Academy of Sciences in Hamburg, and an honorary member of the Mathema- tische Gesellschaft in Hamburg (Mathematical Society in Hamburg). Preface of the Author Scientific priority - In science, priority is the credit given to the individual or group of individuals who first made the discovery or propose the theory. [...] Priority becomes a difficult issue usually in the context of priority disputes, where the priority for a given theory, understanding, or discovery comes into question. Wikipedia en.wikipedia.org/wiki/Scientific_priority (lastly retrieved on 3rd July 2017) Quarrels on the priority of scientific methods, theories or inventions occured often in history, and still occur; almost none was so doggedly fought as the famous priority dispute between Isaac Newton (4th January 1643 – 31st March 1727)1 and Gottfried Wilhelm Leibniz (1st July, 1646 – 14th November, 1716) on the invention of the differential and integral calculus, and none has had such a tremendous impact. Hal Hellman has included this quarrel in his book on the great feuds in mathematics [Hellman 2006] and he described only ten feuds in all. We can therefore be certain we are dealing here with a real scandal. The controversy grew quickly to an international incident: England against the continent! On Leibniz’s side were the pugnacious brothers Jacob and John Bernoulli and all continental mathematicians who understood the new calcu- lus (small in number, of course). Behind Newton stood his English backers and the mathematicians of the Royal Society. Both groups were not really large by comparison with the impact of the quarrel! The huge effect of the priority dispute was the separation of English mathematics from the mathematics on the continent well into the 20. century! The English stood behind Newton and used his cumbersome dot notation x,˙ x¨, and so forth for the derivatives of a 1Protestant England had not yet introduced the Gregorian calendar in Newton’s days since it was thought a papist invention. The English were hence 10 days behind until the year 1700 and 11 days from the 28th February, 1700. In the Julian calendar Newton was born on the 25th December 1642 – he was a Christmas child – and died on 20th March, 1726. Until the year 1752 the New Year began in England at the 25th of March. Therefore, many authors give dates between the 1st of January 1727 and the 24th of March 1727 in the form 1726/27, but in order not to confuse my affectionate readership I have converted all dates to the Gregorian format. Only at a few places I have clearly indicated a Julian date. IX X Preface of the Author function x(t) while the continental mathematicians recognised the superiority of Leibniz’s calculus and used the differential quotient dy/dx instead of y/˙ x˙, which easily led to intuitive calculation schemes. Thus, mathematics on the continent developed with quantum jumps while the English apparently did not add much to it. In the year 1755, one generation after the two adversaries, the first of two volumes of the opus Institutiones Calculi Differentialis of the great Leonhard Euler (1707–1783) appeared, who was a pupil of John Bernoulli. In chapter four Euler remarked in section 116 [Blanton 2000, S.64f.]: ’... but there is no doubt that we have won the prize from the En- glish when it is a question of notation. For differentials, which they call fluxions, they use dots above the letters. Thus, y˙ signifies the first fluxion of y, y¨ is the second fluxion, the third fluxion has three dots, and so forth.