MATHEMATICIANS AND THEIR GODS Interactions between mathematics and religious beliefs Edited by snezana lawrence and mark mccartney 1 1 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Oxford University Press 2015 The moral rights of the authors have been asserted First Edition published in 2015 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2014956601 ISBN 978–0–19–870305–1 Printed in Great Britain by Clays Ltd, St Ives plc Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work. PREFACE he overlap between mathematics and theism may seem at first sight an unpromising topic for a book. But as the many contributors to this volume show, the intersection between the two provides fertile ground Tboth for historians of mathematics and of theology, and for the interested gen- eral reader. The chapters have been written by a range of subject experts, who have given willingly of their time and their knowledge. They have also submitted with good humour and patience to our various editorial queries, suggestions, and proddings, and we thank them for their enthusiasm for, and commitment to, the project. The chapters of the book are ordered broadly chronologically and thus the work can be read beginning with the Pythagoreans and then meandering through a range of times, places, and people, to end with Kurt Gödel. However, each chapter is independent of the others and so the reader can feel free to ‘dip in’ to the book at whichever point he or she finds most interesting. Hopefully, such a reader will then be enticed into the other chapters. As is noted in the introductory chapter, this book makes no attempt to be comprehensive. The most glaring omission is of Islamic mathematics, with the centre of gravity of the book being within the Christian West. The bias is benign and can be accounted for by the interests of the editors, and the desire to keep the scale of the book within manageable proportions. If there is a benefit of this bias, it is that it illustrates that even within such a restricted field of study the interactions between religion and mathematics are surprisingly rich. Snezana Lawrence & Mark McCartney March 2015 CONTENTS 1. Introduction 1 mark mccartney 2. The Pythagoreans: number and numerology 21 andrew gregory 3. Divine light 51 allan chapman 4. Kepler and his Trinitarian cosmology 77 owen gingerich 5. The Lull before the storm: combinatorics in the Renaissance 89 robin wilson and john fauvel 6. Mystical arithmetic in the Renaissance: from biblical hermeneutics to a philosophical tool 105 jean-pierre brach 7. Newton, God, and the mathematics of the two books 121 rob iliffe 8. Maria Gaetana Agnesi, mathematician of God 145 massimo mazzotti 9. Capital G for Geometry: Masonic lore and the history of geometry 167 snezana lawrence 10. Charles Dodgson’s work for God 191 mark richards 11. P.G. Tait, Balfour Stewart, and The Unseen Universe 213 elizabeth f. lewis 12. Faith and Flatland 249 melanie bayley 13. Gödel’s ‘proof’ for the existence of God 279 c. anthony anderson Author biographies 290 Index 293 vi | CONTENTS CHAPTER 1 Introduction mark mccartney t is unfortunate that in popular thought the prevailing description of the interaction between science and religion is one of warfare. God, in some circles it seems, is the enemy of progress, the person we lazily appeal to in Iorder to fill the gaps in our current scientific knowledge, an outdated idea, a delusion, an intellectual non-subject. At best, religious belief is seen as a matter of private devotion which has nothing to do with public life. At worst, some quarters seem to want to take what may be called an Orwellian ‘Animal Farm’ approach to the matter, replacing Snowball the pig’s ‘four legs good, two legs bad’, with a version of scientism which states ‘science good, religion bad’. And yet, dig down a little below the surface of popular assessment to schol- arship on the history and philosophy of science, and a very different picture begins to appear. In academic circles the nineteenth-century ‘conflict model’ to describe the interaction between science and religion has been rejected and replaced with what Andrew Gregory in Chapter 2 of this book describes as the ‘complexity model’. The complexity model recognizes that there is a spectrum of interactions, ranging from conflict or mutual non-engagement to dialogue and synthesis. It recognizes that there are indeed conflicts, but there are also connec- tions and consonances, and that these interactions have cultural and historical contexts. Academics such as John Polkinghorne (1930–) and Alister McGrath (1953–) are examples of two scholars trained both in science and theology who have written widely on the links between those disciplines from a Christian per- spective.1 But they are only two from a long list of scholars, some of faith, some INTRODUCTION | 1 of none, who feel that there is much more to be said, and that much more needs to be said, than the Orwellian ‘science good, religion bad’.2 However, move from science to mathematics and the suggestion that there is an overlap with theism is likely to lead to puzzled looks. Linking algebra with the Almighty seems as sensible as trying to find common ground between bot- any and basketball. The famous story of Leonhard Euler (1707–83) confronting Denis Diderot (1713–84) at the court of Catherine the Great springs to mind: Diderot arrived at the Russian court in the 1770s and, it is said, spoke freely of his atheism. While Catherine was amused, her advisors suggested Diderot should have his atheistic wings clipped. Hence Euler, then at the St Petersburg Academy, was brought before the court and publically confronted Diderot with the statement ‘Sir, (a + bn)/n = x; hence God exists – Respond!’ Diderot, unable to answer, and humiliated by the laughter from all sides, left the court and immediately returned to France. The tale is, of course, apocryphal.3 It is amusing to imagine that the brilliant mathematician Euler would say such a thing, even more amusing that Diderot, editor of the Encyclopédie and well versed in mathematics, should have been taken in by it, and positively ridiculous that any such ‘argument’ could make an impression on anyone. We may seek for links between God and the scien- tific description of the created order, but surely any connections we might wish to make between God and our equations will be as weak as Euler’s fictitious remark? However, it is precisely with the phrases ‘scientific description’ and our‘ equa- tions’ that potential links between mathematics and theism are to be found. The scientific description of nature Galileo Galilei (1564–1642), in his book The Assayer, famously stated that ‘Philosophy is written in this grand book – I mean the universe – which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these one is wandering about in a dark labyrinth.’4 Galileo’s insight that mathematics is the language of the uni- verse has grown in significance since he penned it in 1623. It is not simply that mathematics is the language of nature, but also that, as the Nobel laureate 2 | MARK McCARTNEY Eugene Wigner (1902–95) pointed out in a famous essay, there is an ‘unreason- able effectiveness of mathematics in the natural sciences’.5 In his essay he notes that in theoretical physics, complex and independently discovered branches of mathematics often turn out to be the appropriate language of nature. Thus, in quantum mechanics the use of complex numbers is ‘far from natural or simple and they cannot be suggested by physical observations. Furthermore, the use of complex numbers in this case is not a calculational trick of applied math- ematics but comes close to being a necessity in the formulation of the laws of quantum mechanics.’6 He goes on to quip that: A possible explanation of the physicist’s use of mathematics to formulate his laws of nature is that he is a somewhat irresponsible person. As a result, when he finds a connection between two quantities which resembles a connection well-known from mathematics, he will jump at the conclusion that the connection is that discussed in mathematics simply because he does not know of any other similar connection.