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Oxford Handbook of the History of Mathematics (Oxford Handbooks) PDF

927 Pages·2009·12.48 MB·English
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THE OXFORD HANDBOOK OF THE HISTORY OF MATHEMATICS This page intentionally left blank THE OXFORD HANDBOOK OF T H E H ISTORY OF M AT H E M AT IC S Edited by Eleanor Robson and Jacqueline Stedall 1 3 Great Clarendon Street, Oxford OX2 6DP 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 in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offi ces in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Th ailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Eleanor Robson and Jacqueline Stedall 2009 Th e moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2009 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, 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 book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Th e Oxford handbook of the history of mathematics / edited by Eleanor Robson & Jacqueline Stedall. p. cm. Includes index. ISBN 978–0–19–921312–2 1. Mathematics—History—Handbooks, manuals, etc. I. Robson, Eleanor. II. Stedall, Jacqueline A. QA21.094 2008 510.9 —dc22 2008031793 Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain on acid-free paper by CPI Antony Rowe, Chippenham, Wiltshire ISBN 978–0–19–921312–2 10 9 8 7 6 5 4 3 2 1 TABLE OF CONTENTS Introduction 1 GEOGRAPHIES AND CULTURES 5 1. Global 1.1 What was mathematics in the ancient world? Greek and Chinese perspectives G E R Lloyd 7 1.2 Mathematics and authority: a case study in Old and New World accounting Gary Urton 27 1.3 H eavenly learning, statecraft , and scholarship: the Jesuits and their mathematics in China Catherine Jami 57 1.4 Th e internationalization of mathematics in a world of nations, 1800–1960 Karen Hunger Parshall 85 2. Regional 2.1 Th e two cultures of mathematics in ancient Greece Markus Asper 107 2.2 Tracing mathematical networks in seventeenth-century England Jacqueline Stedall 133 2.3 Mathematics and mathematics education in traditional Vietnam Alexei Volkov 153 2.4 A Balkan trilogy: mathematics in the Balkans before World War I Snezana Lawrence 177 3. Local 3.1 M athematics education in an Old Babylonian scribal school Eleanor Robson 199 3.2 Th e archaeology of mathematics in an ancient Greek city David Gilman Romano 229 3.3 E ngineering the Neapolitan state Massimo Mazzotti 253 3.4 Observatory mathematics in the nineteenth century David Aubin 273 vi Table of Contents PEOPLE AND PRACTICES 299 4. Lives 4.1 Patronage of the mathematical sciences in Islamic societies Sonja Brentjes 301 4.2 J ohn Aubrey and the ‘Lives of our English mathematical writers’ Kate Bennett 329 4.3 I ntroducing mathematics, building an empire: Russia under Peter I Irina Gouzévitch and Dmitri Gouzévitch 353 4.4 H uman computers in eighteenth- and nineteenth-century Britain Mary Croarken 375 5. Practices 5.1 M ixing, building, and feeding: mathematics and technology in ancient Egypt Corinna Rossi 407 5.2 Siyaq: numerical notation and numeracy in the Persianate world Brian Spooner and William L Hanaway 429 5.3 L earning arithmetic: textbooks and their users in England 1500–1900 John Denniss 448 5.4 Algorithms and automation: the production of mathematics and textiles Carrie Brezine 468 6. Presentation 6.1 Th e cognitive and cultural foundations of numbers Stephen Chrisomalis 495 6.2 Sanskrit mathematical verse Kim Plofk er 519 6.3 A ntiquity, nobility, and utility: picturing the Early Modern mathematical sciences Volker R Remmert 537 6.4 Writing the ultimate mathematical textbook: Nicolas Bourbaki’s Éléments de mathématique Leo Corry 565 INTERACTIONS AND INTERPRETATIONS 589 7. Intellectual 7.1 People and numbers in early imperial China Christopher Cullen 591 7.2 Mathematics in fourteenth-century theology Mark Th akkar 619 7.3 Mathematics, music, and experiment in late seventeenth-century England Benjamin Wardhaugh 639 7.4 Modernism in mathematics Jeremy Gray 663 Table of Contents vii 8. Mathematical 8.1 Th e transmission of the Elements to the Latin West: three case studies Sabine Rommevaux 687 8.2 ‘Gigantic implements of war’: images of Newton as a mathematician Niccolò Guicciardini 707 8.3 From cascades to calculus: Rolle’s theorem June Barrow-Green 737 8.4 Abstraction and application: new contexts, new interpretations in twentieth-century mathematics Tinne Hoff Kjeldsen 755 9. Historical 9.1 Traditions and myths in the historiography of Egyptian mathematics Annette Imhausen 781 9.2 Reading ancient Greek mathematics Ken Saito 801 9.3 Number, shape, and the nature of space: thinking through Islamic art Carol Bier 827 9.4 Th e historiography and history of mathematics in the Th ird Reich Reinhard Siegmund-Schultze 853 About the contributors 881 Index 891 This page intentionally left blank INTRODUCTION Eleanor Robson and Jacqueline Stedall We hope that this book will not be what you expect. It is not a textbook, an e ncyclopedia, or a manual. If you are looking for a comprehensive account of the history of mathematics, divided in the usual way into periods and cultures, you will not fi nd it here. Even a book of this size is too small for that, and in any case it is not what we want to off er. Instead, this book explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. Th e book is not descriptive or didactic but investigative, comprising a variety of innovative and imaginative approaches to history. Th e image on the front cover captures, we hope, the ethos of the Handbook (Chapter 1.2, Fig. 1.2.5). At fi rst glance it has nothing to do with the history of mathematics. We see a large man in a headdress and cloak, wielding a ceremonial staff over a group of downcast kneeling women. Who are they, and what is going on? Who made this image, and why? Without giving away too much—Gary Urton’s chapter has the answers—we can say here that the clue is in the phrase written in Spanish above the women’s heads: Repartición de las mugeres donzellas q[ue] haze el ynga ‘categorization (into census-groups) of the maiden women that the Inka made’. As this and many other contributions to the book demonstrate, mathematics is not confi ned to classrooms and universities. It is used all over the world, in all languages and cultures, by all sorts of people. Further, it is not solely a literate activity but leaves physical traces in the material world: not just writings but also objects, images, and even buildings and landscapes. More oft en, math- ematical practices are ephemeral and transient, spoken words or bodily gestures recorded and preserved only exceptionally and haphazardly. A book of this kind depends on detailed research in disparate disciplines by a large number of people. We gave authors a broad remit to select topics and approaches from their own area of expertise, as long as they went beyond straight ‘what-happened-when’ historical accounts. We asked for their writing to be exemplary rather than exhaustive, focusing on key issues, questions, and methodologies rather than on blanket coverage, and on placing mathematical content into context. We hoped for an engaging and accessible style, with strik- ing images and examples, that would open up the subject to new readers and

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