Table Of ContentTHE 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
