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A History of Mathematics
From Mesopotamia to Modernity
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 YorkAuckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With ofﬁces in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and incertain other countries Published in the United States by Oxford University Press Inc., New York © Oxford University Press, 2005 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2005 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 theprior 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 imposethe same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain on acid-free paper by Antony Rowe Ltd., Chippenham, Wiltshire ISBN 0–19–852937–6 (Hbk) 978–0–19–852937–8 1 3 5 7 9 10 8 6 4 2
Thisbook has its origin in notes which I compiled for a course on the history of mathematics at King’s College London, taught for many years before we parted company. My major change in outlook (which is responsible for its form) dates back to a day ten years ago at the University of Warwick, when I was comparing notes on teaching with the late David Fowler. He explained his own history of mathematicscourse to me; as one might expect, it was detailed, scholarly, and encouraged students to do research of their own, particularly on the Greeks. I told him that I gave what I hoped was a critical account of the whole history of mathematics in a series of lectures, trying to go beyond what they would ﬁnd in a textbook. David was scornful. ‘What’, he said, ‘do you mean that you stand up in front ofthose students and tell stories?’ I had to acknowledge that I did. David’s approach meant that students should be taught from the start not to accept any story at face value, and to be interested in questions rather than narrative. It’s certainly desirable as regards the Greeks, and it’s a good approach in general, even if it may sometimes seem too difﬁcult and too purist. I hope he would not be toohard on my attempts at a compromise. The aims of the book in this, its ultimate form, are set out in the introduction; brieﬂy, I hope to introduce students to the history, or histories of mathematics as constructions which we make to explain the texts which we have, and to relate them to our own ideas. Such constructions are often controversial, and always provisional; but that is the nature ofhistory. The original impulse to write came from David Robinson, my collaborator on the course at King’s, who suggested (unsuccessfully) that I should turn my course notes into a book; and providentially from Alison Jones of the Oxford University Press, who turned up at King’s when I was at a loose end and asked if I had a book to publish. I produced a proposal; she persuaded the press to accept...