The History of Mathematical Proof in Ancient Traditions

614 Pages · 2012 · 5.71 MB · English

  • The History of Mathematical Proof in Ancient Traditions

    Th e History of Mathematical Proof in Ancient Traditions

    Th is radical, profoundly scholarly book explores the purposes and

    nature of proof in a range of historical settings. It overturns the

    view that the fi rst mathematical proofs were in Greek geometry and

    rested on the logical insights of Aristotle by showing how much of

    that view is an artefact of nineteenth-century historical scholarship.

    It documents the existence of proofs in ancient mathematical writ-

    ings about numbers, and shows that practitioners of mathematics in

    Mesopotamian, Chinese and Indian cultures knew how to prove the

    correctness of algorithms, which are much more prominent outside

    the limited range of surviving classical Greek texts that historians have

    taken as the paradigm of ancient mathematics. It opens the way to

    providing the fi rst comprehensive, textually based history of proof.

    Jeremy Gray, Professor of the History of Mathematics, Open University

    ‘Each of the papers in this volume, starting with the amazing

    “Prologue” by the editor, Karine Chemla, contributes to nothing less

    than a revolution in the way we need to think about both the sub-

    stance and the historiography of ancient non-Western mathematics,

    as well as a reconception of the problems that need to be addressed if

    we are to get beyond myth-eaten ideas of “unique Western rationality”

    and “the Greek miracle”. I found reading this volume a thrilling intel-

    lectual adventure. It deserves a very wide audience.’

    Hilary Putnam, Cogan University Professor Emeritus, Harvard


    karine chemla is Senior Researcher at the CNRS (Research

    Unit SPHERE, University Paris Diderot, France), and a Senior Fellow

    at the Institute for the Study of the Ancient World at New York

    University. She is also Professor on a Guest Chair at Northwestern

    University, Xi‘an, as well as at Shanghai Jiaotong University and Hebei

    Normal University, China. She was awarded a Chinese Academy of

    Sciences Visiting Professorship for Senior Foreign Scientists in 2009. Th e History of Mathematical

    Proof In Ancient Traditions

    Edited by karine chemla 林力娜 cambridge university press

    Cambridge, New York, Melbourne, Madrid, Cape Town,

    Singapore, São Paulo, Delhi, Mexico City

    Cambridge University Press

    Th e Edinburgh Building, Cambridge CB2 8RU, UK

    Published in the United States of America by Cambridge University Press, New York


    Information on this title: www.cambridge.org/9781107012219

    © Cambridge University Press 2012

    Th is publication is in copyright. Subject to statutory exception

    and to the provisions of relevant collective licensing agreements,

    no reproduction of any part may take place without the written

    permission of Cambridge University Press.

    First published 2012

    Printed in the United Kingdom at the University Press, Cambridge

    A catalogue record for this publication is available from the British Library

    ISBN 9781107012219 Hardback

    Cambridge University Press has no responsibility for the persistence or

    accuracy of URLs for external or third-party internet websites referred to in

    this publication, and does not guarantee that any content on such websites is,

    or will remain, accurate or appropriate. Contents

    List of fi gures [ix]

    List of contributors [xii]

    Note on references [xiv]

    Acknowledgements [xv]

    Prologue Historiography and history of mathematical proof:

    a research programme [1]

    Karine Chemla

    part i views on the historiography

    of mathematical proof

    Shaping ancient Greek mathematics: the critical editions of Greek

    texts in the nineteenth century

    1 Th e Euclidean ideal of proof in Th e Elements and philological

    uncertainties of Heiberg’s edition of the text [69]

    bernard vitrac

    2 Diagrams and arguments in ancient Greek mathematics: lessons

    drawn from comparisons of the manuscript diagrams with those

    in modern critical editions [135]

    ken saito and nathan sidoli

    3 Th e texture of Archimedes’ writings: through Heiberg’s veil [163]

    reviel netz

    Shaping ancient Greek mathematics: the philosophers’ contribution

    4 John Philoponus and the conformity of mathematical

    proofs to Aristotelian demonstrations [206]

    orna harari

    Forming views on the ‘Others’ on the basis of mathematical proof

    5 Contextualizing Playfair and Colebrooke on proof and

    demonstration in the Indian mathematical tradition

    (1780–1820) [228]

    dhruv raina v vi Contents

    6 Overlooking mathematical justifi cations in the Sanskrit tradition:

    the nuanced case of G. F. W. Th ibaut [260]

    agathe keller

    7 Th e logical Greek versus the imaginative Oriental: on the

    historiography of ‘non-Western’ mathematics during the

    period 1820–1920 [274]

    françois charette

    part ii history of mathematical proof in

    ancient traditions: the other evidence

    Critical approaches to Greek practices of proof

    8 Th e pluralism of Greek ‘mathematics’ [294]

    g. e. r. lloyd

    Proving with numbers: in Greece

    9 Generalizing about polygonal numbers in ancient Greek

    mathematics [311]

    ian mueller

    10 Reasoning and symbolism in Diophantus: preliminary

    observations [327]

    reviel netz

    Proving with numbers: establishing the correctness of algorithms

    11 Mathematical justifi cation as non-conceptualized practice: the

    Babylonian example [362]

    jens høyrup

    12 Interpretation of reverse algorithms in several Mesopotamian

    texts [384]

    christine proust

    13 Reading proofs in Chinese commentaries: algebraic proofs in an

    algorithmic context [423]

    karine chemla

    14 Dispelling mathematical doubts: assessing mathematical

    correctness of algorithms in Bhāskara’s commentary on the

    mathematical chapter of the Āryabhatīya [487]


    agathe keller Contents vii

    Th e later persistence of traditions of proving in Asia: late evidence

    of traditions of proof

    15 Argumentation for state examinations: demonstration in

    traditional Chinese and Vietnamese mathematics [509]

    alexei volkov

    Th e later persistence of traditions of proving in Asia: interactions of

    various traditions

    16 A formal system of the G ougu method: a study on Li Rui’s

    Detailed Outline of Mathematical Procedures for the Right-Angled

    Triangle [552]

    tian miao

    Index [574]

    Please note: To fully download this free PDF,EBook files you need know All free.
    Found by internet command,site not saved pdf file
You May Also Like

Related PPT Template in the same category.