HISTORY OF THE MATHEMATICAL SCIENCES

Transcription

1 HISTORY OF THE MATHEMATICAL SCIENCES

2 Volumes containing conference proceedings, workshop lectures, and collection of invited articles in any area of mathematics are published in this series. The aim is to provide an overview of the development through surveys, recent trends, problems and their current status as well as historical background. All contributions for publication should be thoroughly reviewed before submitting to us. We need manuscripts ready for direct reproduction. All articles must be prepared in a uniform format. Necessary instructions for format etc., are available from the publisher. Already Published Volumes Algebra-Some Recent Advances Edited by I. B. S. Passi Number Theory Edited by R. P. Bambah, V. C. Dumir, R. J. Hans-Gill Number Theory and Discrete Mathematics Edited by A. K. Agarwal, Bruce C. Berndt, Christian F. Krattenthaler, Gray L. Mullen, K. Ramachandra and Michel Waldschmidt CurrentTrends in Number Theory Edited by S.D. Adhikari, SA Katre, B. Ramakrishnan Advances in Algebra and Geometry Edited by C. Musili A Tribute to C. S. Seshadri: Perspectives in Geometry and Representation Theory Edited by V. Lakshmibai, V. Balaji, V. B. Mehta, K. R. Nagaraj, K. Pranjape. P. Sankran and R. Sridharan Elliptic Curves, Modular Forms and Cryptography Edited by A. K. Bhandari, D. S. Nagaraj, B. Ramakrishnan, T. N. Venktaraman

3 HISTORY OF THE MATHEMATICAL SCIENCES Chief Editor Ivor Grattan-Guinness Executive Editor B.S.Yadav ~HINDUSTAN U IJlJ UBOOKAGENCY

4 Edited by Ivor Grattan-Guinness, Chief Editor Middlesex University, Enfield, U.K. B.S. Yadav, Executive Editor University of Delhi, Delhi, India Suresh Garg Indira Gandhi National Open University New Delhi, India Vitali Milman Tel Aviv University Tel Aviv, Israel Man Mohan Ramjas College University of Delhi, Delhi, India G.S. Pandey Vikram University Ujjain, India Jean-Paul Pier Centre Universitaire de Luxembourg Luxembourg Norbert H. Schlomiuk Universite de Montreal Montreal, Canada S.L. Singh Gurukul Kangri University Hardwar, India Published by Hindustan Book Agency (India) P 19 Green Park Extension New Delhi India hba@vsnl.com Copyright 2004 by Hindustan Book Agency (India) No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner, who has also the sole right to grant licences for translation into other languages and publication thereof. All export rights for this edition vest exclusively with Hindustan Book Agency (India). Unauthorized export is a violation of Copyright Law and is subject to legal action. ISBN ISBN (ebook) DOI /

5 PREFACE The book is based on the selected papers of the proceedings of the International Conference on History of Mathematical Sciences held at New Delhi from December 20-23, The conference was organized by the Indian Society for History of Mathematics and Ramjas College, University of Delhi, in collaboration with Indira Gandhi' National Open University and Indian Institute of Advanced Study, Shimla. It was the first of its kind ever held in India and covered all aspects of the history of mathematical sciences. About 200 leading mathematicians (and users of mathematics in industry and technology) participated in the deliberations, including leading experts from 11 countries viz. US, UK, Canada, Germany, Luxembourg, Italy, Israel, Iran, Nepal and India. The contents of the book are divided into four parts. Part A consists of papers which concern general and philosophical issues, while Parts B, C, and D contain those on the history of mathematics in India, in the Near East, and in Europe and America, respectively. We are grateful to all the collaborating institutions for generous financial assistance for a successful organisation of the conference. We also thank for liberal Grants made available by various other sources; special menti'on may be made of National Board of Higher Mathematics, University Grants Commission, Council of Scientific & Industrial Research Indian National Science Academy, Power Grid Corporation of India, and Maharaja Agrasen Institute of Technology, Delhi. The organizers greatly appreciate the cooperation received from Prof. H.P. Dikshit, Vice Chancellor, Indira Gandhi National Open University, Prof. K.A. Ross, University of Oregon, Prof. Y.P. Sabharwal, Ramjas College and Prof. Ajit Iqbal Singh, University of Delhi. In the organisation of such events, some faces and voices contribute without being seen or heard. Their initiatives and courage go a long way in keeping schedules and avoiding inconveniences to delegates. We would like to record our most sincere gratitude to the members of various committees, particularly International Steering Committee representing every part of the world, for their help and guidance. Lastly we also appreciate the initiative of Jainendra K. Jain of Hindustan Book Agency in publishing the Proceedings,

6 Vl Dr. S. Venkatraman and Ms. Manju Sharma of Indira Gandhi National Open University for preparing the camera-ready copies of the text. It has been possible to include only some selected Papers presented at the conference. The remaining ones are being considered for publication in the next issues of Garzita Bharatl, the bulletin of the Indian Society for History of Mathematics. EDITORS

7 CONTENTS Preface v Part A: General and Philosophical Issues Evolution of History of Mathematics: Some Trends 01 K.S. CHAUDHURI History or Heritage? A Central Question in the 13 Historiography of Mathematics IvOR GRATTAN-GUINNESS Abstraction and Structural Analogies in Mathematical 33 Sciences R S KAUSHAL The Invented and Propagated Theories in the Origin of 53 Mathematical Sciences V. LAKSHMIKANTHAM Andre Weil: The Man and the Historian of Mathematics 61 NORBERT H SCHLDMIUK Part B: History of Mathematics in India The Vedic Concept of Infinity and Infinitesimal System 65 G. S. PANDEY Mahavlra's geometrical Problems: Traces of unknown 83 Links between Jaina and Mediterranean Mathematics in the classical Ages lens H0YRUP Dignaga's Logic of Invention 97 VOLKER PECKHAUS Concept of Perception in Vedanta Darshna and modern 109 Mathematical Sciences RAI GYAN NARAIN PRASAD Parte: History of Mathematics in the Near East The Egyptian Mathematical Leather Ro~l, Attested Short 119 Term and Long Term MILD GARDNER

8 viii Omar Khayyam, RenE~ Descartes and Solutions to 135 Algebraic Equations K.V. MARDIA A New Source of Evidence for the Lost Arabic 149 Translations of Euclid's Elements Gregg De Young Part D: History of Mathematics in Europe and America Pell's Equation and the Unity of Mathematics CHAHAL History, State of the Art and Future of the Science of 171 Stochastics ELART VON COLLA NI C[a,b] as the Backbone of Evolution of Functional 195 Analysis B.S. YADAV Harmonic Analysis: A historical manifold during the XXth 211 Century lean-paul PIER From Functional Analysis to Asymptotic Geometric 225 Analysis VITALI MILMAN