Mathematical beginnings

Enough and more has been written and said about the historical contributions of India to world mathematics, some of it from serious scholarship, some by an appreciation of the history of ideas, and, regrettably, some of it sparked by cultural jingoism.

The Chennai Mathematical Institute organized a conference in 2008 to explore some aspects of the history of Indian mathematics, and this has now appeared as Studies in the History of Indian Mathematics edited by C. S. Seshadri. This volume, published by the Hindustan Book Agency, New Delhi, contains articles based on the talks of distinguished scholars both from the West and from India.

The topics covered include: (1) geometry in the Sulvasutras; (2) the origins of zero (which can be traced to ideas of lopa in Pànini's grammar); (3) combinatorial methods in Indian music (which were developed in the context of prosody and subsequently applied to the study of tonal and rhythmic patterns in music); (4) a cross-cultural view of the development of negative numbers (from Brahmagupta (c. 628 CE) to John Wallis (1685 CE); (5) Kuññaka, Bhàvanà and Cakravàla (the techniques developed by Indian mathematicians for the solution of indeterminate equations); (6) the development of calculus in India (covering the millennium-long history of discoveries culminating in the work of the Kerala school giving a complete analysis of the basic calculus of polynomial and trigonometrical functions); (7) recursive methods in Indian mathematics (going back to Pànini's grammar and culminating in the recursive proofs found in the Malayalam text Yuktibhàsà (1530 CE)); and (8) planetary and lunar models developed by the Kerala School of Astronomy. The articles in this volume cover a substantial portion of the history of Indian mathematics and astronomy.

This book will serve the dual purpose of bringing to the international community a better perspective of the mathematical heritage of India and conveying the message that much work remains to be done, namely the study of many unexplored manuscripts still available in libraries in India and abroad.

Contributors include C S Seshadri, K Plofker, M S Sriram, S G Dani, Frits Staal, Raja Sridharan, R Sridharan, David Mumford, Amartya Kumar Dutta, K Ramasubramanian and P P Divakaran.

In our History of Science section, in hardcover, 402 pages, Rs. 650. ISBN 9789380250069

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