Mathematics in India

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Princeton University Press, Dec 29, 2008 - Mathematics - 360 pages

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning.


Far more than in other areas of the history of mathematics, the literature on Indian mathematics reveals huge discrepancies between what researchers generally agree on and what general readers pick up from popular ideas. This book explains with candor the chief controversies causing these discrepancies--both the flaws in many popular claims, and the uncertainties underlying many scholarly conclusions. Supplementing the main narrative are biographical resources for dozens of Indian mathematicians; a guide to key features of Sanskrit for the non-Indologist; and illustrations of manuscripts, inscriptions, and artifacts. Mathematics in India provides a rich and complex understanding of the Indian mathematical tradition.


**Author's note: The concept of "computational positivism" in Indian mathematical science, mentioned on p. 120, is due to Prof. Roddam Narasimha and is explored in more detail in some of his works, including "The Indian half of Needham's question: some thoughts on axioms, models, algorithms, and computational positivism" (Interdisciplinary Science Reviews 28, 2003, 1-13).

 

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Contents

Chapter 1 Introduction
1
Chapter 2 Mathematical Thought in Vedic India
13
Chapter 3 Mathematical Traces in the Early Classical Period
43
Chapter 4 The Mathematical Universe
61
Chapter 5 The Genre of Medieval Mathematics
121
Chapter 6 The Development of Canonical Mathematics
173
Chapter 7 The School of Madhava in Kerala
217
Chapter 8 Exchanges with the Islamic World
255
Chapter 9 Continuity and Changes in the Modern Period
279
Appendix A Some Basic Features of Sanskrit Language and Literature
299
Appendix B Biographical Data on Indian Mathematicians
317
Bibliography
327
Index
353
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About the author (2008)

Kim Plofker is visiting assistant professor of mathematics at Union College.

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