Mathematics in India

Mathematics in India

Mathematics in India

Mathematics in India

Synopsis

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).

Excerpt

“Why is it so hard to find information about Indian math?” Many researchers in the history of Indian mathematics have heard (or asked) this plaintive question at one time or another. Usually it’s posed by a frustrated non-Indologist colleague engaged in some attempt to integrate the Indian tradition into the history of mathematical sciences elsewhere in the world: for example, teaching a general history of math course or writing a general history of a mathematical topic.

There’s no denying that the Indian tradition presents some unique challenges for anyone interested in the history of mathematics. It’s not that information about the subject isn’t available, but it’s frequently difficult to separate reliable information from speculation or invention, or to extract from it a coherent and consistent overview of the historical development of Indian mathematical sciences. What other branch of history of math can show, for example, a pair of articles by two widely published researchers, appearing side by side in the same edited volume, whose estimates of their subect’s approximate date of origin differ by as much as two thousand years?

As I explain in more detail in the following chapters, these difficulties are due in large part to the uncertainty of early Indian chronology, the absence of historical or biographical data in many Indian technical works, and the ways that Sanskrit literature deals with authority, intertextuality, and tradition. There are many missing links in the chain of historical fact tracing out the development of Indian mathematical sciences; some of these links will someday be uncovered by new research, while others may remain forever conjectural.

This does not mean that we can’t construct a reasonable narrative for the history of Indian mathematics based on the available data and plausible inferences. The narrative currently accepted by most mainstream historians as consistent with the textual record, linguistic and archaeological evidence, and the known history of other mathematical traditions goes more or less like this: The earliest urban Indian cultures, centered in the river valleys in the northwest of the South Asian subcontinent around the third millenniumBCE, have left no clear record of their mathematical knowledge, although we can infer from the complexity of their infrastructure and global trade that this knowledge must have been substantial. From the second mil-

Compare [Oha2000], p. 342, and [Kak2000a], p. 328; the former follows the mainstream opinion placing the emergence of quantitative astronomy in Vedic India in the second millennium BCE, while the latter suggests it goes back as far as the fourth millennium.

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