Mathematics in India.

• Author: Sarma, S.R.
• Position: Book review

Mathematics in India. By KIM PLOFKER. Princeton: PRINCETON UNIVERSITY PRESS, 2009. Pp. xiii + 357.

Historians of mathematics encounter many hurdles when they try to understand the development of mathematics in India. The texts are composed in a highly compressed form in Sanskrit verse and very few are available in modern English translation. In many cases, the chronology of texts is still unsettled. Moreover, mathematics was not an independent discipline (sastra); it developed largely in the context of astronomy. Even the term ganita is not exclusive to mathematics, for it denotes mathematical astronomy as well. What is more, ganaka, the possible term to designate a mathematician, is more frequently used for astronomers and astrologers.

Kim Plofker's meticulously researched and engagingly written Mathematics in India aims to remove these hurdles and to present the development of mathematics "as a coherent and largely continuous intellectual tradition, rather than a collection of achievements to be measured against the mathematics of other cultures," as was done in earlier histories of Indian mathematics. Though it follows the mainstream narrative, the strong point of the book is that it endeavors to present other points of view quite objectively and admits it whenever there is a lack of supporting evidence for the mainstream narrative. It provides the proper historical and intellectual context to the texts, and introduces the main contents through copious extracts that are impeccably rendered into English and lucidly explained in modern notation.

The narration begins in Chapter 2 with the mathematical thought in the Vedic texts. There are three strands of this thought. First, the Vedic hymns are replete with specific terms to designate higher powers of ten that go far beyond the requirements of computation in daily life. There are also other significant references to numbers and their properties. Second, the rules prescribed in the sulva-sutras for the construction of different types of sacrificial altars involve area-preserving transformations of plane figures, from square to rectangle or to circle and so on. In this context, it is postulated that the squares on the width and length of any rectangle add up to the square on its diagonal, which is otherwise known as the Pythagorean theorem. Third, the Jyotisa-vedanga, which belongs to the post-Vedic, but pre-Classical, Sanskrit corpus and which was composed somewhere around the fifth or fourth century B.C.E., provides "the first available link between the ambiguous celestial and calendric utterances of the Vedas and the full-blown Sanskrit mathematical astronomy of the first millennium C.E."

Chapter 3 deals with the "mathematical ideas and methods during the centuries just before and just after the turn of our Common Era." Important clues are provided by three texts, viz., Artha-sastra, Yavana-jataka, and Panca-siddhantika. The Artha-sastra envisages a large numerate bureaucracy, trained in measurement and quantification. Though the inscriptions of...