2010 | OriginalPaper | Buchkapitel
Development of Calculus in India
verfasst von : K. Ramasubramanian, M. D. Srinivas
Erschienen in: Studies in the History of Indian Mathematics
Verlag: Hindustan Book Agency
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In his pioneering history of calculus written sixty years ago, Carl Boyer was totally dismissive of the Indian contributions to the conceptual development of the subject.
1
Boyer’s historical overview was written around the same time when (i) Ramavarma Maru Thampuran and Akhileswarayyar brought out the first edition of the Mathematics part of the seminal text
Gaṇita-yukti-bhāṣā
, and (ii) C.T. Rajagopal and his collaborators, in a series of pioneering studies, drew attention to the significance of the results and techniques outlined in
Yuktibhāṣā
(and the work of the Kerala School of Mathematics in general), which seem to have been forgotten after the initial notice by Charles Whish in early nineteenth century. These and the subsequent studies have led to a somewhat different perception of the Indian contribution to the development of calculus as may be gleaned from the following quotation from a recent work on the history of mathematics:
2
We have here a prime example of two traditions whose aims were completely different. The Euclidean ideology of proof which was so influential in the Islamic world had no apparent influence in India (as al-Biruni had complained long before), even if there is a possibility that the Greek tables of ‘trigonometric functions’ had been transmitted and refined. To suppose that some version of ‘calculus’ underlay the derivation of the series must be a matter of conjecture.
The single exception to this generalization is a long work, much admired in Kerala, which was known as
Yuktibhāṣā
, by Jyeṣṭhadeva; this contains something more like proofs—but again, given the different paradigm, we should be cautious about assuming that they are meant to serve the same functions. Both the authorship and date of this work are hard to establish exactly (the date usually claimed is the sixteenth century), but it does give explanations of how the formulae are arrived at which could be taken as a version of the calculus.