The Indian Mathematical Tradition with Special Reference to Kerala: Methodology and Motivation
Ancient and medieval India produced a host of eminent scholars who contributed richly to the development of astronomy and mathematics. For about four centuries since the fourteenth century c.e. there was an upsurge in Indian mathematical activities centred at Kerala. The achievements of this period have quite a different flavor in the sense that the barriers of the finite were broken and the highly fertile area of the infinite explored. The discipline attained new heights with the discovery and analysis of the infinite series for the circumference and the power series for half chords. Attempts to increase accuracy and expedite convergence by transforming partial sums using correction terms opened the doors of series approximation and error analysis. En route, heavy knockings on the doors of calculus and infinitesimal analysis can be heard. This article outlines some of these major discoveries and attempts to take a peep into the methodology and motivations. The emphasis laid by Indian mathematicians in general, and Kerala mathematicians in particular, on the notion of proof, the different types of proofs used, the purpose of rationale, the nature, and style of exposition are examined briefly. Commentaries and other expository works are capable of throwing light on the methodology and motivations in Indian mathematics.