| Arguably calculus is one of the amazing intellectual achievements that opened up the gate for the science and engineering to grow by leaps and bounds. Coming to trace its origins, today we understand that starting with Madhava (c.1340 - 1425) of Sangamagrama, the astronomers and mathematicians of Kerala during the medieval period (13th - 16th Century AD) have made significant contributions to the development of calculus. This includes the discovery of power series expansion of the sine and cosine functions, the development of infinite series (and
fast convergent approximations) for the ratio of the circumference of a circle to its diameter, and so on.
Besides this, the Kerala mathematicians also present a careful analysis of how successive partial sums of these infinite series give better and better approximations, thereby displaying a sophisticated understanding of the notion of limit. Today it is too well known that the notion of zero, infinity and limit are tied together as a bundle, and it is in untying this bundle that the flower of calculus unfolds itself.
The present lecture besides giving an overview of the contributions of Kerala school of mathematicians and astronomers, will also attempt to present a glimpse of how in trying to untie the bundle of zero, infinity and limit, same things are discovered by different traditions in different contexts in startlingly different ways. |