A Passage to Infinity: The Contribution of Kerala to Modern Mathematics

Abstract

Two powerful tools contributed to the creation of modern mathematics in the seventeenth century: the discovery of the general algorithms of calculus and the development and application of infinite series techniques. These two streams of discovery reinforced each other in their simultaneous development with each serving to extend the range and application of the other. According to existing literature, the calculus that resulted were invented independently by Newton and Leibniz, building on the works of their European predecessors such as Fermat, Taylor, Gregory, Pascal, and Bernoulli during the preceding half-century.¹ But what appears to be less well-known is that certain fundamental elements of this calculus including numerical integration methods and infinite series derivations for n and of certain trigonometric functions such as sin x, cos x, and tan^-1 x (the so-called Gregory series) were already known about 250 years earlier in Kerala, South India. In recent years there has been some acknowledgment of this fact. But such acknowledgments are quite rare.²

This chapter is based on recent work by Dennis Almeida and the author (Almeida and Joseph, 2004, 2007, 2009) that were the outcomes of their collaboration on a research project funded by Arts and Humanities Research Board (AHRB), United Kingdom. The author owes a considerable debt to Dennis Almeida for his contributions that were crucial to the success of the project. I have reprised short passages from the publications referred to above because, needing to make the same points, I found the way they were expressed there as apt for the task as I could make them.