Essay:
Kerala Mathematics and Its Possible Transmission to Europe
By Dennis Francis Almeida (University of Exeter, UK) and
George Gheverghese Joseph (University of Manchester, UK)

The Kerala School of astronomy and mathematics was an Indian school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, South India, which included among its members several scientists. The school flourished in the 14th-16th centuries. In attempting to solve astronomical problems, the Kerala School independently created a number of important mathematics concepts. In this well documented article, Dennis Francis Almeida and George Gheverghese Joseph reconstruct the mathematics of Kerala School and attempt to show the possible ways of its transmission to modern Europe.

According to the literature, the general methods of the calculus were invented independently by Newton and Leibniz in the late I7th century after exploiting the works of European pioneers such as Fermat, Roberval, Taylor, Gregory, Pascal, and Bernoulli in the preceding half century. However, what appears to be less well known is that the fundamental elements of the calculus including numerical integration methods and infinite series derivations for p and for trigonometric functions such as sin x, cos x and tan-1 x (the so-called Gregory series) had already been discovered over 250 years earlier in Kerala. These developments first occurred in the works of the Kerala mathematician Madhava and were subsequently elaborated on by his followers Nilakantha Somayaji, Jyesthadeva, Sankara Variyar and others between the 14th and 16th centuries.

In the latter half of the 20th century, there has been some acknowledgement of these facts outside India. There are several modem European histories of mathematics which acknowledge the work of the Kerala School. However, it needs to be pointed out that this acknowledgement is not necessarily universal. For example, in the recent past a paper by Fiegenbaum on the history of the calculus makes no acknowledgement of the work of the Kerala School. However, prior to the publication of Fiegenbaum's paper, several renowned publications detailing the Kerala calculus had already appeared in the West. Such a viewpoint may have its origins in the Eurocentrism that was formulated during the period of colonization by some European nations.

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