Madhava—A great Kerala mathematician of medieval times

Abstract

Madhava (c. 1340-1425 AD) of Sangamagrama (a village near the temple of Samgamesvara, modern Irinjalakkuda, lat 10 deg 20' N near Kochi/Cochin is supposed to be one of the greatest mathematicians that medieval Kerala had produced. He was at the top of the lineage of the medieval Kerala mathematicians followed by Paramesvara, Nilakantha, Jyesthadeva, Sankara, Narayana, Acyuta Pisaroti and others. A number of citations are available in the works of later scholars which show Madhava's marvelous achievements in mathematics. Some of these are the values of π correct to 10 places of decimals, imposing corrections to infinite series after certain terms for quick and better results, derivation of Sine and Cosine power series for computing better Sine and Versed- sine tables which are unique by contemporary standard. His π, Sine and Cosine power series were rediscovered about 250 years later in Euroe by scholars - Wilhelm Leibniz (1673), Newton (1675), De Lagney (1682), De Moivre (c. 1720), Euler (1748) and others. The achievements of Madhava in other areas are still to be explored and will be known only when new important manuscripts composed by him are brought to light through new editions and translations. Some of Madhava's derivation and results are critically examined in this paper.