Samgamagr\=ama M\=adhava: An Updated Biography

Abstract

This paper presents an updated biography of Samgamagr\=ama M\=adhava incorporating viewpoints expounded by scholars in the recent past and collecting together in one place more details about his works culled from recent researches into his contributions to mathematics and astronomy. One major updation is with regard to the geographical location in Kerala where M\=adhava flourished. Other updations include observations on M\=adhava's algorithm to compute the numerical values of the sine and cosine functions and on his value of the mathematical constant $\pi$.