Algorithms in Indian Mathematics

Abstract

Indian Mathematics is predominantly algorithmic. In fact, the very word ``Algorithm'' is derived from the name of Al Khwarizmi (c. 9thCentury) whose works played a crucial role in the transmission of Indian algorithmic procedures to the Islamic and later to the Western world. We shall discuss a few selected algorithms that are representative of the Indian mathematical tradition from the ancient Śulbas{\={u}}tr{\={a}}s to the medieval texts of the Kerala School. In particular, we shall outline some of the constructions described in the Śulbas{\={u}}tr{\={a}}s, the algorithm for computing the cube-root given by {\={A}}ryabhaṭa (c.499) and the kuṭṭaka and cakraväla algorithms for solving linear and quadratic indeterminate equations as discussed by {\={A}}ryabhaṭa (c.499), Brahmagupta (c.628), Jayadeva (prior to the 11thcentury) and Bh{\={a}}skara (c.1150). We shall also discuss the efficient algorithms for accurate computation of $Π$ and the sine function due to M{\={a}}dhava (c.14thcentury) as discussed in the texts of the Kerala School of Mathematics and Astronomy.