Mathematics in India has a very rich, long and hallowed history. Starting from the most elementary thing in mathematics namely the representation of numbers, through the way of expressing recursive relations, to arriving at the solutions of indeterminate equations, to the development of sophisticated techniques in handling the infinite and the infititesimals, Indian mathematicians have made remarkable contributions.
Sulbasutras, the oldest extant texts (∼ 800 BCE), explicitly state and make use of the so-called Pythagorean theorem besides giving various interesting approximations to surds. Following this, Pingala’s Chandassastra (∼ 3rd cent. BCE), a text that deals with the prosody, lays foundations for various combinatorial techniques. By the time of Aryabhata (c. 499 CE), the Indian mathematicians were fully conversant with most of the mathematics that we currently teach in our schools, which include the algorithms for extracting square root and cube root based on the decimal place-value system.
Among other things, Aryabhata also presented the differential equation of sine function in its finite-difference form and a method for solving the linear indeterminate equation. Brahmagupta (c. 628), for the first time in the history of mathematics, fully discusses the arithmetic operations with zero. He also introduces the profound ‘bhavana’ law of composition for solving quadratic indeterminate equations. Apart from some of these important landmarks in the evolution of arithmetic, geometry, and algebra, significant contributions have also been made in the development of trigonometry.
The Kerala School of astronomy and mathematics pioneered by Madhava (c. 1340–1420) discovered the infinite series for pi (π)—the so-called Gregory-Leibniz series)—and other trigonometric functions. The series for π/4 being an excruciatingly slowly converging series, Madhava also came up with several brilliant fast convergent approximations to it. This School is also credited with the introduction of non-geocentric planetary models. These two things, namely the introduction of infinite series, and non-geocentric planetary models are in fact, hailed as the hallmarks of the genesis of modern science in Europe a few centuries later. Today, if the modern scholarship is aware of some of these significant achievements of Indians in the development of mathematics, it is primarily because of the dedicated work of few great scholars such as BB Datta, KS Shukla, KV Sarma and so on in the last hundred years.
Much of their painstaking work was largely carried out voluntarily, with hardly any support from the institutions of higher learning. Unfortunately, most Indians are not aware of these remarkable contributions made by Indians to the development of mathematics. The series of talks to be delivered by eminent scholars from all over the world, aims to provide a glimpse of this rich mathematical heritage of India.
K. Ramasubramanian
IIT Bombay