Aryabhata I's achivements in ancient Indian mathematics & Astronomy and their relevance in the Twenty-first century

Abstract

The period from fifth to twelfth century AD witnessed the rise of great scholars and is indeed a golden period in the history of Indian mathematics and astronomy. Aryabhata I is pioneer in this group. He codified knowledge systematically in his Aryabhatiya for the first time into two major sections, gaiiiiapada (mathematics section including geometry) and golapada (celestial sphere section dealing with astronomy). The elementary results are of course given by him in two other sections, gitikapada (elementary) data on astronomy and sine table) and kalakriyapada (section on reckoning time). The tradition of putting both ganita and gola sections in the same text continued more or less up to the time of Brahmagupta, and separate texts began to appear after thatin each section and also on subsections. He wrote another work, Aryabhatasiddhanta* as envisaged from Bhaskara I's commentary. Both the works were popular up to twelfth century AD. Aryabhata I's rules are very short and cryptic. It could be understood only with Bhaskara I's commentary. My main objective in the paper is to give an outline of the major contributions of Aryabhata I. Only one topic will be discussed in little more detail i.e. the solution of first degree indeterminate equation of the type: by = ax + c, and extensions made by other scholars in the field. This topic got a considerable importance, and has a far reaching impact. Lastly it will be emphasized that the mathematics looses its essence and vitality if it is bereft of context and is only restricted to internal logic and intellectual curiosity. The mathematics is getting unpopular day by day. To make it more meaningful, effort might be made to make it also an integral part of culture to avoid further damage from the domain of public perception in the twenty-first century.