From Concrete to Abstract in Indian Mathematics

Despite the extensive amount of scholarly work done on Indian mathematics in the last 200 years, the historical conditions under which it originated and evolved has not been studied much. The focus has been more on achievements than on how they developed. One also tends to read the ancient texts with the present concepts and methods in mind. The absence of writing over a long stretch of Indian history too gets overlooked in such readings. The purpose of this article is to explore the journey of mathematics by examining what the ancient texts on arithmetic, geometry and algebra tell us about the nature of mathematics in their times. These investigations reveal that over a period of a thousand or more years Indian mathematics transitioned from concrete and context-bound phase to context-free, abstract phase accompanied by several conceptual leaps. Invention of writing in the 3rd century BCE greatly facilitated this transition.