From Concrete to Abstract in Indian Mathematics

TL;DR

This paper explores the evolution of Indian mathematics from practical, concrete problem-solving in ancient texts to a more abstract, context-free form with algebra and writing, clarifying its historical development.

Contribution

It provides a historical analysis of Indian mathematics, highlighting its transition from practical to abstract concepts and emphasizing the role of writing in this evolution.

Findings

Mathematics was initially practical and context-bound.

Transition to abstract mathematics occurred with algebra and writing.

Ancient texts reveal the evolution of mathematical ideas over time.

Abstract

Despite the extensive amount of scholarly work done on Indian mathematics in the last 200 years, the conditions under which it originated and evolved is still not clear. Often, one reads the ancient texts with the present concepts and methods in mind. The fact of absence of script over a long stretch of Indian history in ancient times also gets overlooked in such readings. The purpose of this article is to explore the journey of mathematics by examining what the ancient texts tell us about the nature of mathematics in their times. What one finds from the investigation of arithmetic, geometry and algebra is that while it was concrete and context bound, rooted in solving practical problems in ancient times, Indian mathematics transitioned to context free, abstract stage with the advent of algebra supported by writing.