Textual analysis of ancient Indian mathematics

TL;DR

This paper advocates for applying literary analysis to ancient Indian mathematical texts to better understand their exposition, derivation, and conceptual background, thereby clarifying obscure passages and enriching historical comprehension.

Contribution

It introduces a novel method of literary analysis for ancient mathematical texts and provides guidelines for its application to improve understanding of historical mathematical works.

Findings

Clarifies obscure passages in Brahmagupta's and Baudh ext=ayana's texts.

Demonstrates how literary analysis reveals authors' conceptual backgrounds.

Provides guidelines for applying this method to other ancient texts.

Abstract

Recent analyses of Brahmagupta's discourse on the cyclic quadrilateral, and of Baudh\=ayana's approximate quadrature of the circle, have shown that it is useful to submit mathematical texts to a form of literary analysis. Several passages considered as obscure or objectionable may be explained in this way, by taking into account the elements of exposition and derivation of the results that the author has given, as well as his conceptual background. This approach aims at helping the reader set aside his preconceptions about what a mathematical text is supposed to be. In this paper, guidelines for further application of this method are outlined, with illustrations taken from our previous papers.