MATHEMATICAL PURITY VERSUS GANITA INCLUSIVISM: A CASE STUDY OF RINA AND DHANA

Abstract

Mathematics is often imagined as a “pure” realm set apart from ordinary life. Its rigid formalism resembles a closed order: guarded by strict codes and marked by hierarchy. It is accessible mainly to those initiated into its language of axioms, proofs, formulas, and Euclidean logic. Such rigid formalism frequently induces anxiety and alienation in the average learner. We argue that this is not an inherent feature of arithmetic itself but a result of a specific shift toward hyper-formalism and disciplinary purity in the Western tradition. By contrast, the Indian tradition of ganita was grounded in the lived experiences of people. Concepts were explained through familiar examples (udaharanas) and practical needs. As a case study, this paper examines the treatment of negative numbers in Sanskrit mathematical texts, especially through the commercial categories of rina (debt) and dhana (wealth). These examples made mathematical ideas socially accessible. We argue that Indian knowledge systems approach numbers not as an exclusivist domain of mathematicians, but as a body of knowledge meant to serve life. Recovering this older spirit of ganita may help us think beyond the exclusion and intellectual gatekeeping that marks much of mathematics today.