History of Vernacular Mathematics in Medieval South India (Kerala and Tamil Nadu, 9th-16th Centuries)
SNSF Grant
external pageIn collaboration with IFP, Indiacall_made
Background and Rationale: The study of Indian mathematics has traditionally focused on a list of “canonical” Sanskrit treatises. This focus on elite scholarly sources highlighted abstract conceptions, using contemporary or other major historical mathematical cultures as reference points. This research has largely ignored vernacular mathematics, often assuming it was derivative, inferior or insignificant. But mathematics was part of the everyday lives of many Indians through labor, craft, commerce and tax. In South India (in particular Tamil Nadu and Kerala), we also have substantial vernacular mathematical literature (Tamil and Malayalam), of which only one treatise (Gaṇita-Yukti-Bhāṣā, Sarma et al. 2009) has received substantial international attention. This approach has significantly biased our understanding of the history of mathematics in India, and detached it from its particular historical and contextual meanings. Theoretical frameworks that consider mathematics as practice rather than as a set of abstract ideas (Philosophy of Mathematical Practice, Historical Epistemology, Ethnomathematics) provide tools to fix this bias.
Overall Objectives and Specific Aims: With this project we analyze cognitive and socio-political aspects of mathematical practice in Tamil Nadu and Kerala between the 9th and 16th centuries. More specifically, (1) we wish to understand how mathematical notations and measurement units evolved in their practical context, through processes of standardization and measurement practices. (2) We want to study a mathematical professional – the village accountant – through his education, cognitive development, mathematical conceptualization, social position and political role. (3) We want to understand the relations between the various mathematical sub-cultures of South India: mathematics in elementary education, mathematics in professional education, the mathematics of more advanced vernacular treatises, and Sanskrit mathematics. We wish to understand the interactions between these mathematical sub-cultures, their relation to social divisions (such as castes), and the various conceptualizations of mathematics that they represent.