Language Use in Mathematical Practice: An Ethnographic Perspective

Abstract Mathematics is often seen as an epitome of cold objectivity and astounding infallibility. Particularly for the outsiders, it comes across as an extremely rigid and closed system which seems impenetrable owing to its very specific and technical language. This article problematises these assumptions and seeks to study mathematics as a social practice with insights drawn from an anthropology of language and concepts, Wittgenstein’s philosophy of mathematics and semiotics. Using the anthropological insight that a language is always embedded in a form of life, this article shows how mathematical practice generates its own conventions and forms of language use. In particular, two dimensions of language use in mathematics are delineated and their consequences for further research are drawn out. In the first part of the article, the role of concepts in the discourse of mathematics is explored and in the second it is shown how applying a rigid distinction between syntax and semantics to mathematical language obstructs our understanding of its fluid and dynamic character. The argument unfolds through an analyses of interviews, texts and classroom sessions and shows how mathematical practice is heavily context bound and mathematicians often display an ethnographic attentiveness towards their work. The general tenor of the description is such that it attempts to trace the ethical dimension latent in mathematical practice and suggests a possibility of exploring it as a form of life. Connected to this thought is the argument that like any other practice, mathematical practice generates its own forms of reflections which cannot simply be assimilated to philosophical/theoretical knowledge. The question whether this action knowledge regarding mathematics has some relation to the South Asian location where the ethnography unfolds is also tentatively explored