Symbol as Metonymy and Metaphor: A Sociological Perspective on Mathematical Symbolism

As a social practice, mathematics remains shrouded in mystery and seems inaccessible for outsiders. It comes across as a closed formal system that is largely considered independent of the people who practise it and hence totally impervious to sociological investigation. This article seeks to question these assumptions and is offered as a contribution to an emerging sociology of mathematics and abstraction. The argument unfolds on an ethnographic register and follows the reactions to a particular mathematical symbol in two different contexts. The first stretch of the description tracks the responses to this symbol on an online forum devoted to discussing mathematics and the other draws from a classroom context the author was part of as a participant observer. Thus focussing on just one aspect of mathematical practice, the way in which symbols are handled by practitioners, it attempts to underline the character of mathematics as a distinctive form of sociality. In the process it raises and seeks to address the following questions. What do controversies over and reactions to mathematical symbols tell us about mathematics as a practice? What roles do symbols play in the mathematical discourse? And, can a broader sociological perspective on mathematical symbolism be developed