ABSTRACT
This chapter is an introduction to the sociology of mathematics. Mathematical talk can be technical talk about mathematics. This sort of talk is based on the assumption that the secret of mathematical power lies in the formal relations among symbols. But technical talk about mathematics cannot, by itself, provide a complete understanding of mathematics. It obscures and even denies the social dimensions of technical talk. This dimension is highlighted in social talk about mathematics. We can talk about mathematics using terms such as social power, social structure, social class, culture, and values. Whereas technical talk isolates mathematics from other social practices (“spiritualization of the technical”), social talk links mathematics to other social practices, and reveals the social nature of technical talk itself. Just as speech cannot be understood as “a parade of syntactic variations,” and myths are not merely sets of “structural transformations,” so mathematical objects are not simply “concatenations of pure form.” Thus, to study a mathematical form is to study a sensibility, a collective formation, a worldview. The foundations of mathematical forms – like the foundations of art, poetry, religion, and all other human activities and productions – are as wide and as deep as social existence.
