In mathematics disputes can be decided with certainty - Towards a sociology of mathematics

Mathematics constitutes a crucial test case for sociology. In contrast to other epistemic cultures no "interpretative flexibility" seems to exist: controversies can be decided "with certainty", as Ludwig Wittgenstein put it. Based on an ethnographic field study conducted in an international institute, this article outlines a sociological theory of mathematics. It starts our from a critical review of programmatic work by David Bloor and Eric Livingston and develops, in a second parr, a historical argument which shows how the practices of establishing truth in mathematics have changed over time. Within the frame of reference of Luhmann's media theory the paper argues that, in the wake of institutional expansion during the 19(th) century, mathematicians had to develop new strategies for reaching consensus. The most important strategy is constituted by formalization and the establishment of proof as the only accepted form of validation, In a last section recent developments in mathematics are discussed with respect to their potential for undermining the epistemological exclusivity of proof; these developments render mathematics more comparable to the empirical sciences (e.g. computer-aided proofs, long proofs, and experimental mathematics).