Qu’est-ce qu’un théorème (en pratique) ?

Abstract

This article advocates the benefits of a sociological perspective for the philosophy of mathematical practice. Drawing from the literature of the sociology of sciences, it defends a community-centered approach of the study of mathematical practice, and assesses the role of the notion of metamathematics in mathematical change and in stabilized mathematical practices. It relies on the case study of the emergence of geometric control theory at the beginning of the 1970s and of the citational practices associated to the community of control theory since the mid 1990s. This case study shows that the introduction of geometric tools in control theory at the end of the 1960s induced a change in the metamathematical views that control theorists had on their objects. I then demonstrate how membership to the community of control theory shapes the production and the reception of the theorems of Štefan, Sussmann and Nagano. Interpreting the historical development and citational practices of this community through the perspective of metamathematics, I conclude by discussing the role of the orbit theorem in control theory, both as a cognitive label and as a social marker of membership to this community.

Keywords

• scientific community
• mathematical practice
• metamathematics
• co-citation analysis
• control theory