In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little (...) attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects. (shrink)

In the past 10 years, contemporary philosophy of mathematics has seen the development of a trend that conceives mathematics as first and foremost a human activity and in particular as a kind of practice. However, only recently the need for a general framework to account for the target of the so-called philosophy of mathematical practice has emerged. The purpose of the present article is to make progress towards the definition of a more precise general framework for the philosophy of mathematical (...) practice by exploring two strategies. A first strategy is to turn to philosophy of mind and Edwin Hutchins' view of distributed cognition in order to better understand the cognitive issues at play when considering a community of mathematicians; a second strategy is to refer to philosophy of language and focus on Robert Brandom's inferentialism and mathematical conceptual content. A possible combination of these two views, called enhanced material inferentialism, is then put forward as a promising framework to account for the philosophy of mathematical practice. (shrink)