What is mathematics? Perspectives inspired by anthropology

The paper discusses the question “What is mathematics?” from a point of view inspired by anthropology. In this perspective, the character of mathematical thinking and argument is strongly affected - almost essentially determined, indeed - by the dynamics of the specific social, mostly professional environments by which it is carried. Environments where future practitioners are taught as apprentices produce an approach different from that resulting from teaching in a school - the latter inviting to intra-mathematical explanation in a way the former does not. Moreover, once the interaction with the early classical Greek philosophical quest for causes and general explanations had caused mathematical explanation to become an autonomous endeavour in the shape of explicit proof and deductivity, proof and deductivity presented themselves as options - sometimes exploited, sometimes not - even in the teaching of mathematics for practitioners.