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.