Mathematicians.At any one time, the nature of mathematics is determined primarily
by a fuzzy set of persons: mathematicians. The set is partially ordered by the relations
of power and status. The set and the relations on it are continually changing, and thus
mathematics is continuously evolving. The set of mathematicians has different
strengths of membership (which could in theory be quantified from 0 to 1). This
includes ‘strong’ members (institutionally powerful or active research mathematicians)
and ‘weak’ members (teachers of mathematics). The ‘weakest’ members could simply
be numerate citizens. The notion of a fuzzy set usefully models the varying strengths
of individuals’ contribution to the institution of mathematics. Mathematical
knowledge is legitimated through acceptance by the ‘strongest’ members of the set. In
practice the set of mathematicians is made up of many sub-sets pursuing research in
sub-fields, each with a similar sub-structure, but loosely interconnected through
various social institutions (journals, conferences, universities, funding agencies).