Mathematics,Applicable versus Pure‐and‐Applied

‘Applicable mathematics’ is based on the idea that mathematics provides a source of models of proposed and postulated states of affairs. The use of the model is essentially to simulate exploration of the possibilities of the situation to which the model relates. Two main areas where this ‘investigation of the implications of possibilities’ is needed are in discussing putative scientific hypotheses and in discussing the implications of proposed or suggested social and technical innovation. Much of what has been customarily called ‘pure mathematics’ can be regarded as second‐order applicable mathematics, i.e. mathematics which adds to and strengthens our over‐all model building capability.