An overview of the varieties of mathematics that underpin the functioning of a computer is attempted in this paper. Against the backdrop of such an overview, the question is posed whether, and to what extent, the economist has respected these varieties of mathematics in posing economic questions...

Computation over the reals, without abandoning the paradigm of the digital computer, raises difficult issues at the interface between recursion theory, numerical analysis and dynamical systems. In this paper an attempt is made to provide economic and mathematical justifications for returning to...