Hugh Hudson’s classic article on A Model of the Trade Cycle has never, to the best of our knowledge, received the serious attention it deserved (and deserves, even now, 55 years after its original publication). It was written in what we would like to call the classic Hicks-Kaldor mode, i.e.,...

The theory of economic policy, in its mathematical modes, may be said to have had two incarnations, identified in terms of pre-Lucasian and ultra-Lucasian on a time-scale, whose origin can be traced to the Scandinavian works of the 1920s and early 1930s, beginning with Lindahl (1924, 1929),...

Computation and Simulation have always played a role in economics – whether it be pure economic theory or any variant of applied, especially policy oriented, macro and micro economics or what has increasingly come to be called empirical economics. This is a tradition that can, without too much...

An attempt is made, in this paper, to extract a mathematical methodology, underpinned by numerical meaning, from a study of Richard Goodwin’s classic contributions from 1943 to 1967 -- and beyond. The key conceptual notions I use are tâtonnement, computation, approximations, the geometry of...

Stephen Wolfram’s A New Kind of Science should have made a greater impact in economics - at least in its theorising and computational modes – than it seems to have. There are those who subscribe to varieties of agent-based modelling, who do refer to Wolfram’s paradigms - a word I use with...

Real analysis, founded on the Zermelo-Fraenkel axioms, buttressed by the axiom of choice, is the dominant variety of mathematics utilized in the formalization of economic theory. The accident of history that led to this dominance is not inevitable, especially in an age when the digital computer...

The digital and information technology revolutions are based on algorithmic mathematics in many of their alternative forms. Algorithmic mathematics per se is not necessarily underpinned by the digital or the discrete only; analogue traditions of algorithmic mathematics have a noble pedigree,...

An important frontier of business cycle theorising is the 'time-to-build' tradition that lies at the heart of Real Business Cycle theory. Kydland and Prescott (1982) did not acknowledge the rich tradition of 'time-to-build' business cycle theorising - except in a passing, non-scholarly,...

Non-standard analysis can be harnessed by the recursion theorist. But as a computable economist, the conundrums of the Löwenheim-Skolem theorem and the associated Skolem paradox, seem to pose insurmountable epistemological difficulties against the use of algorithmic non-standard analysis....