The Algorithmic Revolution in the Social Sciences: Mathematical Economics, Game Theory and Statistical Inference

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, even in economics. Constructive mathematics of any variety, computability theory and non-standard analysis are intrinsically algorithmic at their foundations. Economic theory, game theory and mathematical finance theory, at many of their frontiers, appear to have embraced the digital and information technology revolutions via strong adherences to experimental, behavioural and so-called computational aspects of their domains - without, however, adapting the mathematical formalisms of their theoretical structures. Recent advances in mathematical economics, game theory, probability theory and statistics suggest that an algorithmic revolution in the social sciences is in the making. In this paper I try to trace the origins of the emergence of this revolution and suggest, via examples in mathematical economics, game theory and the foundations of statistics, where the common elements are and how they may define new frontiers of research and visions. Essentially, the conclusion is that the algorithmic social sciences are unified by an underpinning in Diophantine Decision Problems as their paradigmatic framework