The Reasonable Effectiveness of Mathematics in Economics

Abstract

Economic science is generally considered less viable than the physical sciences. Sophisticated mathematical models of the economy have been developed but their accuracy is questionable to the point that the present economic crisis is often blamed on an unwarranted faith in faulty mathematical models. In this paper, we claim that the mathematical handling of economics has actually been reasonably successful and that models are not the cause behind the present crisis. The science of economics does not study immutable laws of nature but the complex human artefacts that are our economies and our financial markets, artefacts that are designed to be largely uncertain. We could make our economies and our markets less subject to uncertainty, and mathematical models more faithful to empirical data by introducing more rules and collecting more data. Collectively, we have decided not to do so and therefore models can only be moderately accurate. Still, our mathematical models offer a valuable design tool to engineer our economic systems. But the mathematics of economics and finance cannot be that of physics. The mathematics of economics and finance is the mathematics of learning and complexity, similar to the mathematics used in studying biological or ecological systems.