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Cambridge Journal of Economics 2005 29(6):849-872; doi:10.1093/cje/bei084
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© The Author 2005. Published by Oxford University Press on behalf of the Cambridge Political Economy Society. All rights reserved.

Article

The unreasonable ineffectiveness of mathematics in economics

K. Vela Velupillai*

* National University of Ireland and University of Trento, Italy

Address for correspondence: Department of Economics, National University of Ireland, Galway, Galway, Ireland, and Department of Economics, University of Trento, Trento, Italy; email: vela.velupillai{at}nuigalway.ie

Abstract

In this paper, I attempt to show that mathematical economics is unreasonably ineffective. Unreasonable, because the mathematical assumptions are economically unwarranted; ineffective because the mathematical formalisations imply non-constructive and uncomputable structures. A reasonable and effective mathematisation of economics entails Diophantine formalisms. These come with natural undecidabilities and uncomputabilities. In the face of this, I conjecture that an economics for the future will be freer to explore experimental methodologies underpinned by alternative mathematical structures. The whole discussion is framed within the context of the celebrated Wignerian theme: The Unreasonable Effectiveness of Mathematics in the Natural Sciences.

Key Words: General equilibrium theory • Computable general equilibrium • Computable economics • Constructive mathematics • Mathematical economics

JEL classifications: B41, C62, C68, D58

Manuscript received November 14, 2003; final version received July 17, 2004.


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