The Unreasonable Ineffectiveness of Mathematics in Economics.

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 formalizations imply nonconstructive and uncomputable structures. A reasonable and effective mathematization of economics entails Diophantine formalisms. These come with natural undecidabilities and uncomputabilites. 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.