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The unreasonable ineffectiveness of mathematics in economics

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  • K. Vela Velupillai

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. Copyright 2005, Oxford University Press.

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  • K. Vela Velupillai, 2005. "The unreasonable ineffectiveness of mathematics in economics," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 29(6), pages 849-872, November.
    • Handle: RePEc:oup:cambje:v:29:y:2005:i:6:p:849-872
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    File URL: http://hdl.handle.net/10.1093/cje/bei084
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    Cited by:

    1. Bartholo, R.S. & Cosenza, C.A.N. & Doria, F.A. & de Lessa, C.T.R., 2009. "Can economic systems be seen as computing devices?," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 72-80, May.
    2. Lauwers, Luc, 2010. "Ordering infinite utility streams comes at the cost of a non-Ramsey set," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 32-37, January.
    3. Dusek, Tamás, 2012. "A Debreu-féle neowalrasi általános egyensúlyelmélet antiempirista axiomatizmusa [The anti-empirical axiomatism of neo-Walrasian general equilibrium theory]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(9), pages 988-1004.
    4. Gizem Karaali, 2019. "Doing Math in Jest: Reflections on Useless Math, the Unreasonable Effectiveness of Mathematics, and the Ethical Obligations of Mathematicians," The Mathematical Intelligencer, Springer, vol. 41(3), pages 10-13, September.
    5. C. P. Kwong, 2009. "Mathematical analysis of Soros's theory of reflexivity," Papers 0901.4447, arXiv.org.
    6. K. Vela Velupillai, "undated". "Remembering Krishna Bharadwaj," ASSRU Discussion Papers 1209, ASSRU - Algorithmic Social Science Research Unit.
    7. Kakarot-Handtke, Egmont, 2011. "Primary and secondary markets," MPRA Paper 32996, University Library of Munich, Germany.
    8. Guglielmo Chiodi, 2012. "On Richard Goodwin’s Elementary Economics from the Higher Standpoint," ASSRU Discussion Papers 1219, ASSRU - Algorithmic Social Science Research Unit.
    9. Kakarot-Handtke, Egmont, 2012. "The rhetoric of failure: a hyper-dialog about method in economics and how to get things going," MPRA Paper 43276, University Library of Munich, Germany.
    10. David Colander, 2011. "The MONIAC, Modeling, and Macroeconomics," Economia politica, Società editrice il Mulino, issue 1, pages 63-82.
    11. Lukáš Kovanda, 2010. "Kritický realismus: ontologická báze postkeynesovské ekonomie [Critical Realism as an Ontological Basis of Post-Keynesianism]," Politická ekonomie, Prague University of Economics and Business, vol. 2010(5), pages 608-622.
    12. N. C. A. da Costa & Francisco A. Doria, 2014. "On an Extension of Rice’s Theorem and its Applications in Mathematical Economics☆Dedicated to the memory of Professor Saul Fuks (1929–2012)," Advances in Austrian Economics, in: Entangled Political Economy, volume 18, pages 237-257, Emerald Group Publishing Limited.
    13. Lukáš Kovanda, 2011. "Ekonomie budoucnosti: čtyři možné scénáře [The Future of Economics: Four Possible Scenarios]," Politická ekonomie, Prague University of Economics and Business, vol. 2011(6), pages 743-758.
    14. K. Vela Velupillai, 2008. "Uncomputability and Undecidability in Economic Theory," Department of Economics Working Papers 0806, Department of Economics, University of Trento, Italia.
    15. K. Vela Velupillai, 2007. "Variations On The Theme Of Conning In Mathematical Economics," Journal of Economic Surveys, Wiley Blackwell, vol. 21(3), pages 466-505, July.
    16. K. Vela Velupillai, 2007. "Variations on the Theme of Conning in Mathematical Economics," Department of Economics Working Papers 0703, Department of Economics, University of Trento, Italia.

    More about this item

    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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