Friday, December 13, 2013

The Problem with Pure Mathematics

And with analytic a priori systems in general is not only that they do not give us necessary and irrefutable truth about reality, but also that they may be completely irrelevant to the real world:
“Unlike technology, … science is a form of curiosity, tempered by the requirement that its investigative activities lead to an accurate picture of things. This aim distinguishes it from many other disciplines, such as pure mathematics. A mathematician may construct a conceptual scheme of great elegance that has no application to reality. Yet that it doesn’t may not affect its [sc. pure] mathematical significance. But science is different. If a scientific idea doesn’t fit the facts it will eventually be discarded despite its ingenuity.” (Stroll 2009: 31).
Such is the nature of so many mathematical models in neoclassical economics: elegant models that have zero or virtually zero relevance to real world economies, because their assumptions – such as rational expectations, Ricardian equivalence, representative agents, neutral money, the quantity theory of money, the neutral rate of interest and tendencies to general equilibrium – are inapplicable to reality.

Stroll, Avrum. 2009. Informal Philosophy. Rowman & Littlefield Publishers, Lanham, Md. and Plymouth.


  1. You sound like Rothbard today.

    The proof of the pudding is in the eating surely. A model, for that is what these are, can have simpl;ified assumptions if it cranks out good predictions.

    1. I thought that Rothbard was the otherway around: reality has no relevance to economics.

  2. "Such is the nature of many mathematical models in neo-classical economics......"

    And thus, still relevant after 80 years:

    "Too large a proportion of recent 'mathematical' economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols"

    Keynes GT 298

    Our anti-math Austrian friends, with their own idiosyncratic system, have of course shown to us that even no math is needed to lose sight of the complexities of the real world...

    1. Notice the quotation marks used by J.M. Keynes on the word "mathematical". Alfred Marshall's most famous pupil read Mathematics at King's College and wrote a fellowship dissertation on the subject that was supervised by Bertrand Russell, Alfred North Whitehead, and William Ernest Johnson.

  3. "Why neoclassical economics is not a science — the ultimate argument- by Lord Keynes"- Lars P Syll

  4. Pure mathematicians often have the attitude that uselessness is a virtue for their work. Some have gotten annoyed when people find a use for their work afterwards.