Tuesday, 17 January 2012

Why don't more mathematicians see the potential of economics


















1 Mirowski (1991, pp 150–151)
3 MacKenzie (2008, p 63–64)
4 Mirowski (1992, p 134)
5 Mirowski (1992, p 122, quoting von Neumann)
6 Mirowski (1992, p 122–124)
7 Gell-Mann (1992, p 7)
8 Katz (1993, p 685)




  1. Tim,

    Thank you for the great discussion. While there is a great role for mathematics in economics, it does not seem to be comparable to physics, if only for the fact that economics ends up with people in the mix, which is an unpredictable and irrational element.

    Perhaps rather than rely on existing genres of mathematics it is time for economists to develop their own?

  2. Tim, I commented on your previous post. Here I note that mathematicians have to be paid by someone, and most people have wanted a short-term profit, so there has been no obvious incentive to apply, for example, Keynes' mathematics. What was used was quite good enough: we have had a form of arms-race in algorithms, where what matters is the race, not the 'validity' of the arms.

    I was struck that your view of some of the 'Greats' is different from my own. Sometimes (as for Keynes) what the mainstream makes of a body of work is quite different from what they intended. Rather than economists needing more mathematics, I think it more important for them to understand the existing mathematics (and Greats).


  3. Thirty years ago I had a brief chat with the mathematician Karen Uhlenbeck about Bourbaki, who praised Bourbaki for bringing order to mathematics, much as Dewey brings order to the books in any number of libraries. Her point was that mathematicians wished Bourbaki were not necessary, given the abstraction required; Bourbaki is something of a necessary evil.

    The introduction of axiomatic methods into economics, on the other hand, is to be disparaged for two reasons. First, it attempts to substitute deductive for inductive reasoning; second, it distracts economists from examining techniques from applied, rather than pure, mathematics. The elegance of sigma algebras used to model efficient financial markets is a red herring given observed autocorrelative behaviors of markets. I feel a sense of schadenfreude watching option traders take revenge on pure mathematics by calling vega a Greek letter. All this abstraction balanced on the Black Scholes partial differential equation, a parabolic equation: why isn't anyone seeing if the other two classes of equations, the elliptic and the hyperbolic, may have useful application in modeling observed market behavior?

    As to why Formalism was so popular around 1940, Russell's Paradox was a rather nasty blow to mathematics, along with other controversies like the Axiom of Choice. The trouble is that none of this has anything to do with mathematical modeling in the sciences.

  4. Fundamental Value as an economic category (now Russian) http://free.yudu.com/item/details/384742/

  5. Tim,

    I was introduced to your blog after reading What is Financial Mathematics? and found it quite relevant to most of the work I'm doing, both at University and at Let's Learn Finance.

    Thank you for this post. It provided a great context to the role of Mathematics in this particular field of study, especially with the intertwining historical facts you've exposed here.

    However, to answer your question - coming from the 'Commerce' flip-side of your argument, I can't help but agree that mathematics is a core part of economics / finance. The mathematicians of the world need open their eyes to this..


  6. The domination of mathematical economics by strict Bourbakism has been passe for for some time. This is made clear in Roy Weintraub's _How Economics Became a Mathematical Science_ from a decade ago, although he is not fully clear on what has succeeded it, which includes reliance on more inductive methods including computational ones, among other things.