One statement I have been hearing lately is along these lines, “Austrians are not against all math, just SOME math” or, “Austrians are not against math, just mathematical predictions” etc etc. I find these claims to be rather telling of the person arguing on behalf of the Austrian position. These statements tell me right away they do not even know or understand the methodological position of their own school of thought. On their view, these 5 quotes need to be interpreted as only being against some math and/or mathematical predictions. Here are the relevant quotations:
“The only economic problems that matter, defy any mathematical approach” – Ludwig Von Mises
“Now, the mathematical economist does not contribute anything to the elucidation of the market process” – Ludwig Von Mises
“The equations formulated by mathematical economics remain a useless piece of mental gymnastics and would remain so even if they were to express much more than they really do” – Ludwig Von Mises
(These next two are my favorite)
“The mathematical method must be rejected not only on the account of its bareness. It is an entirely vicious method, starting from false assumptions and leading to fallacious inferences. Its syllogisms are not only sterile: they divert the mind from the study of real problems and distort the relations between various phenomena” – Ludwig Von Mises
“Mathematics cannot and does not enter into measuring ideas or values that determine human action. There are no constants in these. There is no equality in market transactions. Therefore, mathematics does not apply. The use of mathematics requires constants. Mathematics cannot be used in economic theory” – Percy L. Greaves.
I am truly baffled as to how someone claiming to be an adherent of the Austrian School could read these, or any Austrian literature, and conclude that Austrians are only against the use of some math. I have read a lot of Austrian literature, and I personally have never read anything that would support that claim. Of course, quotations cannot be “proof” of anything, but I do think they provide rather strong evidence in favor of my argument. Moreover, the Percy Greaves quotation is in response to the question, “is economics completely divorced from mathematics?” Clearly, from his response he thinks it is.
Another statement I hear from Austrians is that Neo-Classicals do not give them any mathematical propositions they should accept. This seems to be a rather silly statement, and in many ways, entirely meaningless. Austrians should accept all mathematical propositions that are true, from 1 + 1 = 2 to the propositions in set theory or algebraic topology etc.
However, to get specific I would like to point out two mathematical fields that have vast applications in economics. First is game theory. Game theory is a branch of mathematics first developed by Emile Borel, and then popularized by the works of Von Neumann, Morgenstern, Nash etc. There is a plethora of economic questions game theory answers. One example of such a question is – how do oligopolies decide on how much to produce given the production of the other firms? Game theory provides the answer to this question.
Second, is functional analysis. In general, functional analysis is the study of infinite dimensional vector spaces. This field answers the question – how can a copper mining company extract Q tons of copper from a mine over T years and maximize its profit? To find this function is one thing, and to prove it is the maximum of all functions is another. I would like to ask an Austrian how to solve this problem without the use of mathematics? In my view, it simply cannot be done.
Mathematics is vitally important to the study of economics, and to denounce it the way influential Austrian scholars have is exactly why I am not an Austrian economist.