Austrians, Mathematics, and Economics

MathematicsThe purpose of this post is to address many of the statements/arguments made by Austrians (in the tradition of Mises) about math, or rather, their position on mathematical use in economics.

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.

All of these quotes can be found in various articles on

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.

John NashHowever, 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.


– JW




Filed under Austrian School of Economics, Chicago School of Economics, Economic Methodology

7 responses to “Austrians, Mathematics, and Economics

  1. lgwestman

    So is it safe to say that you are now backtracking from your previous position of “I want nothing to do with you in the future”?


    • lgwestman

      I just want to be clear on this before I spend time refuting your arguments again.


    • lgwestman

      He will if he chooses to. I am not sure why it matters who replies, since the content of the arguments is what is important, not the messenger. If you are refuted by a total stranger, and not Jacob, it wouldn’t matter one bit.

      Here is the thing Jeff, your arguments are trite. My brother and I have been up and down this street with you on many occasions. It simply doesn’t matter what we say because you are ideologically attached to your economic methodology. I am more than willing to kick the Chicago School to the curb if an Austrian could provide a legitimate argument against the view. I am not ideologically attached to the Chicago School. I am a seeker of truth, and I go to where the evidence and best arguments lead me. Not only has this not been accomplished by the Austrians I have read, I am yet to even read arguments that properly represent the Chicago method. Your previous comment about “mathy looking” is a perfect example of this. Why should I even take that argument seriously? I have never made the argument you claim is being made, and no responsible Chicago School scholar has either. Even in your essay, “Do You Even Prax, Bro?” (which I have read quite a number of times), completely fails to represent the view you are trying to critique. If I remember correctly, you don’t even reference a reputable Chicago School adherent to demonstrate you are properly interpreting their writing. Doing this would allow some kind of scholarly dialogue on the methodological issues, but it is noticeably absent from your paper. I may get Mises wrong, although I don’t think that I do, but at least I provide the passages by him and Rothbard I am discussing so Austrians can make an argument against my interpretation, which you have also never done. Moreover, in your essay you misquote Tarski to bolster your claims about methodology (that is unless you took that Tarski quote out of the essay). I have the book by Tarski that you referenced, and you cut out the portions in the paragraph that would change the entire context in order to fit your view rather than let Tarski speak for himself.

      The last time you were challenged by myself and by a professional philosopher on your arguments about logic, you said you want nothing to do with me in the future. Now, all of a sudden, you are back at it with nothing new to contribute to the conversation. I am more than willing to have the discussion, but you have got to bring something new to the game, Jeff.

      I want to believe what is true. If you hold to the correct view, then convince me with something new to offer. If you don’t have anything new, then we are back right where we started many, many months ago.


  2. lgwestman

    To your last paragraph, obviously, given the references from Austrian economists in the tradition of Mises, everybody does not insist that you can legitimately use math in economics.


  3. I think some comments got erased. The ones that remain now make no sense out of context.


    • PetersonJeffII

      Ok… You think you are correct on game theory, I suggest otherwise. Same applies to functional analysis. I addressed ” from 1 + 1 = 2 to the propositions in set theory or algebraic topology etc” that we do accept this. I even addressed the inverse relationship between price and quantity demand elsewhere with Will.

      It is obvious that this is beating a dead horse. SO instead of going round and round on the same ones, then why don’t you offer a different mathematical proposition that we should accept that we have not discussed.

      I’m asking for a correct mathematical economic proposition. Just one other single example of an equation capable of predicting economic outcomes. One example of what the Austrians say can’t exist and everyone else insists is all around us.


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