A Challenge To (Non-Austrian) Readers
Now I have a new one, though it differs in important aspects from the previous quiz. Most importantly perhaps is that while I knew the answer the last time, I don't know the answer this time. Or more correctly, I don't think there is an answer. The reason I am having this quiz is to make me more sure about this: To either confirm the belief by absence of valid answers, or to finally enable me to see at least some positive aspects of this practice.
The question is about the use of mathematical modeling in economics. I have repeatedly pointed out the problems with that approach (for example here). What really strikes me though is that I have yet to find a single advocate of that approach really point to any positive function with it in helping to understand the real world. I have directly asked a lot of them, both teachers and others, yet no one has come up with a positive answer.
Usually they have either chosen to ignore the question (as was the case when I asked Menzie Chinn about it in this comment thread), or they come up with irrelevant answers. Examples of the latter include that they think the math is (and I quote) "beautiful" (Which is nice for them, but not for those of us with different esthetical preferences), that math is more "precise" (Which might be true in some cases (though not all), and even in those cases this comes at the cost of the realism of the theory) or that in order to be a science, economics must use math (which is nonsense, as there are lots of sciences that don't use math).
Some defenders also try to deter criticism by the use of insulting hints about the intelligence of heretics. Another line of defense against critics that point to the unrealism created by mathematical modeling is that bad theories have arisen without mathematical modeling. That is true, but is no real defense of the practice, anymore than the fact that some people die prematurely even though they receive good medical care is a defense of the use of witchcraft to cure diseases. Verbal praxeological reasoning enables you to reach the truth, but since people can do it wrong it doesn't guarantee it. Mathematical modeling will by contrast at best (like witchcraft in the case of medical care) be useless in reaching the truth, and will usually be counterproductive.
The quiz, or challenge here, is then for someone to name a (or several) theoretical insight about the real world that mathematical modeling has produced. Obviously, "theoretical insights" that are unrealistic don't count. And neither does empirical findings through econometrics count, as they, even if valid in some sense, are not theoretical. I'll return later to that issue. For now, the focus will be on theoretical mathematical modeling. Since the Austrian part of my readership presumably agrees with me, they will likely be as unable as I am to name a theoretical insight about the real world created through mathematical modeling. The question here is then whether any of the many non-Austrians that I know are reading this will be able to come up with a valid example. I doubt it, but I will find attempts to do so interesting.