from Yoshinori Shiozawa (originally a comment)
This is a part of my essay “Between Math and the Occult” written in 2002 for a journal named “The pleasures of mathematics” (in Japanese) No. 30.
There is an interesting parable that points out this. Originally of Arab origin, it was introduced and disseminated in economics by writers like Martin Shubik and Thierry de Montbrial.
At midnight, a drunken person was wandering under a lonely streetlight. He seemed to be looking for something. When a passerby asked, the drunken person said he was looking for a key. The passersby joined in the key hunt, saying it would be a problem. But they couldn’t find the key. After a while, the passerby asked for the drunkard. “Did you really drop the key here?” The drunkard replied calmly. “No, it’s over there where I dropped the key, but it is pitch-dark there and I can’t see anything. That’s why I’m looking for the key in the light.”
Mathematics is a strong light. But, if we consider mathematics as the only tool of theory, it can be the same as the above drunkard. Only problems on which mathematics can spot the light are prone to be studied, leaving other, more important tasks untouched. For 100 years until 1970, theoretical economics was mostly advanced by the light of mathematics. Mathematics is not to be blamed by that fact. However, there are some frameworks that are easy to shed light of mathematics and others that are not. Optimization and equilibrium is such a framework. As a result, huge progress has been made in the logical level. But it was also the cause that economics began to wander in a wrong direction. Ironically, the mistake was hidden as long as light of mathematics continued to shed light on economics. This is also one of the dangerous paths hidden in economics.
Those who can read Japanese can read the whole text here.