Debate About Math In Economics

Noah Smith here criticizes mathematical economics. He points out that when math is used in physics, it is a representation of real things, which was he liked it so much there. By contrast, when it is used in economics it has no connection to reality, which is why dislikes it in economics.

Smith also suggests that the reason advanced math is used is because professors thinks it signals intelligence. Of course, taking IQ tests would be a far less time consuming and a lot more effective way of achieving that, and it wouldn't distort theories.

Paul Krugman responds by claiming that he used math when he came up with his Nobel winning trade theories (which unlike his macro analysis are mostly sensible). Perhaps that is true, but I don't see how they couldn't be derived using verbal logical analysis.

Bryan Caplan responds to Krugman by saying that even if that was true for him, for most people it has a negative effect on economic analysis.

What about the the remaining 5% who do understand some mathematical economics?  An optimist would point out that this 5% does the lion's share of original economic thinking.  Perhaps economath is vital scaffolding for intellectual progress despite its low pedagogical value.

Empirically, even the 5% gain most of their economic understanding via intuition.  Don't believe me?  Show a typical economist a theory article, and watch how he "reads" it: He reads the abstract and introduction, flips the theory pages, then reads the conclusion.  If math is so enlightening, why do even the mathematically able routinely skip the math?

You could reply that mathematical economics shows that economic intuition is often wrong.  I beg to differ.  My experience: When mathematical economics contradicts common sense, there's almost always mathematical sleight of hand at work - a sneaky assumption, a stilted formalization, or bad back-translation from economath to English.  

My main objection to this is mainly Caplan's use of words like "intuition" and "common sense" to describe the alternative to math. "Intuition" is a word which means "the ability to acquire knowledge without inference and/or the use of reason", but of course verbal economic logic does involve the use of logical inference and reason. "Common sense" is similarly misleading since it refers to things that almost everyone is aware of and think is obvious, something that is clearly not applicable to advanced economic theories drived through verbal logic.