Those economists who mainly use the language of mathematics like to say (and perhaps even believe) that mathematical expression is more precise than mere words. But, as Arnold Kling points out, mathematical economics is a language of "faux precision," which is useful only when applied to well defined, narrow problems. It cannot address the big issues -- such as economic growth -- which depend on variables (such as the rule of law) that defy mathematical expression and quantification.
I would go a step further and argue that mathematical economics borders on obscurantism. It is a cult whose followers speak an arcane language not only to communicate among themselves but to obscure the essentially bankrupt nature of their craft from others. Mathematical expression actually hides the assumptions that underlie it. It is far easier to identify and challenge the assumptions of "literary" economics than it is to identify and challenge the assumptions of mathematical economics.
I daresay this is true even for persons who are conversant in mathematics. They may be able to manipulate easily the equations of mathematical economics, but they can do so without grasping the deeper meanings -- the assumptions -- hidden in those equations. In fact, the ease of manipulating the equations gives them a false sense of mastery over the underlying, non-mathematical concepts.
But much of the economics profession is dedicated to the protection and preservation of the essential incompetence of mathematical economists. I quote Arnold Kling again:
One of the best incumbent-protection rackets going today is for mathematical theorists in economics departments. The top departments will not certify someone as being qualified to have an advanced degree without first subjecting the student to the most rigorous mathematical economic theory. The rationale for this is reminiscent of fraternity hazing. "We went through it, so should they."
Mathematical hazing persists even though there are signs that the prestige of math is on the decline within the profession. The important Clark Medal, awarded to the most accomplished American economist under the age of 40, has not gone to a mathematical theorist since 1989.
These hazing rituals can have real consequences. In medicine, the controversial tradition of long work hours for medical residents has come under scrutiny over the last few years. In economics, mathematical hazing is not causing immediate harm to medical patients. But it probably is working to the long-term detriment of the profession.
The hazing ritual in economics has the real consequence of making much of economics irrelevant -- and dead wrong.
About Economic Forecasting
Is Economics a Science?
Economics as Science
Maybe Economics Is a Science
Proof That "Smart" Economists Can Be Stupid
Time to Retire the Fair Model
The Thing about Science
What's Wrong with Game Theory
Debunking "Scientific Objectivity"
Science's Anti-Scientific Bent
A Libertarian Paternalist's Dream World
The Short Answer to Libertarian Paternalism
Second-Guessing, Paternalism, Parentalism, and Choice
Another Thought about Libertarian Paternalism
Another Voice Against the New Paternalism
Ten Commandments of Economics
More Commandments of Economics
Science, Axioms, and Economics