If the history of economic thought teaches us anything, it teaches us that people who don't use the mathematics always, sooner or later, end up saying something badly wrong about economics. Paul Krugman has an essay on the subject with which I profoundly disagree on a number of points, but which contains one highly important truth; there are important ideas in economics which are crystal clear if you understand the mathematics and bloody hard to get your head round if you don't.
Davies has many interesting links in his post. The Krugman essay says in part,
International trade in particular happens to be a subject in which a page or two of algebra and diagrams is worth 10 volumes of mere words. That is why it is the particular subfield of economics in which the views of those who understand the subject and those who do not diverge most sharply.
I may be putting words into Krugman's mouth, but what he is saying is that you can divide the world into people who will say things like, "We're losing all our good jobs to India!" on the one hand and people who believe in a simple general equilibrium model (the famous 2x2x2 model) of trade on the other. International trade always looks like a better deal from a general equilibrium perspective than it does to those who do not have that perspective.
I would like to break out two issues raised by Davies and Krugman. First, can economic education take place without math? I hope that the answer is "yes," because I am trying to outline a book that attempts to do that. Unfortunately, I find it plausible that the case for free trade cannot sink in when it is presented in nonmathematical form.
I also think that when we use math to teach we should use numerical examples and computation rather than calculus. In my business experience, I never encountered a situation in which I used calculus. I had a data point or two and extrapolated the rest. I think that we mislead students who may be headed into business when we describe the world in terms of differentiable functions.
The second issue is, "Should economists use math to communicate with one another?" My personal opinion is that we have carried the use of math well past the point of diminishing returns.
In economics, it is easy to deceive yourself and others. You can deceive using words. But you can also deceive using math. You can say that assumption X drives a result when it really is assumption Y. To this day, I do not think that the "rational expectations" model of macroeconomics was driven by the assumption of rational expectations. I think it was driven by an implicit assumption of perfectly flexible wages and prices. But hundreds of Ph.D dissertations and a Nobel Prize or two were awarded to what I always thought was a mathematical swindle.
For Discussion. Is trying to teach economics without math a misguided project?