Even though I have made considerable use of mathematics in some of my work, for the most part I share Bryan Caplan's views on the overuse of mathematics in economics:
[C]ritics' complaints about excessive math are justified, and not reducible to opposition to "bringing models face to face with empirical evidence." Especially in economic theory, math rarely "brings clarity." Math more often leads to neglect of important facts and confusion about irrelevant mathematical issues. ... Almost all of the advances of the last thirty years that [Coyle] hails are empirical, and almost none of these empirics even hinge on technical econometrics. Yet during these decades, economist theorists enjoyed great status and published vast numbers of "top" papers that Coyle damns with faint praise. Even worse, these theorists have emotionally taxed more empirically-minded economists with soul-crushing coursework and faux incredulity (e.g. "I can't take your claim seriously without a formal model").
... I have no principled objection to mathematical econ. I just think that we should evaluate mathematical econ empirically - and admit that in hindsight, the vast majority of it fails the cost-benefit test. [emphasis added]. While many complaints about econ are unjustified, this one is, and it's time to clean house.
I think the blogosphere is helping to move the profession in the direction favoured by Professor Caplan. Increasingly, some of the best economics is being done for more general audiences in economics blogs. Not many institutions (universities, econ grad schools) will have the required moxie to move in this direction, too. But over time, people will be evaluating econ grad schools by additional criteria beyond just the number of publications in top math-theory journals. This type of competition in the field will work slowly, but it will be better for future generations.