Oh, and a very sensible take on the use of mathematics in economics, from Mark Thoma:
It is really hard to convince new graduate students that mathematics without the underlying economic intuition, i.e. technique for the sake of technique, is pretty useless. It’s the economics that are important — mathematics is simply a tool that allows us to better understand the economic content of the models we work with — the math itself is not the point of the exercise. In fact, the best models are the ones that are boiled down to the essentials so that they isolate important phenomena in a way that makes them transparent. Mathematical complexity is not always the best way to reach this goal. Models should be as complex as needed to highlight the essential issues, to use Krugman’s term they should be “elegant,” and additional complexity beyond that point detracts from their elegance and obscures rather than clarifies the central features of the model. Sometimes a high degree of complexity is required, but not always.
This quotation comes from this post, which is definitely worth reading in its entirety as it also quotes at length some very a propos praise of Peter Diamond that puts the above quotation in good context.