Models

As an economist, I am a great fan of using mathematical models to describe the world and spend a great deal of my time in teaching explaining their advantages to students. They help clarify the thinking and force you to examine your assumptions. Furthermore, they allow you to make testable hypothesis which allows one to make use of the scientific method to determine the truth of some interesting fact about the world. Nevertheless, they do have their shortcomings. The classic, pithy phrase and rejoinder are:

"All models are wrong; but good models are useful."

I recently came across a good description of why one wants to use both model-based and stylized-fact-based approaches. It's from Alan Manning's chapter in the Handbook of Labor Economics, "Imperfect Competition in the Labor Market"

New developments are often thought of as departures from these canonical models. Although the use of very particular models encourages precise thinking, that precision relates to the models and not the world and can easily become spurious precision when the models are very abstract with assumptions designed more for analytical tractability than realism. So a model-based approach to the topic is not always helpful and this survey is based on the belief that it can be useful to think in very broad terms about general principles and that one can say useful things without having to couch them in a complete but necessarily very particular model.

Like any tool, models can be very useful, but much of the skill is in knowing the best tool to use for the problem at hand.