I wrote this in a comment on Google+ today, in a discussion of the death of Elinor Ostrom. I kind of like it, so I am putting it here, too:
Economic theory building proceeds by using abstractions to encapsulate what are thought to be important basic principles of interactive decision-making and then uses mathematics as a language for analysis to reach conclusions. There is also an empirical side that tries to find appropriate values for some of the parameters that are used in theorizing, with disputed success. The social side of human behavior is quite important in some parts of mathematical economic modeling; economic network analysis and the analysis of information diffusion and information cascades being some prominent examples that spring to mind.
The curious incident of DD on the Web 
Economists must realize that their occupation is far closer to literary criticism than physics. Mathematical tools have a place in economics, but they are generally misused and misunderstood by those using them. It may be possible to for economics to grow into a scientific discipline, but until economists actually start reading the scholars they quote and approaching their discipline with a skeptical (but open) mind it is unlikely to happen.
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This comment is consistent with my encapsulation of mathematical modeling in economics. Economists have also started taking empirical evidence in the form of experiments and field work pretty seriously, so if you want to sneer at all of economics because it is not as much as science as physics is, I would advise you to read up on this.
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