For an economist, I put relatively little time or effort into sophisticated, mathematical theory, but that still makes me a fairly high outlier in the development and public health research communities. The stock in trade of an economist is the use of mathematical models of behavior that involve agents maximizing utility. These days, with economics having long since left behind its origins as the pure study of markets, this approach to modeling rational decisionmaking is one of the few things that unites the field as a whole.
Sometimes the effort seems a bit silly. It’s a favorite graduate student cocktail party wheeze to suggest that those ivory tower economists have failed miserably, because their models don’t account for (irrationality, free will, psychology, power dynamics, etc.) and hence are useless. I think that reasoning is misguided in a lot of ways, which I won’t get into here, but there’s a deeper problem: what exactly is the point of all that math? Couldn’t we do all of this better as prose? The snide response is to look at discussions of Keynes’s General Theory or the works of Karl Marx: instead of making any progress toward establishing actual scientific facts, academics spent their time arguing about what some particular Great Sage really meant.
A deeper analysis, argued eloquently in an essay by Paul Krugman about the sad history of theory in development economics, is that math forces us to be precise about exactly what we mean. It also helps lead our logic toward conclusions that might not be obvious while keeping us from ending up at apparently-obvious conclusions that don’t follow from our premises. And, he claims, model-making is the not just the only way to be successful in developing scientific theories, but the only way to even try to theorize:
There are many intelligent writers on economics who are able to convince themselves — and sometimes large numbers of other people as well — that they have found a way to transcend the narrowing effect of model-building. Invariably they are fooling themselves. If you look at the writing of anyone who claims to be able to write about social issues without stooping to restrictive modeling, you will find that his insights are based essentially on the use of metaphor. And metaphor is, of course, a kind of heuristic modeling technique.
The entirety of his essay, The Fall and Rise of Development Economics (written way back in 1994 – this is economist-era Krugman, not editorialist-era Krugman), is readable and interesting. Even mathematically-discinclined readers will be able to understand the simple model he uses as an example (to formalize the Rosenstein-Rodan Big Push theory of development) without too much trouble. Highly recommended.