Just a couple of references on the so called “mathiness” debate launched by Paul Romer’s piece.
First, there is a piece by Paul Samuelson I read back when I was struggling with my first calculus book and provided me with the necessary morale. Samuelson is, imho, likely to be the greatest social scientist of the XXth century, his mind was outstanding and his writing style entertaining.
With reference to the role of math in social science, I’ve always found that double attack on “walrasian” (competitive markets, price taking, representative agents, etc) and mathematical economics was stupid. Surely, in academia there are many mathematically sophisticated “walrasian” economists, but equating both is missing the point. That is why I found at the time Samuel Bowles’ view in his wonderful microeconomic book, refreshing:
But it seems that a more problem-driven and less tool-driven approach will require yet more sophisticated tools. The mathematical demands of the theoretical framework I am proposing will be greater, not less, than that of the Walrasian paradigm. The reason is that models that represent noncontractual social exchanges among individuals who are both heterogeneous and versatile in their behaviors and who interact in the presence of generalized increasing returns do not allow the standard simplifications such as price-taking behavior and convex production sets that made Walrasian models tractable. As has long been recognized in physics and biology, many important problems do not yield simple closed form solutions, or indeed any solutions at all that are susceptible to simple interpretation. In these cases computer simulations of the relevant social interactions will prove insightful as a complement (not a substitute) for more traditional analytical methods.
This put the accent on something close to my heart: the idea that most difficulties you find in social sciences are technical barriers. It is trivial to find questions that seem enigmatic and puzzle you enough. It is much harder to develop a way to pose it in a precise and approachable way. Surely, speculative non-technical treatment goes a long way. My point is however that formal modeling forces you to analyze your causal mechanism closely. It forces you to ask unasked question. A careful analysis of the mechanism in the world of abstraction is often the necessary prelude to a careful and sound empirical analysis that can feed back into something understandable.
Of all the reactions I read to Romer’s piece, the one I appreciated the most was this one, Just as Romer draws the consequences of focusing too much on “mathematical demonstration”, Leopoldo Fergusson does the same to the vice of focusing too much in “causal identification”, by which he means Rubin-like causal identification.