I’m a political scientist, not someone in a policy school or an economist. But I should note that Schelling’s work has had a profound effect on political scientists. I could put out a huge list of works–including a large number in international relations–but just one will suffice.
A few years ago, a political scientist named Gerald Gamm at the University of Rochester published a stupendous work called Urban Exodus: Why the Jews Left Boston and the Irish stayed, whose title tells you the main question. Gamm observed that most of the dominant answers to the general question were of two sorts: a) Jews are nicer, more tolerant people than the Irish or; b) greedy real estate agents and government authorities caused the Jewish exodus.
Gamm found neither of these claims persuasive. Instead, he observed that the situation could be modeled in game theoretic terms, drawing on the work of Schelling. In essence, Jews were playing a game in which coordination was difficult, if not impossible–because of the rules of their faith, it was very easy to pick up and move a temple, and not only that, everyone in the religion knew that to be the case. Given that, there were both no barriers to exit and a strong motivation to avoid being the last one out the door. Catholics were a different case–because there were still, in those days, rules that said that one had to attend the parish church in the neighborhood one lived in, there were very strong barriers to exit (since you and your children could no longer take the sacraments, including marriage, confirmation, etc., in the parish church you grew up in if you moved). And, again, everyone knew that all other Irish Catholics were similarly constrained. So the Catholics were, in essence, playing a game with substantial coordination. And that’s why they stayed and the Jews left.
As Mark notes, most of the work that Schelling did was in beautiful English, not math. Schelling had such an impact because the elegance of his theories made you see the world differently, and (as in the case of Gamm above) look for explanations in different places than you would have otherwise.