Shapley-Folkman-Starr Theorem

While economic theory sometimes uses advanced mathematics, such as Brouwer’s fixed point theorem, it’s less common for economic theory to lead to new mathematical developments. The Shapley-Folkman-Starr Theorem is an example of the latter. Roughly, the theorem states that the (Minkowski) sum of a large number of arbitrary sets in a finite-dimensional vector space will be close to convex. Starr was an economics undergraduate who was working on a term paper on approximating non-convex optimization problems with convex ones. This led to collaboration with Shapley (a game theorist), and Folkman (a mathematician), and the eponymous theorem.