Hardy, Littlewood and polymath

In the early twenty-first century the polymath experiments saw some of the most distinguished mathematicians in the world work together on significant research problems, writing down what they were doing on a blog for all to see as they went along. They drew widespread attention as they offered an unusual opportunity to see mathematics in progress. In this paper we contrast polymath with a famous collaboration from the early twentieth century, that of the Cambridge mathematicians G H Hardy and J E Littlewood. We look at the collaborations, and the institutions and structures that enabled them, as a contribution to understanding how collaboration enables mathematical advance.