An American mathematical research community emerged over the course of the closing quarter of the nineteenth century. In its efforts to shape itself, it looked abroad and especially to Germany, France, and Great Britain, three countries long established as mathematical leaders. What it found there were three very different systems for training future mathematical researchers. This chapter compares and contrasts those systems—at the same time that it examines the American system ultimately influenced by them—as they had evolved by the turn of the twentieth century. In so doing, it casts a comparative eye on what have traditionally been treated as four largely separate and distinct national mathematical communities and identifies shared standards of and practices in research-level training as a critical component of the internationalization of the field in the twentieth century.
Joining a Mathematical Research Community
