One of the more striking features in the development of higher mathematics at the German universities during the nineteenth century was the prominent role played by various rival centers. Among these, Berlin and Göttingen stood out as the two leading institutions for the study of research-level mathematics. By the 1870s they were attracting an impressive array of aspiring talent not only from within the German states but also from numerous other countries as well. The rivalry between these two dynamos has long been legendary, yet little has been written about the sources of the conflicts that arose or the substantive issues behind them. Here I hope to shed some light on this theme by recalling some episodes that tell us a good deal about the competing forces that animated these two centers. Most of the information I will draw on concerns events from the last three decades of the nineteenth century. But to understand these it will be helpful to begin with a few remarks about the overall development of mathematics in Germany, so I will proceed from the general to the specific. In fact, we can gain an overview of several of the more famous names in German mathematics simply by listing some of the better-known figures who held academic positions in Göttingen or Berlin. As an added bonus, this leads to a very useful tripartite periodization: