During the final phase of Felix Klein’s life, his “Erlangen Program” attained the status of a true classic, even if little read. His successor in Göttingen, Constantin Carathéodory, attended several of Klein’s wartime lectures on the history of mathematics in the nineteenth century. Inspired by their breadth, he later wrote of that period as the century of geometry, culminating with Klein’s essay, which for the first time posed and answered the fundamental question: what is a geometry? For Carathéodory, Klein’s “Erlangen Program” appeared like the sunshine breaking through clouds to illumine an entire landscape that no one had been able to clearly see before [Carathéodory 1919]. Its author had just turned seventy when this appeared, and he hardly intended just to rest on his laurels.