 Complete the following phrase:  Sources are not completely consistent as to when she embarked on her university education, much of which coincided with the First World War. She attended the University of Bonn, studying Geography, Mathematics and Physics. There are at least two reference to her having also studied at the University of Göttingen. It was from Bonn that in 1918 she received her doctorate: the work was supervised by Hans Hahn. Her dissertation was entitled Über die Randmenge einfach-zusammenhängender ebener Gebiete: a core conclusion has become known among her scholarly admirers as the Carathéodory-Torhorst theorem or, more simply, as the Torhorst theorem. It might have been thought that her doctorate should have provided a launch pad for a life-long career in the universities sector. There were still vanishingly few women working in high-level academic research at this time, however, and at least one commentator has identified a lack of confidence in her own mathematical ability in her autobiography. Also, with Germany economically, militarily and politically broken and on the brink of 