Over the last twenty years Reinhard Siegmund-Schultze has done groundbreaking research on the reciprocal relations of the German and American mathematical communities. His work has helped produce a clearer picture of the shifting trends in research in both countries and the often marginalized role of applied mathematics in both. A fairly detailed account of the initial phase in the story can be found in the book by Parshall and Rowe from 1994. There the role of Göttingen in the special influence of Klein and Hilbert was highlighted, though with less attention paid to the impact of their respect research programs. In the present talk I will concentrate on the tradition of model making in Germany, while offering a general reassessment of its role within the research activities of American mathematicians.