After discussing some general methodological points this paper investigates in some detail the use of mathematics (not necessarily confined to academic mathematicians) in military work in the German and American cases, where as of now most knowledge is available. With respect to five other countries (Soviet Union, Great Britain, Italy, France, Japan) the discussion has to be restricted to a rough outline of problems and a collection of the rather scattered sources available. A case study is presented of mathematical war work in ballistics (Wolfgang Haack) which illustrates the complexity of the problems involved and the short distance between basic academic research and applied work for the military. The paper is concluded by appendices (tables) giving condensed information on mathematical war work in the seven countries considered. 23 See Siegmund-Schultze (2003) and some further remarks below.24 Birkhoff (1977), p. 63. 25 On the use of the differential analyzer in dealing with the many variables in ballistical calculations, for example in order to take into account the Magnus effect see Gray (1943), p. 90. S.