Over the past twenty years, historians of science have examined the role played by the Second World War in the development of physics in the United States. They have pointed to upheavals in scientific practices and consequent changes in social and cultural behaviours. The present paper is concerned with similar topics, taking the case of mathematics. Institutional patterns are analysed, as set up by the military during the war years, to allow ongoing collaboration with mathematicians, and the rise of new fields in applied mathematics is examined, together with the major groups involved in such work. Established divisions and hierarchies, as prevailing of old between branches of mathematics, underwent upheavals in the process. The emergence is noted of a socially and culturally different persona for the mathematicians ; John von Neumann being the symbol and exemplar of such a type. The post-war consolidation of a number of centers of repute is then surveyed, most notably with the case of the Courant Institute, along with the attempts to achieve institutionalisation of applied mathematics in the United States, be it as a research activity or at university faculty level, as well as the resistances encountered. Finally, the paper addresses — and proffers some tentative answers — the following question: Why, in spite of questioned advances in the field, was the discipline of applied mathematics sidelined and marginalised in the international mathematical community, up till the 1970s ?