This paper investigates scientific, institutional, and political conflict and collaboration between two different disciplines in the first part of the 20th century: applied mathematics and fluid dynamics. It argues for the catalytic role of Richard von Mises (1883–1953) in this process and analyzes the reasons for von Mises’s considerable fame in the former and limited posthumous reputation in the latter field. I argue that von Mises’s contributions to fluid dynamics and aerodynamics suffered chiefly from two somewhat interconnected deficiencies compared to the work of his principal competitors. There was, on the one hand, von Mises’s methodological preference for applied mathematics as opposed to the reigning hybrid theories of fluid dynamics, which were usually more prone to ad hoc adaptation of theory to experimental data. There was, on the other hand, von Mises’s geographical remoteness from the main experimental facilities of fluid dynamics and the data produced there. Additionally, there were external reasons that limited von Mises’s influence, among them his fate as a refugee from Nazi Germany. Despite his occasionally polemical mind, von Mises’s work as a bridge builder prevailed, as evidenced by the success of his journal ZAMM . Indisputably, von Mises was a rare example of an engineer and a mathematician combined.