Before the First World War, Tullio Levi-Civita (1873–1941) was already a well-known mathematician in Italy and abroad, in particular in France. Professor at the University of Padua since 1898, he had published important contributions to tensor calculus, theory of relativity, differential geometry, hydrodynamics, and the three-body problem. In 1918, when he moved to the University of Rome, he created an international school of mathematics. In this paper, we focus on d'Alembert's paradox to which Levi-Civita and some of his Italian and French followers contributed remarkable solutions. This case-study is used to illustrate Levi-Civita's approach to hydrodynamics and its influence in Italy and France, especially in the period 1910–1914.