Joseph Boussinesq was the most prolific of all French contributors to nineteenth-century fluid mechanics. His scientific production included a novel theory of solitary waves, the KdV equation for finite deformations of the water surface in an open channel, a systematic study of open channel and pipe flow based on the concept of effective viscosity, pioneering derivations of boundary layers and entrance effects, new exact solutions of the Navier–Stokes equation under geometrically simple boundary conditions, and the ‘Boussinesq approximation’ for heat convection in a moving fluid under gravity. Although his extraordinary skills were quickly recognized and rewarded, other experts in the field were often unaware even of his most important results and they ended up rediscovering some of them. Boussinesq's unusual background and the resulting peculiarities of his style explain this problematic diffusion. They also account for the richness of his legacy.