The Navier-Stokes equations are a set of second-order partial differential equa-tions relating first and second derivatives of fluid velocity, which is representedas a smooth vector field. While simple in principle, they are enormously dif-ficult to solve; in fact, no proof has yet been found guaranteeing even theexistence of a smooth solution in just three dimensions. Annoying as this isto mathematicians, the consequences of a lack of solution are far-reaching: theNavier-Stokes equations govern continuum phenomena in all areas of science,from basic hydrodynamical applications to even cosmology.