Yann Brenier - Centre National de la Recherche Scientifique (CNRS) The mathematical description of fluids like water goes back to the Swiss mathematician Leonard Euler in the middle of the 18th century. If we think at a discrete level, for instance in terms of pixels, the motion of water looks very much like a very fast succession of permutations exchanging pixels, a little like a "melting rubik cube". We will discuss this analogy in more details, in connection with the mathematical theory of optimal transportation and its numerous applications.