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September 11, 2012 Tuesdays at Espace des sciences with Cédric Villani, Mathematician, professor at Lyon 1 University, director of the Henri-Poincaré Institute, Fields Medal 2010. The brilliant mathematician Henri Poincaré remained famous for his flashes of brilliance and intuition, but also his approximate style and imprecisions. One of his errors, leading to the discovery of the phenomenon of sensitivity to initial conditions and carrying the seeds of chaos theory, was also his triumph; another, however, made him take sides, for the wrong reasons, against the kinetic theory of gases developed by Ludwig Boltzmann. Through these two errors, we will discuss two conceptual scientific revolutions of the late nineteenth century.