  The application of classical methods of statistical mechanics, originally
developed by Ludwig Boltzmann in gas dynamics, to the description of social
phenomena is a successful story that we try to outline in this paper. On one
hand, it is nowadays a flourishing research line, which is more and more
permeating different contexts such as the econophysics, sociophysics,
biomathematics, transportation engineering to name just a few of them. On the
other hand, it is a fascinating mathematical challenge, because it requires the
interplay of various complementary expertises: modelling, model analysis,
numerics. In this paper, we try to give a taste of all of this using the social
phenomenon of opinion formation as a motivating example.
