Industrial Mathematics: a real opportunity or a chimera?

This is a talk on the real experiences of a professor of Mathematics which, incidentally, in the last 20 years has faced problems of Industrial Mathematics. Mathematics is, by its intrinsic nature, a pure science. The mathematicians who do the so-called Applied Mathematics, in general, have never had contact with industrial companies. The last meeting of the SIMAI (Italian Society of Industrial and Applied Mathematics) had no industrial sponsors. In academic language, the word “applied mathematics" means a mathematics that could be applied, but it is not specified nor when nor in what context nor by whom. This talk, describing my experiences, wants to show that there are spaces for an effective industrial mathematics.