Uso euristico degli elaboratori nella ricerca matematica

The influence that computers can have on mathematical research is discussed here. We present some applications to problems of Computational Complexity, Number Theory and Numerical Analysis. Namely, we deal with the following topics: the euristic search of upper bounds to the tensorial rank of tree way arrays, the Waring problem for cubes, the problem of primes and powers of two and the behaviour of some condition numbers of linear systems.