  The standard model of elementary interactions has long qualified as a theory
of matter, in which the postulated conservation laws (one baryonic and three
leptonic) acquire theoretical meaning. However, recent observations of lepton
number violations -- neutrino oscillations -- demonstrate its incompleteness.
We discuss why these considerations suggest the correctness of Ettore
Majorana's ideas on the nature of neutrino mass, and add further interest to
the search for an ultra-rare nuclear process in which two particles of matter
(electrons) are created, commonly called neutrinoless double beta decay. The
approach of the discussion is mainly historical and its character is
introductory. Some technical considerations, which highlight the usefulness of
Majorana's representation of gamma matrices, are presented in the appendix.
