Every specialist needs to be fully conversant with the basic facts of his subject and the methods of investigating them. For a physicist specializing in
the general theory of relativity, his "subject" comprises the field as a physical object and the four-dimensional Riemann manifold as the mathematical
description of this field. The methods of investigation comprise experiments followed by hypotheses and assembly of data defining four-dimensional Riemannian geometry with signature ( f-). Naturally, contemporary mathematicians cannot be satisfied with the methods of analysis used by Einstein, Hilbert and the other founders of general relativity; this explains the present tendencies to devise up-to-date experiments and to apply new mathematical methods to investigate new topics.