  The very early dismissal of Schwarzschild's original solution and manifold,
and the rise, under Schwarzschild's name, of the inequivalent solution and
manifold found instead by Hilbert, are scrutinised and commented upon, in the
light of the subsequent occurrences.
  It is reminded that Hilbert's manifold suffers from two defects, that are
absent in Schwarzschild's manifold. It does not admit a consistent drawing of
the arrow of time, and it allows for an invariant, local, intrinsic singularity
in its interior. The former defect is remedied by the change of topology of the
extensions proposed by Synge, Kruskal and Szekeres. The latter persists
unaffected in the extensions, since it is of local character.
