  This review devoted to the centenary of Alexander Friedmann's prediction of
the Universe expansion presents the results obtained by him in 1922 and 1924
and the sketch of their further developments. Special attention is paid to the
role of mathematics which enabled Friedmann to perform a radical departure from
the conventional practice of considering our Universe as a static system. The
effect of particle creation in expanding Universe is discussed concurrently
with the earlier investigated phenomenon of pair creation from vacuum by
external electric field. The numbers of scalar and spinor particles created at
different stages of the Universe evolution are presented, and the possible role
of the effect of creation of particles in the formation of relativistic plasma
and cold dark matter after the inflationary period is noted. It is stressed
that by introducing the concept of expanding Universe Friedmann made a
contribution to understanding of the world around us compatible to those made
by Ptolemy, Copernicus, and Newton in previous epochs.
