The interplay
between generality
and individuality,
deduction and
construction, logic
and imagination -
this is the profound
essence of live
mathematics. Any
one or another of
these aspects of
mathematics can be
at the center of a
given achievement.
In a far reaching
development all of
them will be
involved. Generally
speaking, such a
development will
start from the
"concrete" ground,
then discard ballast
by abstraction
and rise to the
lofty layers of thin
air where navigation
and observation are
easy; after this
flight comes the
crucial test of
landing and reaching
specific goals in
the newly surveyed
low plains of
individual
"reality." In
brief, the flight
into abstract
generality must
start from and
return again to the
concrete and
specific.