  Observational constraints on the theory of the IMF are reviewed. These
observations include the new result that star formation is very rapid, usually
going from start to finish in only 1 or 2 dynamical times on a wide range of
scales. This result, combined with the observation that the IMF is independent
of cluster density over a factor of several hundred, implies that protostar
coagulation during orbital motions in a cloud are not important for the IMF:
there is not enough time. The observation that the IMF in individual clusters
is about the same as the IMF in whole galaxies implies that stars of all masses
form randomly in self-gravitating clouds of all masses. There cannot be a
sequence of stellar masses in a cluster, based on stirring or heating for
example, where the largest star that forms keeps increasing until the cloud is
destroyed. The uniformity of the IMF over time and space argues for a process
that is independent of specific properties of molecular clouds. This
uniformity, along with the common observation of young stars in hierarchical
clusters that resemble the structures of interstellar gas, suggests that the
IMF, at least in the power law range, is a by-product of turbulence. Detailed
physical processes may affect the turnover at low mass, but even this may have
a universal character arising from a combination of turbulence-induced
variations in the local cloud properties, and fragmentation in unstable cloud
pieces.
