  The ``breathing mode'' of neutron-rich nuclei is our window into the
incompressibility of neutron-rich matter. After much confusion on the
interpretation of the experimental data, consistency was finally reached
between different models that predicted both the distribution of isoscalar
monopole strength in finite nuclei and the compression modulus of infinite
matter. However, a very recent experiment on the Tin isotopes at the Research
Center for Nuclear Physics(RCNP) in Japan has again muddled the waters.
Self-consistent models that were successful in reproducing the energy of the
giant monopole resonance (GMR) in nuclei with various nucleon asymmetries (such
as 90Zr, 144Sm, and 208Pb) overestimate the GMR energies in the Tin isotopes.
As important, the discrepancy between theory and experiment appears to grow
with neutron excess. This is particularly problematic as models artificially
tuned to reproduce the rapid softening of the GMR in the Tin isotopes become
inconsistent with the behavior of dilute neutron matter. Thus, we regard the
question of ``why is Tin so soft?'' as an important open problem in nuclear
structure.
