  The recent atmospheric neutrino data from Super-Kamiokande provide strong
evidence of neutrino oscillations and therefore of non-zero neutrino mass.
These data imply a lower limit on the hot dark matter (i.e., light neutrino)
contribution to the cosmological density $\Omega_\nu >~ 0.001$ --- almost as
much as that of all the stars in the universe --- and permit higher
$\Omega_\nu$. The ``standard'' COBE-normalized critical-matter-density (i.e.,
$\Omega_m=1$) Cold Dark Matter (CDM) model has too much power on small scales.
But adding to CDM neutrinos with mass of about 5 eV, corresponding to
$\Omega_\nu \approx 0.2$, results in a much improved fit to data on the nearby
galaxy and cluster distribution. Indeed, the resulting Cold + Hot Dark Matter
(CHDM) cosmological model is arguably the most successful $\Omega_m=1$ model
for structure formation. However, other recent data has begun to make the case
for $\Omega_m <~ 0.6$ fairly convincing. In light of all this new data, we
reconsider whether cosmology still provides evidence favoring neutrino mass of
a few eV in flat models with cosmological constant $\Omega_\Lambda = 1 -
\Omega_m$. We find that the possible improvement of the low-$\Omega_m$ flat
(LCDM) cosmological models with the addition of light neutrinos appears to be
rather limited.
