There is a puzzling contradiction: direct observations favor a low-mass-density universe ($0.2\le��_m\le0.6$), but the only model which fits universe structure over more than three orders of magnitude in distance scale has a mix of hot (neutrino) and cold dark matter providing a critical density universe. Models of an open universe (low $��_m$) or one adding a cosmological constant ($��$) to provide a critical energy density ($��_m+ ��_��=1$) have probabilities of $<10^{-3}$. Two-neutrino dark matter works better than having the needed $\sim5$ eV of neutrino mass in one species of neutrino, and this is consistent with the only model which fits all present indications for neutrino mass: $��_��\to��_��$ accounting for the atmospheric anomaly (with $��_��$ and $��_��$ being the hot dark matter), $\bar��_��\to\bar��_e$ being observed by LSND, and $��_e\to��_s$ explaining the solar $��_e$ deficit. The LSND/KARMEN results are consistent with the needed mass of hot dark matter. Further support for this mass pattern is provided by the need for the sterile neutrino, $��_s$, to make possible heavy-element nucleosynthesis in supernovae. It is a fascinating question as to whether the hot dark matter paradox will be resolved by better measurements or by the introduction of new physics.

10 pages, 1 figure, talk given at 23rd Johns Hopkins Workshop, "Neutrinos in the Next Millenium"