  We have performed a careful analysis of constraints on the neutrino mass from
current cosmological data. Combining data from the cosmic microwave background
and the 2dF galaxy survey yields an upper limit on the sum of the three
neutrino mass eigenstates of \sum m_nu < 3 eV (95% conf.), without including
additional priors. Including data from SNIa observations, Big Bang
nucleosynthesis, and HST Hubble key project data on H_0 tightens the limit to
\sum m_nu < 2.5 eV (95% conf.). We also perform a Fisher matrix analysis which
illustrates the cosmological parameter degeneracies affecting the determination
of \sum m_nu.
