  We present a quantitative analysis of superfluidity and superconductivity in
dense matter from observations of isolated neutron stars in the context of the
minimal cooling model. Our new approach produces the best fit neutron triplet
superfluid critical temperature, the best fit proton singlet superconducting
critical temperature, and their associated statistical uncertainties. We find
that the neutron triplet critical temperature is likely $2.09^{+4.37}_{-1.41}
\times 10^{8}$ K and that the proton singlet critical temperature is
$7.59^{+2.48}_{-5.81} \times 10^{9}$ K. However, we also show that this result
only holds if the Vela neutron star is not included in the data set. If Vela is
included, the gaps increase significantly to attempt to reproduce Vela's lower
temperature given its young age. Further including neutron stars believed to
have carbon atmospheres increases the neutron critical temperature and
decreases the proton critical temperature. Our method demonstrates that
continued observations of isolated neutron stars can quantitatively constrain
the nature of superfluidity in dense matter.
