  In algebraic statistics, the maximum likelihood degree of a statistical model
is the number of complex critical points of its log-likelihood function. A
priori knowledge of this number is useful for applying techniques of numerical
algebraic geometry to the maximum likelihood estimation problem. We compute the
maximum likelihood degree of a generic two-dimensional subspace of the space of
$n\times n$ Gaussian covariance matrices. We use the intersection theory of
plane curves to show that this number is $2n-3$.
