  We calculate the density of stationary points and minima of a $N\gg 1$
dimensional Gaussian energy landscape. We use it to show that the point of
zero-temperature replica symmetry breaking in the equilibrium statistical
mechanics of a particle placed in such a landscape in a spherical box of size
$L=R\sqrt{N}$ corresponds to the onset of exponential in $N$ growth of the
cumulative number of stationary points, but not necessarily the minima. For
finite temperatures we construct a simple variational upper bound on the true
free energy of the $R=\infty$ version of the problem and show that this
approximation is able to recover the position of the whole de-Almeida-Thouless
line.
