  Random fields in nature often have, to a good approximation, Gaussian
characteristics. We present the mathematical framework for a new and simple
method for investigating the non-Gaussian contributions, based on counting the
maxima and minima of a scalar field. We consider a random surface, whose height
is given by a nonlinear function of a Gaussian field. We find that, as a result
of the non-Gaussianity, the density of maxima and minima no longer match and
calculate the relative imbalance between the two. Our approach allows to detect
and quantify non-Gaussianities present in any random field that can be
represented as the height of a smooth two-dimensional surface.
