The Ensemble Kalman Filter (EnKF) is a widely used tool for assimilating data with high dimensional nonlinear models. Nevertheless, our theoretical understanding of the filter is largely supported by observational evidence rather than rigorous statements. In this talk we attempt to make rigorous statements regarding "filter divergence", where the filter loses track of the underlying signal. To be specific, we focus on the more exotic phenomenon known as "catastrophic filter divergence", where the filter reaches machine infinity in finite time.