Mathematics for us today is the well defined world of algebra, metric spaces, & general (Hausdorff separable) topology. Partial mathematics is taken to be the 1969 non-Hausdorff asymmetric topology of Dana Scott giving meaning to the 1930s incomplete mathematics of Kurt G矣del. Discrete mathematics is the complexity theory of time & space for expressing cost of well defined computations. But! Partial mathematics is rarely costed, and conversely the partiality of discrete mathematics is rarely considered. In fact, Warwick has its own Centre for Discrete Mathematics & its Applications (DIMAP), a surging research center for algorithms & complexity, but, no partiality. Yet, resulting from the collapse of the Hilbert Program, partiality has been at least as intrinsic to computer science as is complexity theory. So, is there a reconciled form we can term Discrete Partial Mathematics?