The idea of an exact science unified and complete has been advocated throughout the history of thought, but the sciences continue to cover only small patches of the world we live in. We may dream that the exact sciences will some day cover everything. But I argue that the very ways we do our exact sciences when they are most successfully done seems likely to confine them within limited domains. I discuss three cases to illustrate: the use of broad-scale non-experimental statistics for causal modelling across the social sciences, an economic model on skill-loss during unemployment, and the quantum theory of superconductivity. In all cases, where we can expect exact order depends on where we can fit our models. And by the nature of how models do-and should-get constructed in exact science, they fit readily onto only very special bits of the world around us. I also maintain that an ill-supported belief in the universality of our favourite exact science can lead us to adopt bad methodologies for carrying out the central aim of the sciences, namely to make the world the way it ought to be.