 Some representations, in particular models and theories, are mathematized and their mathematical aspects are crucial to their cognitive and representational function. This forces us to reconsider a time-honoured philosophical puzzle: the applicability of mathematics in the empirical sciences. The problem can be traced back at least to Plato’s Timaeus, but its modern expression is due to Wigner who challenged us to find an explanation for the enormous usefulness of mathematics in the sciences (1960: 2). The question how a mathematized model represents its target implies the question how mathematics applies to a physical system (see Pincock 2012 for an explicit discussion of the relationship between scientific representation and the applicability of mathematics). For this reason, our fifth and final condition of adequacy is that an account of representation has to explain how mathematics is applied to the physical world. We call this the Applicability of Mathematics Condition.