In this paper, I critically discuss two of Mark Colyvan's case studies. After a short exposition of Colyvan's program, I first comment on the Lotka-Volterra predator-prey model. I agree with Colyvan's thesis that mathematical models in population ecology can be explanatory. The historical fathers of mathematical population ecology anticipated this thesis. However, the issue of idealization is not sufficiently emphasized; Volterra's discussion of the predator-prey model shows that he was acutely aware of the problem of idealization. As to the second case, I point out that the explanation of the structure of the bee's honeycomb, based on the mathematical honeycomb conjecture, is not a scientific explanation at all.