I have written a short discussion note of Batterman's recent article on mathematical explanation in science. If you have looked at the article, you may recall that he criticizes my "mapping account" as an account of how mathematics helps in explanation, especially the sorts of explanations using asymptotic reasoning which Batterman himself has spent so much time on. The basic point I make in my reply is that I was trying to provide an account of descriptive or representational content in terms of mappings and that I agree that this approach to description is not sufficient to ground explanatory power in all cases. Still, I argue that a theory of explanatory power can build on what I offer for descriptions, and that any account of explanation must say something about how explanations differ from descriptions.
Comments are, of course, appreciated!