  Questions about this case focus on whether the mathematics is really contributing to the explanation (or whether it is merely standing in for the biological facts and it is these that really do the explaining), whether the alleged explanation is an explanation at all, and whether the mathematics in question is involved in the explanation in the right kind of way. Finally, it is worth mentioning that although the recent interest in mathematical explanation arose out of debates over the indispensability argument, the status of mathematical explanations in the empirical sciences has also attracted interest in its own right. Moreover, such explanations (sometimes called “extra-mathematical explanations”) lead one very naturally to think about explanations of mathematical facts by appeal to further mathematical facts (sometimes called “intra-mathematical explanation”). These two kinds of mathematical explanation are related, of course. If, for example, some theorem of mathematics has its explanation rest in an explanatory proof, then any applications of that theorem in the empirical realm would give rise to a prima facie case that the full explanation of the empirical phenomenon in question involves the intra-mathematical explanation of the theorem. For these and other reasons, both kinds of mathematical explanation have attracted a great deal of interest from philosophers of mathematics and philosophers of science in recent years.