The Ins and Outs of Mathematical Explanation

Mark Colyvan (Sydney) gives a talk at the MCMP Colloquium titled "The Ins and Outs of Mathematical Explanation". Abstract: Proofs of mathematical theorems tell us that the theorem is true, but some proofs go further and tell us why the theorem is true. That is, some, but not all, proofs are explanatory. Call this intra-mathematical explanation. It has been argued that whenever there are physical applications of the theorems in question, we also have mathematical explanations of physical phenomena. Call this extra-mathematical explanation. In this paper I will consider both intra- and extra-mathematical explanations and discuss why they are of philosophical interest. I will also make some speculative remarks about two promising accounts for a theory of mathematical explanation.