Two flavours of mathematical explanation

Abstract

A proof of a mathematical theorem tells us that the theorem is true (or should be accepted), but some proofs go further and tell us why the theorem is true (or should be accepted). That is, some, but not all, proofs are explanatory. Call this intra-mathematical explanation and it is to be contrasted with extra-mathematical explanation, where mathematics explains things external to mathematics. This chapter focuses on the intra-mathematical case. The authors consider a couple of examples of explanatory proofs from contemporary mathematics. They determine whether these proofs share some common feature that may account for their explanatoriness. The authors conclude with two plausible, but competing, accounts of mathematical explanation and suggest that there might be more than one kind of explanation at work in mathematics. Show more