Explanatory and Non-explanatory Proofs in Mathematics (Guest Lecturer Professor Mark Colyvan)

In this talk I look at the contrast between explanatory and non-explanatory proofs in mathematics. This is done with the aim of shedding light on what distinguishes the explanatory proofs. I argue that there may be more than one notion of explanation in operation in mathematics: there does not seem to be a single account that ties together the different explanatory proofs. I then attempt to give a characterisation of the different notions of explanation in play and how these sit with standard accounts of explanation found outside of mathematics. I also hope to be directed towards further examples of explanatory and non-explanatory proofs of theorems from various branches of mathematics.