Mathematical Explanation beyond Explanatory Proof

Much recent work on mathematical explanation has presupposed that the phenomenon involves explanatory proofs in an essential way. I argue that this view, ‘proof chauvinism’, is false. I then look in some detail at the explanation of the solvability of polynomial equations provided by Galois theory, which has often been thought to revolve around an explanatory proof. The article concludes with some general worries about the effects of chauvinism on the theory of mathematical explanation. 1. Introduction 2. Why I Am Not a Proof Chauvinist 2.1. Proof chauvinism and mathematical practice 2.2. Proof chauvinism and philosophy 3. An Example: Galois Theory and Explanatory Proof 4. Conclusion