Abstract

Some theorists are bewildered by the effectiveness of mathematical concepts. For example, Steiner attempts to show that there can be no rational explanation of mathematical applicability in physics. Others (notably Penrose) are concerned primarily with the unexpected effectiveness within mathematics. Both views consist of two parts: a puzzle and a positive solution. I defend their paradoxical parts against the sceptics who do not believe that the very problem of effectiveness is a genuine one. Utilising Horwich’s theory of surprise, I argue that the central cases of effectiveness discussed by Steiner and Penrose are indeed surprising and call for an explanation.