Abstract

Philosophical analysis of the interplay between mathematics and the empirical sciences concentrate on the effectiveness of mathematics in science but leave unaddressed an important component of the applicability issue, namely the successful application of physical considerations in mathematics. In this talk, after a short presentation of the current debate, I focus on this yet unexplored topic. I illustrate some cases of successful application of physics to mathematics and I argue that they essentially depend on the successful application of conservation laws in mathematics. I also outline some strategies to account for the effectiveness of conservation laws in mathematics.