Mathematical structuralism and its basic assumptions

The notion of a structure is one of fundamental notions in mathematics: we speak of geometrical, topological, probabilistic, differential etc. structures. This notion is also important in the philosophical discussion concerning ontology for mathematics. In the last decades, the stance of mathematical structuralism attracts more and more attention. In this article I discuss the motivations which lie behind mathematical structuralism and briefly present Shapiro’s ante rem structuralism.