Introduction and Overview

Abstract

The core idea of mathematical structuralism is that mathematical theories, always or at least in many central cases, are meant to characterize abstract structures (as opposed to more concrete, individual objects). As such, structuralism is a general position about the subject matter of mathematics, namely abstract structures; but it also includes, or is intimately connected with, views about its methodology, since studying such structures involves distinctive tools and procedures. The goal of the present collection of essays is to discuss mathematical structuralism with respect to both aspects. This is done by examining contributions by a number of mathematicians and philosophers of mathematics from the second half of the 19th and the early 20th centuries.