What is diagrammatic reasoning in mathematics?

Abstract

In recent years, epistemological issues connected with the use of diagrams and visualization in mathematics have been a subject of increasing interest. In particular, it is open to dispute what role diagrams play in justifying mathematical statements. One of the issues that may appear in this context is: what is the character of reasoning that relies in some way on a diagram or visualization and in what way is it distinct from other types of reasoning in mathematics? In this paper it is proposed to distinguish between several ways of using visualization or diagrams in mathematics, each of which could be connected with a different concept of diagrammatic/visual reasoning. Main differences between those types of reasoning are also hinted at. A distinction between visual (diagrammatic) reasoning and visual (diagrammatic) thinking is also considered.