In contemporary philosophy ‘visual thinking in mathematics’ refers to studies of the role of visual representations, or diagrams/figures, in mathematics. Currently three main areas and questions are being investigated. The first concerns the role of diagrams, or the diagram-based reasoning, found in Euclid’s Elements. Second is the epistemic role of diagrams: the question whether reasoning based on diagrams can be rigorous. This debate includes the question whether beliefs based on visual input can be justified, and whether visual perception may lead to mathematical knowledge. The third observes that diagrams abound in (contemporary) mathematical practice, and so tries to understand the role they play, going beyond the traditional debates on the legitimacy of using diagrams in mathematical proofs.

The first part of the talk introduces some of the contributions to the first two areas. This part also mentions a few relevant episodes from the history of use of figures in mathematics. In the last part, we will consider a question that belongs to the third area, namely to what extent diagrams lead to discoveries in mathematics