The article discusses the role of diagrams in mathematical reasoning based on a case study in analysis. In the presented example certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures are replaced by reasoning about permutation groups. This paper argues that, even though the diagrams are not present in the papers, they still play a role in the formulation of the proofs. It is shown that they play a role in concept formation as well as representations of proofs. In addition we note that `visualizaton' is used in different ways. In the first sense visualization denotes our inner mental pictures, which enables us to see that a certain fact holds, whereas in the other sense, `visualization' denotes a diagram or representation of something.
International Studies in the Philosophy of Science, 2010, Vol 24, Issue 1, p. 1-14