This chapter shows that some general arithmetical theorems almost certainly can be discovered by visualizing. First, it describes two examples of what look like acceptable routes to general theorems in which visualization has a non-redundant role. It then canvasses and assesses two natural objections to the acceptability of these examples. Finally, focusing on a modified version of the first example, the chapter gives a positive account of how it is possible to use visual imagery together with arithmetical concepts to reach a general theorem in a reliable way.
Keywords: arithmetic, visualizing, theorems, triangular numbers, square numbers, particularity objection, unintended exclusions