AbstractMathematical images occur in lectures, books, notes and posters, and on the internet. We extend Kennedy's proposal for classifying these images. In doing so we distinguish three uses of images in mathematics: iconic images; incidental images; and integral images. An iconic image is one that so captures the essence of a concept or proof that it serves for a community of mathematicians as a motto or a meme for an area or a result. A system such as Euclid's can combine such apprehensions with other forms of logical inference and an image that is built into a system of exposition is called an integral image. An incidental image is an image used by a mathematician to reason with a particular concept. In addition to this thematic characterization, we also explore one concept, infinity, in some depth by comparing representations of the infinite by mathematicians and artists.