Three Remarks on Mathematical Perception

The paper discusses three themes – the dependency of mathematical knowledge and truth on proof; the claim that sense-perception cannot be of mathematical objects; and the robustness of mathematical concepts – and uses them as a platform to examine the notion of mathematical perception. The three themes are developed in relation to the works of Rota, Tragesser, and Hauser, respectively. I argue that, while mathematical and geometrical concepts cannot be derived from pictures (actual or imagined) by a limit process or by abstraction, they are nonetheless seen in them, much in the way that internal states, such as anger, can be seen by looking at a person’s facial expression.