Ugly, Literally

Abstract

In this chapter computer-assisted proofs are discussed. This discussion allows the introduction of multiple issues. The perceived ugliness of such proofs is the main subject of analysis; this further serves to highlight some limitations of the idea of the aesthetic induction. We conclude that an account of beauty based merely on the passive contemplation of properties of objects is insufficient to account for mathematical items that involve the active use of our attention. Special emphasis is placed on the importance of mental contents and mental activities in mathematical beauty; the crucial notion of intentional object is thus introduced.