This article discusses the concepts of "key ideas" and "memorability" and how they relate to the metric "width of a proof" put forward by the Fields medalist Timothy Gowers (2007) in a recent essay entitled "Mathematics, memory and mental arithmetic". The paper looks at the meaning of these concepts and attempts to show whether and how they are congruent with other aspects of proof discussed in literature on the teaching of proof and proving. It also explores how the insights behind "width of a proof" and "memorability" might in themselves mesh with various teaching perspectives.