Difficulties with Symbolism: Synonymy and Homonymy

Abstract

We know that the confusion between meaning and sign (in French: signifié/ significant) is the root of a great number of mistakes in mathematics. Particularly, instead of making easier the approach to the mathematical concept represented, the sight of the design often produces a disturbance to understanding; it leads to mistaking the drawing for the presented idea, as idolatrous people do. I will demonstrate — by presenting many genuine examples which I have met in mathematical classrooms at every level — the mathematical roles of synonymy and homonymy.