The role of representations in mathematical reasoning

Abstract

This paper discusses the role of representations in mathematical proofs. It is proposed that representations enable us to break a proof down into manageable parts. We illustrate with an example from current mathematical practice how the value of an expression is found by gradually breaking it down into simpler parts. In addition I explain which role icons and indices play in this process. Icons ensure that there is likeness between the expression and the obtained results. Indices acting as sign-posts enable us to reinsert the results at the appropriate places.