The Effectiveness of Representations in Mathematics

This article focuses on particular ways in which visual representations contribute to the development of mathematical knowledge. I give examples of diagrammatic representations that enable one to observe new properties and cases where representations contribute to classi fi cation. I propose that fruitful representations in mathematics are iconic representations that involve conventional or symbolic elements, that is, iconic metaphors. In the last part of the article, I explain what these are and how they apply in the considered examples