The study of the historiographies by Paul Karlson, Konstantin Ríbnikov, Howard Eves and Bento de Jesus Caraça: different ways of looking at and conceiving the concept of function

Abstract: This article aims to present some of the studies that have been done on the historiographies written by Paul Karlson, Konstantin Ríbnikov, Howard Eves and Bento de Jesus Caraça. The ways of looking at and conceiving the concept of function by those authors is underscored. These studies are part of theoretical research, characterized as documentary and qualitative. They consider that the historiographical aspects of the History of Mathematics describe the logic of infinite historical facts that occurred in diverse contexts, at certain times and spaces, which are systematized, from time to time. It is assumed that if the historiographies of Mathematics address the history of the knowledge of mathematical concepts, while studying them, especially those who teach mathematics can delineate some conceptual links (internal and external) that make up the concepts. In the case of the concept of function, the following are the nexuses: irregular and regular movements, interdependence, variation, field of variation, relations and representations.