Research procedures to understand algebraic structures: A hermeneutic approach

Abstract

The authors question how hermetic texts in mathematics, history, and philosophy of mathematics, specifically those referring to abstract algebra, can be open to the understanding of researchers, teachers and students who are intentionally willing to understand them. This discussion suggests that the openness may happen through hermeneutic procedures. These procedures, in the wake of Gadamerian thinking, take the dialectic of the process of formulating the question and pursuing possible ways of answering it, going into the intricacies of the historicity of knowledge constitution based on the Husserlian perspective and the production of algebra itself, in order to explain a methodology of research. They advance by bringing a hermeneutic study on algebraic structures, explaining the research methodology that aims at the formation of the ideality of algebraic structures and their maturation in the living present as notions of algebraic structures, as objects of study and as subjects of algebra.