Abstract: The notion of a formally stated equivalence relation is a somewhat recent development in the history of mathematics, with the term "equivalence relation" itself not appearing in print until the mid-twentieth century. Based on the findings of Asghari's historical phenomenology of equivalence, I propose a first-order conceptual analysis to account for productive approaches to considering equivalence relations from a global perspective (i.e., one that focuses on collections of equivalent elements), grounded in the ways that mathematicians historically reasoned about such contexts prior to the statement of a definition of equivalence relation, and detail my ongoing work to refine this conceptual analysis with empirical data from students.
Mathematics Seminars and Colloquia