Aesthetic Considerations in Mathematics

Drawing on some of the principles of humanistic mathematics first outlined by Alvin White, this paper seeks to examine the way in which value judgments are implicated in the growth of the mathematics discipline. After a short overview of some of the roles ascribed to the mathematical aesthetic historically, I turn to more contemporary positioning of the aesthetic in order to develop a framework that offers insight into the particular values, assumptions and desires that constrain what is done in mathematics, how it is done and why. My goal, at least in part, is to bring together under one umbrella some of the recent work that is being done in the cultural ethnography and cognitive history of mathematics and, in so doing, provide a stronger rationale for the importance and relevance of aesthetic considerations in the history and philosophy of mathematics. Finally, I use this framework to promote the idea of a mathematics critic, who could do for mathematics what art critics do for the arts, namely, to not only evaluate and explain art, but to work toward establishing its accessibility and credibility. In the edited collection Essays in Humanistic Mathematics, Alvin M. White [58] describes the humanistic dimension of mathematics as including both: “an appreciation of the role of intuition in understanding and creating concepts” and “An understanding of the value judgments implied in the growth of any discipline [...] what is investigated, how it is investigated, or why it is investigated” (vii). For me, both these aspects relate strongly to the mathematical aesthetic in two ways. First, in writing about the importance of the value judgments made in the discipline, White points to the axiological dimension of the philosophy of mathematics, which include both aesthetic and ethical questions of what is beautiful or ugly, good or bad, and why. Second, in pointing to the role of intuition in understanding and creating concepts, I interpret White as being concerned with the informal and nonpropositional ways in which mathematical ideas derive their meaning, which Journal of Humanistic Mathematics Vol 1, No 1, January 2011