Aesthetic Considerations in Mathematics

Abstract

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 con-strain 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.