The Practices of Mathematicians: What do They Tell us About Coming to Know Mathematics?

Abstract

In 1997, an interview-based study of 70 research mathematicians was undertaken with a focus on how they ‘come to know’ mathematics, i.e. their epistemologies. In this paper, I discuss how these mathematicians understand their practices, locating them in the communities of which they claim membership, identifying the style which dominates their organisation of research and looking at their lived contradictions. I examine how they talk about ‘knowing’ mathematics, the metaphors on which they draw, the empiricist connections central to the work of the applied mathematicians and statisticians, and the importance of connectivities to the construction of their mathematical Big Picture. I compare the stories of these research mathematicians with practices in mathematics classrooms and conclude with an appeal for teachers to pay attention to the practices of research mathematicians and their implications for coming to know mathematics.