Chalk: Materials and concepts in mathematics research

This chapter devotes close empirical attention to the social and material achievement of proofs, theorems, and other mathematical constructions. Mathematics is often treated as the most abstract and idealized of human practices, so that mathematicians’ words, gestures, handwriting, and chalkboard marking appear to be merely incidental and secondary ways of expressing and conveying mathematical truths. In contrast to that view, the chapter argues that mathematical concepts do not speak for themselves, and that mundane communicative practices and tools provide carefully circumscribed surrogates for idealized mathematical phenomena. Though blackboards are primarily used for teaching and seminars, their material, visual, and narrative features extend across all areas of mathematics pedagogy and research. These features, in many ways analogous to inscriptions and demonstrations in the natural science, also permit an account of the distinctive uses and meanings of formal representations in the mathematical sciences.