The materiality of mathematics: Presenting mathematics at the blackboard

Abstract

This article has been accepted for publication in the journal, British Journal of Sociology [Wiley © London School of Economics and Political Science] and the definitive version is available at: http://dx.doi.org/ 10.1111/1468-4446.12037Sociology has been accused of neglecting the importance of material things in\ud human life and the material aspects of social practices. Efforts to correct this have\ud recently been made, with a growing concern to demonstrate the materiality of\ud social organization, not least through attention to objects and the body.As a result,\ud there have been a plethora of studies reporting the social construction and effects\ud of a variety of material objects as well as studies that have explored the material\ud dimensions of a diversity of practices. In different ways these studies have questioned\ud the Cartesian dualism of a strict separation of ‘mind’ and ‘body’. However,\ud it could be argued that the idea of the mind as immaterial has not been entirely\ud banished and lingers when it comes to discussing abstract thinking and reasoning.\ud The aim of this article is to extend the material turn to abstract thought, using\ud mathematics as a paradigmatic example.\ud This paper explores how writing mathematics (on paper, blackboards, or even in\ud the air) is indispensable for doing and thinking mathematics.The paper is based on\ud video recordings of lectures in formal logic and investigates how mathematics is\ud presented at the blackboard. The paper discusses the iconic character of blackboards\ud in mathematics and describes in detail a number of inscription practices\ud of presenting mathematics at the blackboard (such as the use of lines and boxes,\ud the designation of particular regions for specific mathematical purposes, as well\ud as creating an ‘architecture’ visualizing the overall structure of the proof). The\ud paper argues that doing mathematics really is ‘thinking with eyes and hands’\ud (Latour 1986). Thinking in mathematics is inextricably interwoven with writing\ud mathematics