Situating Mathematical Communication: the Settings, Interactions and Material Practices of Contemporary Mathematical Research
This thesis is an artist’s communicative ethnography of mathematics, using multiple methods and outputs to put forward a rich picture of mathematics as inextricably entwined with the minds and materials involved in its development. In this research I take an ethnographic position and approach mathematics as an artist explorer, taking excerpts from recordings of everyday mathematical work and engaging in a process of reflective sense-making with the material, carried out with person, medium and place in mind. The discussion proceeds through a blend of written analysis informed by linguistic pragmatics and the situated cognition paradigm, and creative practice experiments that enact and test the core ideas proposed. A particular goal of the research is to examine the role played by mathematical writing in the variety of different material and social situations that make up mathematical work.
The key claim made is that while mathematics is known for abstraction and pure ideas, and often seems to exist somewhat apart from messy human reality, its practitioners reach these sophisticated cognitive heights through a variety of heavily situated, interactive practices that are not so separate from the improvised, social world of everyday communication. A key perspective on communication is relevance theory, as put forward by Dan Sperber and Deirdre Wilson, which emphasises the inferences that communicators make about one another’s minds; just such inferences are seen coming into play in essential ways throughout mathematical communication, which demonstrates that interpersonal interaction has an important role to play in the achievement of on-the-ground mathematical understanding. In addition the situated position on cognition taken by researchers such as Andy Clark and Edwin Hutchins, recognising the part that external resources play in cognition, allows us to understand mathematical writing as an important component in a collective cognitive system. Heavy use is made in mathematics of mark-making practices that are richly embedded in discourse in such a way as to extend the cognitive possibilities open to practitioners, and it is this that makes such incredibly complex ideas tractable. As such, this highly refined interaction between person and representation defines mathematics in an important way.
This thesis is a portrayal of mathematics as built up from interactions between persons and stabilised representations, and so situated and interactive in an essential way. It is also an application of relevance theory in such a way as to test the boundaries both of the theory and of what should be called communication. In its design, it proposes a method of doing artistic research that blends readily with other disciplines and is truly ethnographic while staying true to properly artistic aims.