I am working towards a PhD, funded by the TECHNE AHRC consortium, studying communication among research mathematicians using art practice research methods in combination with linguistic pragmatic analysis. The aim is to create an artist’s ethnography of the field, taking into account the indispensable roles played by interpersonal relationships and physical materials in the communication of cutting-edge mathematics. The documentation of my ongoing research is published online at infiltratemathematics.wordpress.com.
This research expands upon the framework used in my MRes research (which focused closely on knot theory diagramming) and uses a synthesis of concepts from art, mathematics and linguistic pragmatics in an ethnographic study of mathematics communication. Practitioners and laypersons alike tend to draw a divide between ‘mathematics’ as an ideal, and the everyday practices and processes that characterise its place in human lives. Ethnographies at the cutting edge of mathematics are very rare, but have remarkable light to shed on a discipline that is often seen as separate from human concerns. My intention for this research is to build up an ethnography of communication in mathematical research that not only considers and takes seriously these underdiscussed situated and material aspects but also itself operates across different modes, in recording, analysis and presentation. A question at the heart of this research is to what extent knowledge can be divorced from its settings and the persons involved in its production; this is a question very appropriate to ask of mathematical knowledge, as a very large and long-developed field of studies that is very often perceived as acultural.
Following the ideas of Grice, and work that has developed upon them, it would seem that perceived intentions are central to the understanding of deliberate communication; bringing such considerations into an analysis of communication in such a depersonalised field is a move likely to have exciting consequences (as evidenced by my previous MRes work). I augment a pragmatic, cognitivist approach to analysing communicative strategies from real-world observations with the attention to material settings, collaborative cognition, and multimodality found in situated cognition ethnographies such as that presented by Edwin Hutchins (2010). I am observing communicative events surrounding developing mathematical work as it progresses, drawing upon the field of linguistic pragmatics to produce a written analysis of the resources used and expectations coming into play in an act of communication. I use an art practice approach to record and explore data in a way that foregrounds materials and situations, photographing workplaces and experimenting with the materials and configurations that I observe through my sculptural practice.
 In my MRes thesis I presented a set of observations of knot theory diagramming practices showing how essential performance and gloss are to creating mutuality of understanding in diagram interpretation. The role of perceived intentions was particularly salient, showing that interpersonal understandings are important even in the understanding of formalised diagrams.