Mathematics, relevance theory and the situated cognition paradigm

Abstract

Abstract Mathematics is a highly specialised arena of human endeavour, one in which complex notations are invented and are subjected to complex and involved manipulations in the course of everyday work. What part do these writing practices play in mathematical communication, and how can we understand their use in the mathematical world in relation to theories of communication and cognition? To answer this, I examine in detail an excerpt from a research meeting in which communicative board-writing practices can be observed, and attempt to explain the observed exchanges with reference to relevance theory (a cognitivist theory of pragmatics), in combination with the situated cognition paradigm. Successful communication in the excerpt appears well described by the notion of metacognitive acquaintance, as described in Sperber & Wilson (2015), especially when a situated view of cognition is adopted. Though this example is taken from a relatively informal face-to-face communicative situation, characteristics of such situations extend even into formal written mathematics, since even the technical terminology developed in the course of the meeting includes details that may provide readers with a kind of access to the mathematicians’ cognitive processes.