Vol. 22, No. 1
Dynamic construals, static formalisms: Evidence from co-speech gesture during mathematical proving
Department of Cognitive Science, UC San Diego
This paper presents results from ongoing research using co-speech gesture to investigate the nature of mathematical concepts. Traditional accounts of the content of mathematical concepts have focused on formal language and definitions. In analysis, key concepts such as continuity are defined by means of static existential and universal quantifiers ranging over static numbers. Recent evidence from Cognitive Science, however, suggests that mathematical concepts are construed through various mechanisms of everyday cognition — such as conceptual metaphor and fictive motion — which are at odds with static conceptions. We analyse the co-speech gesture produced by graduate students while collaborating on a proof in analysis. The results support the claim that many mathematical concepts, which formally make use of static entities and relations, are, cognitively, inherently dynamic.