My research focuses mainly on visualization in mathematics. Visual representations of various kinds are ubiquitous in pure and applied mathematics, in the natural and social sciences, as well as in many other human activities. In the literature, these representations have been commonly labeled ‘visualizations’. Broadly speaking, they can be considered as ‘externalizations’ of thought akin to linguistic or semiotic systems. Unlike the latter, however, the ‘grammar’ or conditions for the proper use of such scaffolding structures has hardly been investigated, and the relations between these ‘extensions’ of the mind and our capacities such as vision, agency or reasoning remain largely unexplored. In my research, I will propose a new way of identifying and interpreting core specific cognitive and epistemic aspects pertaining to a particular class of visualizations: mathematical diagrams.
More specifically, my research interests focus on the epistemic and cognitive roles of written notations in mathematics. Having been trained in mathematics I have spent several years analyzing the role of diagrams and visual representations in distinct fields of contemporary mathematics, ranging from topology to homological algebra. My current research aim is to assess the criteria underlying the effectiveness of different notations and diagram types in promoting mathematical inferences. I claim that, in order to give a faithful account of the epistemic role of diagrams, it is necessary to understand them as dynamic reasoning tools and not merely as static representations summarizing propositional content. This claim informs my on-going doctoral dissertation: “Reasoning with Diagrams: the Case of Mathematics”. Since different diagrams support different kinds of operations and various degrees of expressiveness and transparency, I consider several case studies of a heterogeneous nature in order to appreciate the specificity of distinct mathematical practices involving diagrams.