•  162
    The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the pra…Read more
  •  154
    An Inquiry into the Practice of Proving in Low-Dimensional Topology
    In Gabriele Lolli, Giorgio Venturi & Marco Panza (eds.), From Logic to Practice, Springer International Publishing. pp. 315-116. 2015.
    The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three these…Read more
  •  265
    ‘Chasing’ the diagram—the use of visualizations in algebraic reasoning
    Review of Symbolic Logic 10 (1): 158-186. 2017.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It wi…Read more
  •  207
    Forms and Roles of Diagrams in Knot Theory
    Erkenntnis 79 (4): 829-842. 2014.
    The aim of this article is to explain why knot diagrams are an effective notation in topology. Their cognitive features and epistemic roles will be assessed. First, it will be argued that different interpretations of a figure give rise to different diagrams and as a consequence various levels of representation for knots will be identified. Second, it will be shown that knot diagrams are dynamic by pointing at the moves which are commonly applied to them. For this reason, experts must develop a s…Read more