
162Envisioning Transformations – The Practice of TopologyIn Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 20122014, Birkhäuser. pp. 2550. 2016.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

154An Inquiry into the Practice of Proving in LowDimensional TopologyIn Gabriele Lolli, Giorgio Venturi & Marco Panza (eds.), From Logic to Practice, Springer International Publishing. pp. 315116. 2015.The aim of this article is to investigate speciﬁc aspects connected with visualization in the practice of a mathematical subﬁeld: lowdimensional 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 lowdimensional topology, justiﬁcations can be based on sequences of pictures. Three these…Read more

265‘Chasing’ the diagram—the use of visualizations in algebraic reasoningReview of Symbolic Logic 10 (1): 158186. 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

207Forms and Roles of Diagrams in Knot TheoryErkenntnis 79 (4): 829842. 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
Technische Universität Berlin
PhD, 2013
Princeton, New Jersey, United States of America
Areas of Specialization
Philosophy of Mathematics 
Areas of Interest
Epistemology 
General Philosophy of Science 
Philosophy of Literature 
PhilPapers Editorships
Visualization in Mathematics 
Mathematical Practice 