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Irina Starikova
Bristol University
  1. Why Do Mathematicians Need Different Ways of Presenting Mathematical Objects? The Case of Cayley Graphs.Irina Starikova - 2010 - Topoi 29 (1):41-51.
    This paper investigates the role of pictures in mathematics in the particular case of Cayley graphs—the graphic representations of groups. I shall argue that their principal function in that theory—to provide insight into the abstract structure of groups—is performed employing their visual aspect. I suggest that the application of a visual graph theory in the purely non-visual theory of groups resulted in a new effective approach in which pictures have an essential role. Cayley graphs were initially developed as exact mathematical (...)
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  2.  9
    From Practice to New Concepts: Geometric Properties of Groups.Irina Starikova - 2012 - Philosophia Scientae 16:129-151.
    The paper aims to show how mathematical practice, in particular with visual representations, can lead to new mathematical results. The argument is based on a case study from a relatively recent and promising mathematical subject—geometric group theory. The paper discusses how the representation of groups by Cayley graphs made possible to discover new geometric properties of groups.
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  3.  12
    Thought Experiments in Mathematics.Irina Starikova & Marcus Giaquinto - unknown
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  4. Mathematical Knowledge: Intuition, Visualization, and Understanding.Leon Horsten & Irina Starikova - 2010 - Topoi 29 (1):1-2.
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  5.  11
    Aesthetic Preferences in Mathematics: A Case Study†.Irina Starikova - 2018 - Philosophia Mathematica 26 (2):161-183.
    Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to their visualisations? Using an example from graph theory, this paper argues that, in making aesthetic judgements, mathematicians may be responding to a combination of perceptual properties of visual representations and mathematical properties of abstract structures; the latter seem to carry greater weight. Mathematical beauty thus primarily involves mathematicians’ sensitivity to aesthetics of the abstract.
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  6.  44
    Picture-Proofs and Platonism.Irina Starikova - 2007 - Croatian Journal of Philosophy 7 (1):81-92.
    This paper concerns the role of intuitions in mathematics, where intuitions are meant in the Kantian sense, i.e. the “seeing” of mathematical ideas by means of pictures, diagrams, thought experiments, etc.. The main problem discussed here is whether Platonistic argumentation, according to which some pictures can be considered as proofs (or parts of proofs) of some mathematical facts, is convincing and consistent. As a starting point, I discuss James Robert Brown’s recent book Philosophy of Mathematics, in particular, his primarily examples (...)
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