•  80
    The literature on mathematical explanation contains numerous examples of explanatory, and not so explanatory proofs. In this paper we report results of an empirical study aimed at investigating mathematicians’ notion of explanatoriness, and its relationship to accounts of mathematical explanation. Using a Comparative Judgement approach, we asked 38 mathematicians to assess the explanatory value of several proofs of the same proposition. We found an extremely high level of agreement among mathema…Read more
  •  888
    Using corpus linguistics to investigate mathematical explanation
    with Lara Alcock, Kristen Lew, Paolo Rago, Chris Sangwin, and Matthew Inglis
    In Eugen Fischer & Mark Curtis (eds.), Methodological Advances in Experimental Philosophy, Bloomsbury Press. 2019.
    In this chapter we use methods of corpus linguistics to investigate the ways in which mathematicians describe their work as explanatory in their research papers. We analyse use of the words explain/explanation (and various related words and expressions) in a large corpus of texts containing research papers in mathematics and in physical sciences, comparing this with their use in corpora of general, day-to-day English. We find that although mathematicians do use this family of words, such use is …Read more
  •  72
    Functional explanation in mathematics
    Synthese 198 (26): 6369-6392. 2019.
    Mathematical explanations are poorly understood. Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld’s suggestion that explanations are those sorts of things that generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all de…Read more
  •  84
    On the persuasiveness of visual arguments in mathematics
    with Matthew Inglis and Juan Pablo Mejía-Ramos
    Foundations of Science 14 (1-2): 97-110. 2009.
    Two experiments are reported which investigate the factors that influence how persuaded mathematicians are by visual arguments. We demonstrate that if a visual argument is accompanied by a passage of text which describes the image, both research-active mathematicians and successful undergraduate mathematics students perceive it to be significantly more persuasive than if no text is given. We suggest that mathematicians’ epistemological concerns about supporting a claim using visual images are le…Read more
  •  18
    The issue of what constitutes a valid logical inference is a difficult question. At a minimum, we believe a permissible step in a proof must provide the reader with rational grounds to believe that the new step is a logically necessary consequence of previous assertions. However, this begs the question of what constitutes these rational grounds. Formalist accounts typically describe valid rules of inferences as those that can be found by applying one of the explicit rules of inference in the for…Read more