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Using corpus linguistics to investigate mathematical explanation

In Eugen Fischer & Mark Curtis (eds.), Methodological Advances in Experimental Philosophy. London: Bloomsbury Academic. pp. 239–263 (2019)

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  1. Functional Explanation in Mathematics.Matthew Inglis & Juan Pablo Mejía-Ramos - 2019 - Synthese 198 (Suppl 26):6369-6392.
    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 derivable consequences of Wilkenfeld’s ‘functional explanation’ proposal. We therefore argue that (...)
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  • Mathematicians’ Assessments of the Explanatory Value of Proofs.Juan Pablo Mejía Ramos, Tanya Evans, Colin Rittberg & Matthew Inglis - 2021 - Axiomathes 31 (5):575-599.
    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 mathematicians, and some inconsistencies between their assessments and claims in the (...)
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  • Using Crowdsourced Mathematics to Understand Mathematical Practice.Alison Pease, Ursula Martin, Fenner Stanley Tanswell & Andrew Aberdein - 2020 - ZDM 52 (6):1087-1098.
    Records of online collaborative mathematical activity provide us with a novel, rich, searchable, accessible and sizeable source of data for empirical investigations into mathematical practice. In this paper we discuss how the resources of crowdsourced mathematics can be used to help formulate and answer questions about mathematical practice, and what their limitations might be. We describe quantitative approaches to studying crowdsourced mathematics, reviewing work from cognitive history (comparing individual and collaborative proofs); social psychology (on the prospects for a measure of (...)
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