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  1.  34
    Explanation in Mathematical Conversations: An Empirical Investigation.Alison Pease, Andrew Aberdein & Ursula Martin - 2019 - Philosophical Transactions of the Royal Society A 377.
    Analysis of online mathematics forums can help reveal how explanation is used by mathematicians; we contend that this use of explanation may help to provide an informal conceptualization of simplicity. We extracted six conjectures from recent philosophical work on the occurrence and characteristics of explanation in mathematics. We then tested these conjectures against a corpus derived from online mathematical discussions. To this end, we employed two techniques, one based on indicator terms, the other on a random sample of comments lacking (...)
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  2.  19
    Argumentation Theory for Mathematical Argument.Joseph Corneli, Ursula Martin, Dave Murray-Rust, Gabriela Rino Nesin & Alison Pease - 2019 - Argumentation 33 (2):173-214.
    To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. (...)
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  3.  1
    Enabling Mathematical Cultures: Introduction.Benedikt Löwe, Ursula Martin & Alison Pease - 2021 - Synthese 198 (Suppl 26):6225-6231.
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  4.  8
    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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  5. The Order Types of Termination Orderings on Monadic Terms, Strings and Monadic Terms, Strings and Multisets.Ursula Martin & Elizabeth Scott - 1997 - Journal of Symbolic Logic 62 (2):624-635.
    We consider total well-founded orderings on monadic terms satisfying the replacement and full invariance properties. We show that any such ordering on monadic terms in one variable and two unary function symbols must have order type $\omega, \omega^2$ or $\omega^\omega$. We show that a familiar construction gives rise to continuum many such orderings of order type $\omega$. We construct a new family of such orderings of order type $\omega^2$, and show that there are continuum many of these. We show that (...)
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  6.  14
    The Order Types of Termination Orderings on Monadic Terms, Strings and Multisets.Ursula Martin & Elizabeth Scott - 1997 - Journal of Symbolic Logic 62 (2):624-635.
    We consider total well-founded orderings on monadic terms satisfying the replacement and full invariance properties. We show that any such ordering on monadic terms in one variable and two unary function symbols must have order typeω,ω2orωω. We show that a familiar construction gives rise to continuum many such orderings of order typeω. We construct a new family of such orderings of order typeω2, and show that there are continuum many of these. We show that there are only four such orderings (...))
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