•  80
    Developments in Research on Mathematical Practice and Cognition
    with Markus Guhe and Alan Smaill
    Topics in Cognitive Science 5 (2): 224-230. 2013.
    We describe recent developments in research on mathematical practice and cognition and outline the nine contributions in this special issue of topiCS. We divide these contributions into those that address (a) mathematical reasoning: patterns, levels, and evaluation; (b) mathematical concepts: evolution and meaning; and (c) the number concept: representation and processing
  •  55
    Bridging the gap between argumentation theory and the philosophy of mathematics
    with Alan Smaill, Simon Colton, and John Lee
    Foundations of Science 14 (1-2): 111-135. 2009.
    We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Eu…Read more
  •  37
    The Argument Web: an Online Ecosystem of Tools, Systems and Services for Argumentation
    with Mark Snaith, John Lawrence, Barbara Konat, Mathilde Janier, Rory Duthie, Katarzyna Budzynska, and Chris Reed
    Philosophy and Technology 30 (2): 137-160. 2017.
    The Argument Web is maturing as both a platform built upon a synthesis of many contemporary theories of argumentation in philosophy and also as an ecosystem in which various applications and application components are contributed by different research groups around the world. It already hosts the largest publicly accessible corpora of argumentation and has the largest number of interoperable and cross compatible tools for the analysis, navigation and evaluation of arguments across a broad range …Read more
  •  29
    Explanation in mathematical conversations: An empirical investigation
    with Andrew Aberdein and Ursula Martin
    Philosophical Transactions of the Royal Society A 377. 2019.
    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, th…Read more
  •  18
    Mathematical reasoning with higher-order anti-unifcation
    with Markus Guhe, Alan Smaill, Martin Schmidt, Helmar Gust, Kai-Uwe Kühnberger, and Ulf Krumnack
    In S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society, Cognitive Science Society. 2010.
  •  9
    Abstract or not abstract? Well, it depends…
    with Alan Smaill and Markus Guhe
    Behavioral and Brain Sciences 32 (3-4): 345-346. 2009.
    The target article by Cohen Kadosh & Walsh (CK&W) raises questions as to the precise nature of the notion of abstractness that is intended. We note that there are various uses of the term, and also more generally in mathematics, and suggest that abstractness is not an all-or-nothing property as the authors suggest. An alternative possibility raised by the analysis of numerical representation into automatic and intentional codes is suggested
  •  9
    A cognitive model of discovering commutativity
    with Markus Guhe and Alan Smaill
    In N. A. Taatgen & H. van Rijn (eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society, . pp. 727--732. 2009.
  •  6
    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 (compar…Read more
  •  3
    Ethical challenges in argumentation and dialogue in a healthcare context
    with Mark Snaith, Rasmus Øjvind Nielsen, and Sita Ramchandra Kotnis
    Argument and Computation 1-16. forthcoming.
    As the average age of the population increases, so too do the number of people living with chronic illnesses. With limited resources available, the development of dialogue-based e-health systems that provide justified general health advice offers a cost-effective solution to the management of chronic conditions. It is however imperative that such systems are responsible in their approach. We present in this paper two main challenges for the deployment of e-health systems, that have a particular …Read more
  • Modelling serendipity in a computational context
    with Joseph Corneli, Simon Colton, Anna Jordanous, and Christian Guckelsberger
  • Lakatos-style collaborative mathematics through dialectical, structured and abstract argumentation
    with John Lawrence, Katarzyna Budzynska, Joseph Corneli, and Chris Reed
    Artificial Intelligence 246 181-219. 2017.
  • A Computational Model Of Lakatos-style Reasoning
    Philosophy of Mathematics Education Journal 27. 2013.
  • Enabling mathematical cultures: introduction
    with Benedikt Löwe and Ursula Martin
    Synthese 1-7. forthcoming.