Citations of:
Explanation in mathematics: Proofs and practice
Philosophy Compass 14 (11):e12629 (2019)
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In this paper we argue that questions about which mathematical ideas mathematicians are exposed to and choose to pay attention to are epistemologically relevant and entangled with power dynamics and social justice concerns. There is a considerable body of literature that discusses the dissemination and uptake of ideas as social justice issues. We argue that these insights are also relevant for the epistemology of mathematics. We make this visible by a journalistic exploration of relevant cases and embed our insights into (...) |
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Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...) |
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The idea that there are some facts that call for explanation serves as an unexamined premise in influential arguments for the inexistence of moral or mathematical facts and for the existence of a god and of other universes. This book is the first to offer a comprehensive and critical treatment of this idea. It argues that calling for explanation is a sometimes-misleading figure of speech rather than a fundamental property of facts. |
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Opinionated state of the art paper on mathematical explanation. After a general introduction to the subject, the paper is divided into two parts. The first part is dedicated to intra-mathematical explanation and the second is dedicated to extra-mathematical explanation. Each of these parts begins to present a set of diverse problems regarding each type of explanation and, afterwards, it analyses relevant models of the literature. Regarding the intra-mathematical explanation, the models of deformable proofs, mathematical saliences and the demonstrative structure of (...) |
