Mathematicians’ Assessments of the Explanatory Value of Proofs

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Axiomathes 31 (5):575-599 (2021)
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Abstract

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 literature regarding the explanatoriness of certain types of proofs.

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10.1007/s10516-021-09545-8

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original Inglis, Matthew; Rittberg, Colin; Evans, Tanya; Mejía Ramos, Juan Pablo (2021) "Mathematicians’ Assessments of the Explanatory Value of Proofs". Global Philosophy 31(5):575-599

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Citations of this work

Using Large Language Models to Study Mathematical Practice.William D'Alessandro - forthcoming - In Deborah Kant, José Antonio Pérez-Escobar, Sarikaya Deniz & Mira Sarikaya, Mathematicians at Work: Empirically Informed Philosophy of Mathematics. Springer (Synthese Library).
What mathematical explanation need not be.Elijah Chudnoff & Silvia De Toffoli - 2025 - Journal of Mathematical Behavior 79 (101255):1-12.

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References found in this work

Explanatory unification.Philip Kitcher - 1981 - Philosophy of Science 48 (4):507-531.
An introduction to the philosophy of mathematics.Mark Colyvan - 2012 - Cambridge: Cambridge University Press.
Mathematical explanation.Mark Steiner - 1978 - Philosophical Studies 34 (2):135 - 151.
The explanatory power of phase spaces.Aidan Lyon & Mark Colyvan - 2008 - Philosophia Mathematica 16 (2):227-243.

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