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Mathematicians’ Assessments of the Explanatory Value of Proofs

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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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Notes

  1. Delarivière et al. (2017) clarified that ontic accounts do not necessarily deny a possible relationship between explanation and understanding; ontic accounts simply do not use understanding as a defining criterion of the explanatory value of a proof (p. 312).

  2. Data and code are available at https://doi.org/10.17028/rd.lboro.12458486

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Acknowledgements

This work was iniated during Matthew Inglis’s visit to Auckland in 2019, which was funded by the University of Auckland’s Department of Mathematics. Colin Rittberg and Matthew Inglis are part-funded by Research England. We are grateful for this financial support. We thank Joachim Frans and two anonymous reviewers for helpful remarks.

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Authors and Affiliations

  1. Rutgers University, New Brunswick, NJ, US

    Juan Pablo Mejía Ramos

  2. University of Auckland, Auckland, New Zealand

    Tanya Evans

  3. Loughborough University, Loughborough, England

    Colin Rittberg & Matthew Inglis

  4. Vrije Universiteit Brussel, Brussels, Belgium

    Colin Rittberg

Authors
  1. Juan Pablo Mejía Ramos
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  2. Tanya Evans
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  3. Colin Rittberg
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  4. Matthew Inglis
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Correspondence to Juan Pablo Mejía Ramos.

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Appendix

Appendix

One-line

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Two-column

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Elementary

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Visual

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Contradiction

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Substitution

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Taylor series

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Experimental

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Mejía Ramos, J.P., Evans, T., Rittberg, C. et al. Mathematicians’ Assessments of the Explanatory Value of Proofs. Axiomathes 31, 575–599 (2021). https://doi.org/10.1007/s10516-021-09545-8

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