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Acceptable gaps in mathematical proofs

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Abstract

Mathematicians often intentionally leave gaps in their proofs. Based on interviews with mathematicians about their refereeing practices, this paper examines the character of intentional gaps in published proofs. We observe that mathematicians’ refereeing practices limit the number of certain intentional gaps in published proofs. The results provide some new perspectives on the traditional philosophical questions of the nature of proof and of what grounds mathematical knowledge.

Keywords

Mathematical practice Gaps in proofs Peer review in mathematics The nature of proofs 
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Notes

Acknowledgements

Part of the research for this paper was conducted while I was a postdoc at the Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Brussels, Belgium. Two years ago, I had the pleasure of interviewing eight mathematicians about their refereeing practices. I thank them for their time and openness. The paper has benefited greatly from comments from Henrik Kragh Sørensen, Karen Francois, Mikkel Willum Johansen, and two anonymous referees. I also thank Henrik and Mikkel for their help in developing the interview questions. Earlier versions of the paper were presented at the 2016 Society for Philosophy of Science in Practice conference (Glassboro, New Jersey), the 2016 Novembertagung on the history and philosophy of mathematics (Sønderborg, Denmark), the workshop ‘Mathematical evidence and argument: Historical, philosophical, and educational perspectives’ (Bremen, Germany, 2017), the workshop ‘Group knowledge and mathematical collaboration’ workshop (Oxford, UK, 2017), and the 2017 Nordic Network for Philosophy of Science meeting (Copenhagen, Denmark). I would like to thank the audiences for useful comments.

Compliance with ethical standards

Conflict of interest

The author declares that she has no conflict of interest.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Centre for Science Studies, Department of MathematicsAarhus UniversityAarhus CDenmark

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