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Mathematicians writing for mathematicians

  • Line Edslev AndersenEmail author
  • Mikkel Willum Johansen
  • Henrik Kragh Sørensen
S.I.: Enabling Mathematical Cultures


We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised Adam’s very detailed first draft. At the beginning of this collaboration, Adam was very knowledgeable about the subject of the paper and had good presentational skills but, as a new PhD student, did not yet have experience writing research papers for mathematicians. Thus, one main purpose of revising the paper was to make it take into account the intended audience. For this reason, the changes made to the initial draft and the authors’ purpose in making them provide a window for viewing how mathematicians write for mathematicians. We examined how their paper attracts the interest of the reader and prepares their proofs for validation by the reader. Among other findings, we found that their paper prepares the proofs for two types of validation that the reader can easily switch between.


Mathematical publication Mathematical audience Mathematical argument The nature of proof Contextualization 



We are deeply indebted to Adam and Thomas for letting us into their space of collaboration and supervision. We have presented our research in local groups and at the Oxford conference, and we are very grateful for the feedback and discussion, we have received, in particular from Alan Bundy and from colleagues. We are also very grateful for the challenging and constructive feedback we received from two anonymous referees. Part of the research for this paper was conducted while the first author was a postdoctoral researcher at the Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Brussels, Belgium. At Aarhus University, she is supported by K. Brad Wray’s Grant, AUFF-E-2017-FLS-7-3.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Centre for Science StudiesAarhus UniversityAarhus CDenmark
  2. 2.Section for History and Philosophy of Science, Department of Science EducationUniversity of CopenhagenCopenhagen KDenmark

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