Mathematical Problem Choice and the Contact of Minds

  • Zoe AshtonEmail author
Conference paper
Part of the Proceedings of the Canadian Society for History and Philosophy of Mathematics/ Société canadienne d’histoire et de philosophie des mathématiques book series (PCSHPM)


Testimonial accounts of mathematical problem choice typically rely on intrinsic constraints. They focus on the worth of the problem and feelings of beauty. These are often developed as both descriptive and normative constraints on problem choice. In this paper, I aim to add an extrinsic constraint of no less importance: the assurance of contact of minds with a desired audience. A number of elements for the relationship between mathematician and his audience make up this contact. This constraint stems from the mathematician’s role as an arguer, as one of the pre-requisites to argumentation is contact of minds. I examine two exceptional cases which fail to be explained by intrinsic constraints on motivation and posit how this contact could influence usual cases. While not the only constraint or drive in problem choice, establishing contact of minds plays an important role worth further examination.



I am very grateful to Andrew Aberdein, Ian Dove, Christopher Tindale, Nic Fillion, and two anonymous reviewers for comments on earlier drafts. I have also benefited from comments from members of the audience at both SFU and the 2017 CSHPM meeting.


  1. 1.
    Aberdein A, Dove I (2009) Mathematical argumentation. Found Sci 14Google Scholar
  2. 2.
    Aberdein A, Dove I (2013) The argument of mathematics. Springer, DordrechtCrossRefGoogle Scholar
  3. 3.
    Fallis D (2003) Intentional gaps in mathematical proofs. Synthese 134:45–69MathSciNetCrossRefGoogle Scholar
  4. 4.
    Franklin J (1987) Non-deductive logic in mathematics. Br J Philos Sci 38(1):1–18MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hadamard J (1945) An essay on the psychology of invention in the mathematical field. Princeton University Press, PrincetonzbMATHGoogle Scholar
  6. 6.
    Hardy GH (1940) A mathematician’s apology. Cambridge University Press, CambridgezbMATHGoogle Scholar
  7. 7.
    Lakatos I (1976) Proofs and refutations: the logic of mathematical discovery. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  8. 8.
    Nasar S (1998) A beautiful mind. Simon & Schuster, New YorkzbMATHGoogle Scholar
  9. 9.
    Perelman C, Olbrechts-Tyteca L (1969) The new rhetoric: a treatise on argumentation. University of Notre Dame Press, Notre DameGoogle Scholar
  10. 10.
    Sinclair N (2004) The roles of the aesthetic in mathematical inquiry. Math Think Learn 6(3): 261–284MathSciNetCrossRefGoogle Scholar
  11. 11.
    Thurston W (1994) On proof and progress in mathematics. Bull Am Math Soc 30:161–171MathSciNetCrossRefGoogle Scholar
  12. 12.
    Ziman JM (1987) The problem of “problem choice.” Minerva 25(1): 92–106CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Simon Fraser UniversityBurnabyCanada

Personalised recommendations