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The characteristics of mathematical creativity

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Abstract

Mathematical creativity ensures the growth of mathematics as a whole. However the source of this growth, the creativity of the mathematician is a relatively unexplored area in mathematics and mathematics education. In order to investigate how mathematicians create mathematics; a qualitative study involving five creative mathematicians was conducted. The mathematicians in this study verbally reflected on the thought processes involved in creating mathematics. Analytic induction was used to analyze the qualitative data in the interview transcripts and to verify the theory driven hypotheses. The results indicate that in general, the mathematicians’ creative process followed the four-stage Gestalt model of preparation–incubation–illumination–verification. It was found that social interaction, imagery, heuristics, intuition, and proof were the common characteristics of mathematical creativity. In addition contemporary models of creativity from psychology were reviewed and used to interpret the characteristics of mathematical creativity.

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Notes

  1. In all vignettes I = interviewer; A, B, C, D, E = mathematicians.

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Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, 59812, USA

    Bharath Sriraman

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  1. Bharath Sriraman
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Correspondence to Bharath Sriraman.

Additional information

Reprint of Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator. 14 (1), 19–34. Reprinted with permission from Mathematics Education Student Association at The University of Georgia. ©2004 Bharath Sriraman.

Appendix: Interview protocol

Appendix: Interview protocol

(The interview instrument was developed by modifying questions from questionnaires in L’Enseigement Mathematique (1902) and Muir (1988))

  1. 1.

    Describe your place of work and your role within it?

  2. 2.

    Are you free to choose the mathematical problems you tackle or are they determined by your work place?

  3. 3.

    Do you work and publish mainly as an individual or as part of a group?

  4. 4.

    Is supervision of Research a positive or negative factor in your work?

  5. 5.

    Do you structure your time for mathematics?

  6. 6.

    What are your favorite leisure activities apart from mathematics?

  7. 7.

    Do you recall any immediate family influences, teachers, colleagues or texts, of primary importance in your mathematical development?

  8. 8.

    In which areas were you initially self-educated? In which areas do you work now? If different, what have been the reasons for changing?

  9. 9.

    Do you strive to obtain a broad overview of mathematics, not of immediate relevance to your area of research?

  10. 10.

    Do you make a distinction between thought processes in learning and research?

  11. 11.

    When you are about to begin a new topic, do you prefer to assimilate what is known first or do you try your own approach?

  12. 12.

    Do you concentrate on one problem for a protracted period of time or on several problems at the same time?

  13. 13.

    Have your best ideas been the result of prolonged deliberate effort, or have they occurred when you were engaged in other unrelated tasks?

  14. 14.

    How do you form an intuition about the truth of a proposition?

  15. 15.

    Do computers play a role in your creative work (mathematical thinking)?

  16. 16.

    What types of mental imagery do you use when thinking about mathematical objects?

Questions regarding foundational and theological issues have been omitted in this protocol. The discussion resulting from these questions are reported in Sriraman, B. (2004). The influence of Platonism on mathematics research and theological beliefs. Theology and Science, 2 (1), 131–147.

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Sriraman, B. The characteristics of mathematical creativity. ZDM Mathematics Education 41, 13–27 (2009). https://doi.org/10.1007/s11858-008-0114-z

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