Uncertainty as a catalyst and condition for creativity: the case of mathematics

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Abstract

In this paper, the construct of ‘uncertainty’ in professional mathematics is investigated in relation to mathematical creativity. Specific focus is on ‘Big C’ research mathematicians’ conceptions of what uncertainty means and ways in which it influences their research. Based on the hypothesis that uncertainty is both a catalyst and a necessary condition for creativity, a qualitative research design was used to obtain and analyze data from a 4-year study involving 18 research mathematicians who were at the forefront of their research domains. Data analysis using analytic induction confirmed the hypothesis that uncertainty plays an important role as a catalyst of mathematical creativity. The emergent categories from qualitative analysis revealed a dialectic or tension between (1) logic versus heuristics (synthetic versus analytic), (2) learner-researcher and researcher-learner transition, (3) axiom tweaking versus constraints. The findings of the study indicate that textbooks, unexpected moments, risk taking, and a community of support play a crucial role and characterize the interplay of uncertainty with mathematical creativity. The schema for understanding the dialectics of uncertainty sheds new light on an hitherto unexplored aspect of mathematical creativity, namely, uncertainty, vital for the development of mathematicians as researchers in addition to the growth of their discipline.

Original languageEnglish
Pages (from-to)19-33
Number of pages15
JournalZDM - International Journal on Mathematics Education
Volume54
Issue number1
DOIs
StatePublished - Apr 2022

Keywords

  • Axioms
  • Big C—creativity
  • Dialectics of knowledge
  • Heuristics
  • Logic
  • Mathematical creativity
  • Mathematicians
  • Textbooks
  • Uncertainty

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