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Methods of mathematical struggle

  • Author(s): Smith, Michael Arthur
  • Smith, Michael Arthur
  • et al.
Abstract

Mathematicians frequently report feeling an intense kind of internal effort when doing their research. There's some reason to believe that this experience of struggle is integral to developing skill and familiarity with novel mathematical ways of thinking. Yet surprisingly little is known about the structure of this experience as mathematicians know it in their research, in part because of the scarcity of studies examining mathematicians in the midst of working on problems that are novel to them. In order to help contribute to our understanding of this domain, I examine the practices of three pairs of mathematicians working together on some problem from their research. Using a framework of embodied cognition to enact a phenomenological analysis, I note three ways in which we can see mathematicians structuring their experiences of struggle: proximal inhibition, invoking the continuum, and the use of transformation mappings. I propose that these three phenomenological constructs combine to offer us insight into the nature of mathematical practice and of mathematical objects as they are experienced

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