Discussions of Part I Chapters

  • Luc Trouche
  • Jonathan M. Borwein
  • John Monaghan
Part of the Mathematics Education Library book series (MELI, volume 110)


This chapter is an opportunity for one of the authors of this book to question the other two authors in the light of issues raised in Chaps.  2 5. It constitutes both a follow-up to discussions between authors which occurred over the writing process, and emergent issues—new discussions once the book was almost complete. Some fundamental issues are addressed, about the birth of mathematics (and its deep links with the birth of writing), the relationships between mathematics and other sciences, the interactions between conjecture and proof, and the role of visualisation and of gestures. The text is kept short in order to provoke the readers to reflect on these issues rather than for the authors to ‘provide answers’.


Mathematical Object Steam Engine Dynamic Geometry Software Archaic Period Computer Science Teaching 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Luc Trouche
    • 1
  • Jonathan M. Borwein
    • 2
  • John Monaghan
    • 3
  1. 1.Institut Français de l’EducationEcole Normale Supérieure de LyonLyonFrance
  2. 2.Centre for Computer Assisted Research Mathematics and its ApplicationsSchool of Mathematical and Physical Sciences, University of NewcastleNewcastleAustralia
  3. 3.Department of Mathematical SciencesUniversity of AgderKristiansandNorway

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