Discussions of Part I Chapters

Abstract

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'.