Mathematics and the Aesthetic

A majority of the chapters in this book first saw the light of day as talks at a conference organised and held at Queen’s University in Kingston, Ontario, Canada in April 2001. This small, invitational meeting, tellingly entitled Beauty and the Mathematical Beast, brought together a range of academics int- ested in and committed to exploring connections between mathematics and aesthetics. The enthusiastic response of participants at this gathering enco- aged the presenters to expand upon their initial contributions and persuaded the organisers to recruit further chapters in order to bring a greater balance to the whole. The timing of this event was not arbitrary. The preceding decade had seen a resurgence in serious writing dealing with deeper relations between mathematics (and science) and ‘the beautiful’. In many ways, we the editors of this volume found these contributions to the literature were revisiting and drawing on themes that had been prominent over two thousand five h- dred years ago, in certain writings of the Pythagoreans. While not intending to offer a historical reappraisal of these ancient thinkers here, we have none the less chosen to invoke this profound interweaving of the mathematical and the aesthetic to which this reputedly secretive philosophical sect was ext- sively attuned. This book is divided into three sections comprising three chapters each, each with its own short introduction discussing the particular chapters within.

The essays in this book explore the ancient affinity between the mathematical and the aesthetic, focusing on the fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine the ways in which the aesthetic is ever present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

This book includes the following essays:

• A Historical Gaze at the Mathematical Aesthetic, by Nathalie Sinclair and David Pimm

• Aesthetics for the Working Mathematician, by Jonathan M. Borwein

• Beauty and Truth in Mathematics, by Doris Schattschneider

• Experiencing Meanings in Geometry, by David W. Henderson and Daina Taimina

• The Aesthetic Sensibilities of Mathematicians, by Nathalie Sinclair

• The Meaning of Pattern, by Martin Schiralli

• Mathematics, Aesthetics and Being Human, by William Higginson

• Mechanism and Magic in the Psychology of Dynamic Geometry, by R. Nicholas Jackiw

• Drawing on the Image in Mathematics and Art, by David Pimm

• Sensible Objects, by Dick Tahta

• Aesthetics and the ‘Mathematical Mind’, by David Pimm and Nathalie Sinclair