Mathematics and the Aesthetic (eBook)
XVI, 288 Seiten
Springer New York (Verlag)
978-0-387-38145-9 (ISBN)
This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on 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 ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.
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.
PREFACE 7
ACKNOWLEDGEMENTS 9
CONTENTS 11
NOTES ABOUT AUTHORS 12
A Historical Gaze at the Mathematical Aesthetic 15
Section A The Mathematician’s Art 32
Aesthetics for the Working Mathematician 34
Beauty and Truth in Mathematics 54
Experiencing Meanings in Geometry 71
Section B A Sense for Mathematics 97
The Aesthetic Sensibilities of Mathematicians 99
The Meaning of Pattern 117
Mathematics, Aesthetics and Being Human 138
Section C Mathematical Agency 155
Mechanism and Magic in the Psychology of Dynamic Geometry 157
Drawing on the Image in Mathematics and Art 172
Sensible Objects 203
Aesthetics and the ‘ Mathematical Mind’ 235
REFERENCES 267
INDEX OF NAMES 289
INDEX 292
Erscheint lt. Verlag | 28.12.2007 |
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Reihe/Serie | CMS Books in Mathematics |
Zusatzinfo | XVI, 288 p. 78 illus., 13 illus. in color. |
Verlagsort | New York |
Sprache | englisch |
Themenwelt | Kunst / Musik / Theater ► Allgemeines / Lexika |
Geisteswissenschaften ► Philosophie | |
Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika | |
Technik | |
Schlagworte | Geometry • Mathematica • Mathematics • Pattern |
ISBN-10 | 0-387-38145-7 / 0387381457 |
ISBN-13 | 978-0-387-38145-9 / 9780387381459 |
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