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Circles Disturbed: The Interplay of Mathematics and Narrative

by Apostolos Doxiadis and Barry Mazur Princeton University Press
Pub Date:
03/2012
ISBN:
9780691149042
Format:
Hbk 552 pages
Price:
AU$133.00 NZ$138.26
Product Status: In Stock Now
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Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier--'Don't disturb my circles'--words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds--stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of 'myths of origins' in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more. In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.


Introduction vii

Chapter 1: From Voyagers to Martyrs: Toward a Storied History of Mathematics 1

By AMIR ALEXANDER

Chapter 2 Structure of Crystal, Bucket of Dust 52

By PETER GALISON

Chapter 3: Deductive Narrative and the Epistemological Function of Belief in Mathematics: On Bombelli and Imaginary Numbers 79

By FEDERICA LANAVE

Chapater 4: Hilbert on Theology and Its Discontents: The Origin Myth of Modern Mathematics 105

By COLIN MCLARTY

Chapter 5: Do Androids Prove Theorems in Their Sleep? 130

By MICHAEL HARRIS

Chapter 6: Visions, Dreams, and Mathematics 183

By BARRY MAZUR

Chapter 7: Vividness in Mathematics and Narrative 211

By TIMOTHY GOWERS

Chapter 8: Mathematics and Narrative: Why Are Stories and Proofs Interesting? 232

By BERNARD TEISSIER

Chapter 9: Narrative and the Rationality of Mathematical Practice 244

By DAVID CORFIELD

Chapter 10: A Streetcar Named (among Other Things) Proof: From Storytelling to Geometry, via Poetry and Rhetoric 281

By APOSTOLOS DOXIADIS

Chapter 11: Mathematics and Narrative: An Aristotelian Perspective 389

By G .E .R . LLOYD

Chapter 12: Adventures of the Diagonal: Non-Euclidean Mathematics and Narrative 407

By ARADY PLOTNITSKY

Chapter 13: Formal Models in Narrative Analysis 447

By DAVID HERMAN

Chapter 14: Mathematics and Narrative: A Narratological Perspective 481

By URI MARGOL N

Chapter 15: Tales of Contingency, Contingencies of Telling: Toward an Algorithm of Narrative Subjectivity 508

By JAN CHRISTOPH MEISTER

Contributors 541

Index 545

''Circles Disturbed offers a range of possibilities for how narrative can function in mathematics and how narratives themselves show signs of a mathematical structure. An intelligent, exploratory collection of writings by a distinguished group of contributors.''--Theodore Porter, University of California, Los Angeles

''This collection is a pioneering effort to trace the hidden connections between mathematics and narrative. It succeeds magnificently, and represents a very significant contribution that will appeal to the professional mathematician as well as the general educated reader. The articles are written by top authorities in their fields.''--Doron Zeilberger, Rutgers University

''The idea of a volume devoted to mathematics and narrative is a good one. The strength of the present volume is the breadth of its outlook, and I would imagine a fairly diverse readership from a wide variety of perspectives.''--Robert Osserman, professor emeritus, Stanford University
Apostolos Doxiadis is a writer whose books include Uncle Petros and Goldbach's Conjecture and Logicomix. Barry Mazur is the Gerhard Gade University Professor in the Department of Mathematics at Harvard University. His books include Imagining Numbers and Arithmetic Moduli of Elliptic Curves (Princeton).