The BEST WRITING on MATHEMATICS 2011 Pitici.indb 1 8/20/2011 2:22:41 PM Pitici.indb 2 8/20/2011 2:22:42 PM The BEST WRITING on MATHEMATICS 2011 Mircea Pitici, Editor princeton university press princeton and oxford Pitici.indb 3 8/20/2011 2:22:43 PM Copyright © 2012 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu All Rights Reserved ISBN 978-0-691-15315-5 This book has been composed in Perpetua Std Printed on acid-free paper. ∞ Printed in the United States of America 1 3 5 7 9 10 8 6 4 2 Pitici.indb 4 8/20/2011 2:22:43 PM To my teacher, Ioan Candrea In memoriam Pitici.indb 5 8/20/2011 2:22:44 PM Pitici.indb 6 8/20/2011 2:22:44 PM Contents Foreword: Recreational Mathematics Freeman Dyson xi Introduction Mircea Pitici xvii What Is Mathematics For? Underwood Dudley 1 A Tisket, a Tasket, an Apollonian Gasket Dana Mackenzie 13 The Quest for God’s Number Rik van Grol 27 Meta-morphism: From Graduate Student to Networked Mathematician Andrew Schultz 35 One, Two, Many: Individuality and Collectivity in Mathematics Melvyn B. Nathanson 43 Reflections on the Decline of Mathematical Tables Martin Campbell-Kelly 51 Under-Represented Then Over-Represented: A Memoir of Jews in American Mathematics Reuben Hersh 55 Did Over-Reliance on Mathematical Models for Risk Assessment Create the Financial Crisis? David J. Hand 67 Pitici.indb 7 8/20/2011 2:22:45 PM viii Contents Fill in the Blanks: Using Math to Turn Lo-Res Datasets into Hi-Res Samples Jordan Ellenberg 75 The Great Principles of Computing Peter J. Denning 82 Computer Generation of Ribbed Sculptures James Hamlin and Carlo H. Séquin 93 Lorenz System Offers Manifold Possibilities for Art Barry A. Cipra 115 The Mathematical Side of M. C. Escher Doris Schattschneider 121 Celebrating Mathematics in Stone and Bronze Helaman Ferguson and Claire Ferguson 150 Mathematics Education: Theory, Practice, and Memories over 50 Years John Mason 169 Thinking and Comprehending in the Mathematics Classroom Douglas Fisher, Nancy Frey, and Heather Anderson 188 Teaching Research: Encouraging Discoveries Francis Edward Su 203 Reflections of an Accidental Theorist Alan H. Schoenfeld 219 The Conjoint Origin of Proof and Theoretical Physics Hans Niels Jahnke 236 What Makes Mathematics Mathematics? Ian Hacking 257 What Anti-realism in Philosophy of Mathematics Must Offer Feng Ye 286 Seeing Numbers Ivan M. Havel 312 Pitici.indb 8 8/20/2011 2:22:45 PM Contents ix Autism and Mathematical Talent Ioan James 330 How Much Math is Too Much Math? Chris J. Budd and Rob Eastaway 336 Hidden Dimensions Marianne Freiberger 347 Playing with Matches Erica Klarreich 356 Notable Texts 367 Contributors 371 Acknowledgments 379 Credits 381 Pitici.indb 9 8/20/2011 2:22:46 PM