The Best Writing on Mathematics 2012

"Compiling a good anthology is no easy task, but here Mircea Pitici has succeeded in putting together a wonderful and varied bouquet of texts related to mathematics... I highly recommend this book to everyone with an interest in mathematics, whether they are professional mathematician, graduate or undergraduate students, teachers, or enthusiastic amateurs."--Stephen Buckley, Irish Mathematical Society Bulletin "The book addresses not only mathematicians but everyone who is interested in this field. The range of topics that are covered in this book is really impressing... The editor has selected articles that really deserve to be read again. I can warmly recommend this book."--Ehrhard Behrends, Zentralblatt MATH "I recommend this book to Gazette readers as enjoyable bedside reading."--Phill Schultz, Australian Mathematics Society Gazette "The volume is suitable for casual browsing and for extended reading. The choices are entirely worthy of inclusion in a volume of the 'best' mathematics writing."--Mark Bollman, Mathematical Reviews "Mircea Pitici, the editor, pulls together work at various levels of complexity and from authors who pursue their subjects from a number of angles: historical or biographical narrative, philosophical speculation both professional and amateur, journalistic commentary on the state of math education and its discontents. And the arrangement of the material is ... intelligent and even artful. Certain figures and questions weave in and out of this volume--making it more unified than 'best of' annuals tend to be."--ScottMcLemee, Inside Higher Ed "Each of the essays is interesting, readable, and purposeful... The contributors are some of the best brains from universities all over the world."--R. Balashankar, Organiser "This is indeed a collection of the most wonderful writings on mathematics that have appeared recently. Not elementary at all and yet accessible to a general audience. Of course this is just the top of a gigantic iceberg, a top that has been selected on the basis of space and copyright limitations."--A. Bultheel, European Mathematical Society "[B]e sure to take a look at the book; odds are good that you'll find something in it that strikes your fancy. As somebody who enjoys expository articles but generally doesn't have the time to track them down and read them, finding a hand-picked collection like this assembled in one place was a delight."--Mark Hunacek, MAA Reviews "Long ago it was possible for physics and mathematics (both applied and pure) to coexist in one person's mind, where developments in all three could occur. Archimedes calculated the volume of a sphere and created the lever. Newton did calculus and studied gravity. With the growth of these fields, however, it is no longer possible to deeply study them all. This is why, even with expositions for the layperson, writings like this are so important."--Edward Charles Keppelmann, Mathematical Reviews Clippings "It is clear from this, and from many other essays in this book, that mathematical creativity is still alive and well."--Gerry Leversham, Mathematical Gazette

Mircea Pitici holds a PhD mathematics education from Cornell University, where he teaches math and writing. He has edited The Best Writing on Mathematics since 2010.

Foreword: The Synergy of Pure and Applied Mathematics, of the Abstract and the Concrete David Mumford ix Introduction Mircea Pitici xvii Why Math Works Mario Livio 1 Is Mathematics Discovered or Invented? Timothy Gowers 8 The Unplanned Impact of Mathematics Peter Rowlett 21 An Adventure in the Nth Dimension Brian Hayes 30 Structure and Randomness in the Prime Numbers Terence Tao 43 The Strangest Numbers in String Theory John C. Baez and John Huerta 50 Mathematics Meets Photography: The Viewable Sphere David Swart and Bruce Torrence 61 Dancing Mathematics and the Mathematics of Dance Sarah-Marie Belcastro and Karl Schaffer 79 Can One Hear the Sound of a Theorem? Rob Schneiderman 93 Flat-Unfoldability and Woven Origami Tessellations Robert J. Lang 113 A Continuous Path from High School Calculus to University Analysis Timothy Gowers 129 Mathematics Teachers' Subtle, Complex Disciplinary Knowledge Brent Davis 135 How to Be a Good Teacher Is an Undecidable Problem Erica Flapan 141 How Your Philosophy of Mathematics Impacts Your Teaching Bonnie Gold 149 Variables in Mathematics Education Susanna S. Epp 163 Bottom Line on Mathematics Education David Mumford and Sol Garfunkel 173 History of Mathematics and History of Science Reunited? Jeremy Gray 176 Augustus De Morgan behind the Scenes Charlotte Simmons 186 Routing Problems: A Historical Perspective Giuseppe Bruno, Andrea Genovese, and Gennaro Improta 197 The Cycloid and Jean Bernoulli Gerald L. Alexanderson 209 Was Cantor Surprised? Fernando Q. Gouvea 216 Why Is There Philosophy of Mathematics at All? Ian Hacking 234 Ultimate Logic: To Infinity and Beyond Richard Elwes 255 Mating, Dating, and Mathematics: It's All in the Game Mark Colyvan 262 Contributors 273 Notable Texts 281 Acknowledgments 285 Credits 287