The Best Writing on Mathematics 2012 (ebook)

Argumento de The Best Writing on Mathematics 2012 (ebook)

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more.

In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

"[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

"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

"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

"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

"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

"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

"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

"I recommend this book to Gazette readers as enjoyable bedside reading."--Phill Schultz, Australian Mathematics Society Gazette

"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, Organiser0Foreword: 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. Gouvêa 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