The Best Writing on Mathematics (Best Writing on Mathematics)

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.

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.

    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. Gouv?a 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