Foreword: The Synergy of Pure and Applied Mathematics, of the Abstract and the Concrete / David Mumford
Introduction / Mircea Pitici
Why Math Works / Mario Livio
Is Mathematics Discovered or Invented? / Timothy Gowers
The Unplanned Impact of Mathematics / Peter Rowlett
An Adventure in the Nth Dimension / Brian Hayes
Structure and Randomness in the Prime Numbers / Terence Tao
The Strangest Numbers in String Theory / John C. Baez and John Huerta
Mathematics meets Photography: The Viewable Sphere / David Swart and Bruce Torrence
Dancing Mathematics and the Mathematics of Dance / Sarah-Marie Belcastro and Karl Schaffer
Can One Hear the Sound of a Theorem? / Rob Schneiderman
Flat-Unfoldability and Woven Origami Tesselations / Robert J. Lang
A Continuous Path from High School Calculus to University Analysis / Timothy Gowers
Mathematics Teacher's Subtle, Complex Disciplinary Knowledge / Brent Davis
How to Be a Good Teacher Is an Undecidable Problem / Erica Flapan
How Your Philosophy of Mathematics Impacts Your Teaching / Bonnie Gold
Variables in Mathematics Education / Susanna S. Epp
Bottom Line on Mathematics Education / David Mumford and Sol Garfunkel
History of Mathematics and History of Science Reunited? / Jeremy Gray
Augustus de Morgan behind the Scenes / Charlotte Simons
Routing Problems: A Historical Perspective / Giuseppe Bruno, Andrea Genovese, and Gennaro Improta
The Cycloid and Jean Bernoulli / Gerald L. Alexanderson
Was Cantor Surprised? / Fernando Q. Gouvêa
Why Is There Philosophy of Mathematics at All? / Ian Hacking
Ultimate Logic: To Infinity and Beyond / Richard Elwes
Mating, Dating, and Mathematics: It's All in the Game / Mark Colyvan.
