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