TABLE OF CONTENTS: Foreword by William P. Thurston xi Introduction by Mircea Pitici xv Mathematics Alive The Role of the Untrue in Mathematics by Chandler Davis 3 Desperately Seeking Mathematical Proof by Melvyn B. Nathanson 13 An Enduring Error by Branko Grunbaum 18 What Is Experimental Mathematics? By Keith Devlin 32 What Is Information-Based Complexity? By Henryk Woz´niakowski 37 What Is Financial Mathematics? By Tim Johnson 43 If Mathematics Is a Language, How Do You Swear in It? By David Wagner 47 Mathematicians and the Practice of Mathematics Birds and Frogs by Freeman Dyson 57 Mathematics Is Not a Game But . . . by Robert Thomas 79 Massively Collaborative Mathematics by Timothy Gowers and Michael Nielsen 89 Bridging the Two Cultures: Paul Valery by Philip J. Davis 94 A Hidden Praise of Mathematics by Alicia Dickenstein 99 Mathematics and Its Applications Mathematics and the Internet: A Source of Enormous Confusion and Great Potential by Walter Willinger, David L. Alderson, and John C. Doyle 109 The Higher Arithmetic: How to Count to a Zillion without Falling Off the End of the Number Line by Brian Hayes 134 Knowing When to Stop: How to Gamble If You Must--The Mathematics of Optimal Stopping by Theodore P. Hill 145 Homology: An Idea Whose Time Has Come by Barry A. Cipra 158 Mathematics Education Adolescent Learning and Secondary Mathematics by Anne Watson 163 Accommodations of Learning Disabilities in Mathematics Courses by Kathleen Ambruso Acker, Mary W. Gray, and Behzad Jalali 175 Audience,Style and Criticism by David Pimm and Nathalie Sinclair 194 Aesthetics as a Liberating Force in Mathematics Education? By Nathalie Sinclair 206 Mathematics Textbooks and Their Potential Role in Supporting Misconceptions by Ann Kajander and Miroslav Lovric 236 Exploring Curvature with Paper Models by Howard T. Iseri 247 Intuitive vs Analytical Thinking: Four Perspectives by Uri Leron and Orit Hazzan 260 History and Philosophy of Mathematics Why Did Lagrange "Prove" the Parallel Postulate? By Judith V. Grabiner 283 Kronecker's Algorithmic Mathematics by Harold M. Edwards 303 Indiscrete Variations on Gian-Carlo Rota's Themes by Carlo Cellucci 311 Circle Packing: A Personal Reminiscence by Philip L. Bowers 330 Applying Inconsistent Mathematics by Mark Colyvan 346 Why Do We Believe Theorems? By Andrzej Pelc 358 Mathematics in the Media Mathematicians Solve 45-Year-Old Kervaire Invariant Puzzle by Erica Klarreich 373 Darwin: The Reluctant Mathematician by Julie Rehmeyer 377 Loves Me, Loves Me Not (Do the Math) by Steven Strogatz 380 The Mysterious Equilibrium of Zombies and Other Things Mathematicians See at the Movies by Samuel Arbesman 383 Strength in Numbers: On Mathematics and Musical Rhythm by Vijay Iyer 387 Math-hattan by Nick Paumgarten 391 Contributors 395 Acknowledgments 403 Credits 405 Return to Book Description File created: 7/11/2014 |