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