The Best Writing on Mathematics 2010

Foreword xi
Introduction xv
@=30
The Role of the Untrue in Mathematics 3
Desperately Seeking Mathematical Proof 13
An Enduring Error 18
What Is Experimental Mathematics? 32
What Is Information-Based Complexity? 37
What Is Financial Mathematics? 43
If Mathematics Is a Language, How Do You Swear in It? 47
Birds and Frogs 57
Mathematics Is Not a Game But... 79
Massively Collaborative Mathematics 89
Bridging the Two Cultures: Paul Valéry 94
A Hidden Praise of Mathematics 99
Mathematics and the Internet: A Source of Enormous Confusion and Great Potential 109
The Higher Arithmetic: How to Count to a Zillion without Falling Off the End of the Number Line 134
Knowing When to Stop: How to Gamble if You Must \em The Mathematics of Optimal Stopping 145
Homology: An Idea Whose Time Has Come 158
Adolescent Learning and Secondary Mathematics 163
Accommodations of Learning Disabilities in Mathematics Courses 175
Audience, Style and Criticism 194
Aesthetics as a Liberating Force in Mathematics Education? 206
Mathematics Textbooks and Their Potential Role in Supporting Misconceptions 236
Exploring Curvature with Paper Models 247
Intuitive vs Analytical Thinking: Four Perspectives 260
Why Did Lagrange \l"Prove\r" the Parallel Postulate? 283
Kronecker's Algorithmic Mathematics 303
Indiscrete Variations on Gian-Carlo Rota's Themes 311
Circle Packing: A Personal Reminiscence 330
Applying Inconsistent Mathematics 346
Why Do We Believe Theorems? 358
Mathematicians Solve 45-Year-Old Kervaire Invariant Puzzle 373
Darwin: The Reluctant Mathematician 377
Loves Me, Loves Me Not (Do the Math) 380
The Mysterious Equilibrium of Zombies and Other Things Mathematicians See at the Movies 383
Strength in Numbers: On Mathematics and Musical Rhythm 387
Math-hattan 391
Contributors 395
Acknowledgments 403
Credits 405