Contents
The Role of the Untrue in Mathematics
Desperately Seeking Mathematical Proof
What Is Experimental Mathematics?
KEITH DEVLIN 32
What Is Information-Based Complexity?
What Is Financial Mathematics?
TIM JOHNSON 43
If Mathematics Is a Language, How Do You Swear in It?
DAVID WAGNER 47
Mathematicians and the Practice of Mathematics
Mathematics Is Not a Game But . . .
Massively Collaborative Mathematics
TIMOTHY GOWERS AND MICHAEL NIELSEN 89
Bridging the Two Cultures: Paul Valéry
A Hidden Praise of Mathematics
Mathematics and Its Applications
Mathematics and the Internet: A Source of Enormous Confusion and Great Potential
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
BRIAN HAYES 134
Knowing When to Stop: How to Gamble If You Must—The Mathematics of Optimal Stopping
Homology: An Idea Whose Time Has Come
Adolescent Learning and Secondary Mathematics
ANNE WATSON 163
Accommodations of Learning Disabilities in Mathematics Courses
KATHLEEN AMBRUSO ACKER, MARY W. GRAY, AND BEHZAD JALALI 175
DAVID PIMM AND NATHALIE SINCLAIR 194
Aesthetics as a Liberating Force in Mathematics Education?
Mathematics Textbooks and Their Potential Role in Supporting Misconceptions
ANN KAJANDER AND MIROSLAV LOVRIC 236
Exploring Curvature with Paper Models
Intuitive vs Analytical Thinking: Four Perspectives
URI LERON AND ORIT HAZZAN 260
History and Philosophy of Mathematics
Why Did Lagrange “Prove” the Parallel Postulate?
JUDITH V. GRABINER 283
Kronecker’s Algorithmic Mathematics
HAROLD M. EDWARDS 303
Indiscrete Variations on Gian-Carlo Rota’s Themes
CARLO CELLUCCI 311
Circle Packing: A Personal Reminiscence
Applying Inconsistent Mathematics
MARK COLYVAN 346
ANDRZEJ PELC 358
Mathematicians Solve 45-Year-Old Kervaire Invariant Puzzle
ERICA KLARREICH 373
Darwin: The Reluctant Mathematician
JULIE REHMEYER 377
Loves Me, Loves Me Not (Do the Math)
STEVEN STROGATZ 380
The Mysterious Equilibrium of Zombies and Other Things Mathematicians See at the Movies
SAMUEL ARBESMAN 383
Strength in Numbers: On Mathematics and Musical Rhythm
VIJAY IYER 387
NICK PAUMGARTEN 391
Contributors 395
Acknowledgments 403
Credits 405