A Century of Advancing Mathematics

Stephen F. Kennedy, Editor
Donald J. Albers, Gerald L. Alexanderson, Della Dumbaugh, Frank A. Farris, Deanna B. Haunsperger, and Paul Zorn; Associate Editors



The MAA was founded in 1915 to serve as a home for The American Mathematical Monthly. The mission of the Association-to advance mathematics, especially at the collegiate level-has, however, always been larger than merely publishing world-class mathematical exposition. MAA members have explored more than just mathematics; we have, as this volume tries to make evident, investigated mathematical connections to pedagogy, history, the arts, technology, literature, every field of intellectual endeavor. Essays, all commissioned for this volume, include exposition by Bob Devaney, Robin Wilson, and Frank Morgan; history from Karen Parshall, Della Dumbaugh, and Bill Dunham; pedagogical discussion from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural commentary from Bonnie Gold, Jon Borwein, and Steve Abbott.

This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics-more mathematics has been created and published since 1915 than in all of previous recorded history. We've solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA's first century. Mathematics is the most thrilling, the most human, area of intellectual inquiry; you will find in this volume compelling proof of that claim.

Table of Contents

Preface

Part I Mathematical Developments
The Hyperbolic Revolution: From Topology to Geometry, and Back Francis Bonahon
A Century of Complex Dynamics Daniel Alexander and Robert L. Devaney
Map-Coloring Problems Robin Wilson
Six Milestones in Geometry Frank Morgan
Defying God: the Stanley-Wilf Conjecture, Stanley-Wilf Limits, and a Two-Generation Explosion of Combinatorics Eric S. Egge
What Is the Best Approach to Counting Primes? Andrew Granville
A Century of Elliptic Curves Joseph H. Silverman

Part II Historical Developments
The Mathematical Association of America: Its First 100 Years David E. Zitarelli
The Stratification of the American Mathematical Community: The Mathematical Association of America and the American Mathematical Society, 1915–1925 Karen Hunger Parshall
Time and Place: Sustaining the American Mathematical Community Della Dumbaugh
Abstract (Modern) Algebra in America 1870–1950: A Brief Account Israel Kleiner

Part III Pedagogical Developments
The History of the Undergraduate Program in Mathematics in the United States Alan Tucker
Inquiry-Based Learning Through the Life of the MAA Michael Starbird
A Passport to Pleasure Bob Kaplan and Ellen Kaplan
Strength in Numbers: Broadening the View of the Mathematics Major Rhonda Hughes
A History of Undergraduate Research in Mathematics Joseph A. Gallian
The Calculus Reform Movement: A Personal Account Paul Zorn
Introducing ex Gilbert Strang

Part IV Computational Developments
Computational Experiences in the Pre-Electronic Days Philip J. Davis
A Century of Visualization: One Geometer’s View Thomas F. Banchoff
The Future of Mathematics: 1965 to 2065 Jonathan M. Borwein

Part V Culture and Communities
Philosophy of Mathematics: What Has Happened Since Gödel’s Results? Bonnie Gold
Twelve Classics People who Love Mathematics Should Know; or, “What do you mean, you haven’t read E. T. Bell?” Gerald L. Alexanderson
The Dramatics Life of Mathematics: A Centennial History of the Intersection of Mathematics and Theater in a Prologue, Three Acts, and an Epilogue Stephen D. Abbott
2007: The Year of Euler William Dunham
The Putnam Competition: Origin, Lore, Structure Leonard F. Klosinski
Getting Involved with the MAA: A Path Less Traveled Ezra “Bud” Brown
Henry L. Alder Donald J. Albers and Gerald L. Alexanderson
Lida K. Barrett Kenneth A. Ross
Ralph P. Boas Daniel Zelinsky
Leonard Gillman—Reminiscences Martha J. Siegel
Paul Halmos: No Apologies John Ewing
Ivan Niven Kenneth A. Ross
George Pólya and the MAA Gerald L. Alexanderson