THE BEST WRITING ON MATHEMATICS 2015

Introduction - Mircea Pitici xi
A Dusty Discipline - Michael J. Barany and Donald MacKenzie 1
How Puzzles Made Us Human - Pradeep Mutalik 7
Let the Games Continue - Colm Mulcahy and Dana Richards 14
Challenging Magic Squares for Magicians - Arthur T. Benjamin and Ethan J. Brown 26
Candy Crush's Puzzling Mathematics - Toby Walsh 38
Chaos on the Billiard Table - Marianne Freiberger 47
Juggling with Numbers - Erik R. Tou 63
The Quest for Randomness - Scott Aaronson 69
Synthetic Biology, Real Mathematics - Dana Mackenzie 93
At the Far Ends of a New Universal Law - Natalie Wolchover 99
Twisted Math and Beautiful Geometry - Eli Maor and Eugen Jost 107
Kenichi Miura's Water Wheel, or The Dance of the Shapes of Constant Width - Burkard Polster 119
Dürer: Disguise, Distance, Disagreements, and Diagonals! - Annalisa Crannell, Marc Frantz, and Fumiko Futamura 132
The Quaternion Group as a Symmetry Group - Vi Hart and Henry Segerman 141
The Steiner-Lehmus Angle-Bisector Theorem - John Conway and Alex Ryba 154
Key Ideas and Memorability in Proof - Gila Hanna and John Mason 167
The Future of High School Mathematics - Jim Fey, Sol Garfunkel, Diane Briars, Andy Isaacs, Henry Pollak, Eric Robinson, Richard Scheaffer,
Alan Schoenfeld, Cathy Seeley, Dan Teague, and Zalman Usiskin 181
Demystifying the Math Myth: Analyzing the Contributing Factors for the Achievement Gap between Chinese and U.S. Students - Guili Zhang and Miguel A. Padilla 187
The Pigeonhole Principle, Two Centuries before Dirichlet - Benoît Rittaud and Albrecht Heeffer 201
A Prehistory of Nim - Lisa Rougetet 207
Gödel, Gentzen, Goodstein: The Magic Sound of a G-String - Jan von Plato 215
Global and Local - James Franklin 228
Mathematical Beauty, Understanding, and Discovery - Carlo Cellucci 241
A Guide for the Perplexed: What Mathematicians Need to Know to Understand Philosophers of Mathematics - Mark Balaguer 265
Writing about Math for the Perplexed and the Traumatized - Steven Strogatz 280
Is Big Data Enough? A Reflection on the Changing Role of Mathematics in Applications - Domenico Napoletani, Marco Panza, and Daniele C. Struppa 293
The Statistical Crisis in Science - Andrew Gelman and Eric Loken 305
Color illustration section follows page 316
Statistics and the Ontario Lottery Retailer Scandal - Jeffrey S. Rosenthal 319
Never Say Never - David J. Hand 332
Contributors 337
Notable Writings 349
Acknowledgments 359
Credits 361

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2015makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates.
Here David Hand explains why we should actually expect unlikely coincidences to happen; Arthur Benjamin and Ethan Brown unveil techniques for improvising custom-made magic number squares; Dana Mackenzie describes how mathematicians are making essential contributions to the development of synthetic biology; Steven Strogatz tells us why it’s worth writing about math for people who are alienated from it; Lisa Rougetet traces the earliest written descriptions of Nim, a popular game of mathematical strategy; Scott Aaronson looks at the unexpected implications of testing numbers for randomness; and much, much more.
In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Author
Mircea Pitici holds a PhD mathematics education from Cornell University, where he teaches math and writing. He has edited The Best Writing on Mathematics since 2010.