The Best Writing on Mathematics 2015

by Mircea Pitici (Editor)

Overview

The year's finest writing on mathematics from around the world

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 2015 makes 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.

Product Details

ISBN-13:	9780691169651
Publisher:	Princeton University Press
Publication date:	01/12/2016
Series:	The Best Writing on Mathematics , #14
Edition description:	2015 ed.
Pages:	392
Product dimensions:	5.50(w) x 8.50(h) x 1.30(d)

About the Author

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

Table of Contents

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

Editorial Reviews

11/16/2015
Pitici, a teacher of math and writing at Cornell University, continues the series he has edited since 2010, collecting another wonderful variety of mathematical writings, this time with a distinct focus on mathematical games and puzzles. These intriguing—and sometimes unsolved—puzzles provide fuel for much contemplation and exploration of varied topics such as billiards, juggling, and the game Candy Crush. Supplementing that focus are pieces that cover other facets and applications of math, including the beautiful geometry of spirals, the value of mathematics in other disciplines such as synthetic biology, and even potential ways to improve American high school math education. There is little about actual mathematical discoveries; instead, Pitici selects writing that addresses the study of math, use of chalkboards, aesthetics in math, and how proofs work. Though most of the entries are understandable to amateurs, many chapters verge on the niche or esoteric, requiring a depth of familiarity and technicality that renders them accessible only to those with a background in math. Those picking up this collection for the math itself should be pleasantly surprised by the enlightening interdisciplinary work in philosophy, history, and art. Illus. (Jan.)

Publishers Weekly

"The Best Writing on Mathematics does not shy away from mathematics, and that is why it shines. Pitici has done a wonderful job curating articles that form a cohesive . . . volume for readers seeking more than what popular mathematics books have to offer. Overall, this is a great book for the mathematically-experienced reader seeking to connect to mathematics outside of the world of textbooks and tests."—-Douglas Whitaker, Key Reporter

From the Publisher

12/01/2015
Pitici offers his annual selection of intriguing mathematical articles, and happily, 2015 was a banner year. This eclectic collection of nontechnical papers understandable to any reader addresses, for example, the ubiquity of chalkboards in math departments; mathematical games and magic; the contributions of popular science writer Martin Gardner; mathematics education, today and in the future; the game Candy Crush; how to write mathematics; geometric oddities; and offers some historical research. The volume particularly emphasizes discussions of randomness and the use and misuse of probability and statistical arguments. The latter are typified by papers on the likelihood of extremely unlikely events and how statistical reasoning revealed skullduggery in the Canadian provincial lotteries. VERDICT A well-chosen collection supplemented by an outstanding further reading list.—Harold D. Shane, mathematics emeritus, Baruch Coll. Lib., CUNY

Library Journal