The Best Writing on Mathematics 2015

Published by Princeton University Press 2016

The Best Writing on Mathematics 2015

Edited by: Mircea Pitici

Volume 14 in the series The Best Writing on Mathematics

https://doi.org/10.1515/9781400873371

Overview
Contents

About this book

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.

Author / Editor information

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.

Reviews

"Pitici offers his annual selection of intriguing mathematical articles, and happily, 2015 was a banner year. [An] eclectic collection of nontechnical papers understandable to any reader. . . . A well-chosen collection supplemented by an outstanding further reading list."---Harold D. Shane, Library Journal

"[A]nother 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. . . . Those picking up this collection for the math itself should be pleasantly surprised by the enlightening interdisciplinary work in philosophy, history, and art."

"I found this book to be a great resource. The articles are easy to read and interesting to ponder. This book will be a valuable resource when my students in algebra and geometry want to look at a math concept for a project. The recent math applications in this book are a valuable resource."---Matthew Tucker, National Council of Teachers of Mathematics

"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

"The idea behind this great series, which Pitici describes as ‘accessible but nontrivial content that presents for mathematicians and for the general public a wide assortment of informed and insightful perspectives on pure and applied mathematics, on topics related to the learning and teaching of mathematics, on the practice and practicality of mathematics, on the social and institutional aspects in which the mathematics themes, or on other themes related to mathematics,' was clearly presented in last year’s book and successfully continued in the one in front of us. We trust and hope that this will carry on in future years and we are definitely looking forward to it."---Aleksandar M. Nikolić, MathSciNet

"Dealing with topics of general interest--as history and philosophy, teaching, the occurrence of mathematics in everyday life, etc.--presented in an attractive and accessible manner, the books appeals to a large audience, including mathematicians of all levels of instruction, but also to anyone interested in the development of science and its applications."---Horia F. Pop, Studia Mathematica

"I like expository articles on mathematics, but seldom have the time during the academic year to seek them out, so it is always a pleasure to have somebody like Pitici assemble a collection of good ones for me. This year's assortment, like those of the last few years, did not disappoint."---Mark Hunacek, MAA Reviews

Topics

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