In Code: A Mathematical Journey

As the father of three children about to iterate into their teen years, I often cringe when I see what they view as inspiration from the media. Sometimes, I really have to press them to read books and challenge their minds. One thing that we have done for years is have what we call questions after supper is done. I ask them questions about many different things, although we concentrate on geography, history and mathematics. The mathematics questions are generally in the form of a puzzle and we have covered basic proof techniques such as the pigeonhole principle. On several occasions, they have explained the solutions to mathematics problems by citing and explaining the pigeonhole principle. Therefore, I was overjoyed when I read this book about Sarah Flannery, who won Ireland's Young Scientist of the Year in 1999. She won it for her work in cryptography for use over the Internet and she credits much of her success to all of the puzzles that she was given to solve by her parents. Sarah is obviously a bright girl, but what is most impressive about the book is how ordinary she claims to be. Outside of her mathematical success, Sarah is very much a regular girl with normal interests. There is no hint of her being forced into mathematics and she wears a Teflon coat concerning any label equivalent to nerd. The book is also very well written, I was fascinated by her story, even sneaking in a few pages during a session at a math conference. It is a story about success, which just happens to be in mathematics. While basic knowledge of congruences is necessary to understand everything, you will enjoy this book even if you have never heard of a congruence. Sarah's story is an inspiration to all people, it keeps your interest and you cannot help but wish her great success in her life, whatever she ultimately decides to do. Published in Journal of Recreational Mathematics, reprinted with permission.

This book was such a delight to read! I'll admit, I am fascinated by mathematics, so it was right up my alley. But mathematics aside, it was still a refreshing read of stories of Sarah's youth and her family, and an entertaining account of her preparation and performance in competitions. I loved reading of how her father inspired her family to love mathematics through brain teasing puzzles and how she was enticed to want to learn more and more about the mathematics behind cryptography. She includes several puzzles that she enjoyed growing up, and those were very fun to figure out. There are a couple chapters that are heavy on mathematics, but someone who does not enjoy this subject could easily skip over them and still enjoy the rest of the book without feeling as they are behind and in the dark. In this mathematical section she does a great job of "teaching" the concepts in a way that keeps the readers attention and curiosity peaked. I wish in my math classes I would have had a teacher with the same type of style rather than the dull non-exciting teaching that seems to be more typical! She also gives some great history behind cryptography and the work that lead up to our cryptographic systems today. I learned quite a bit in that area. I do recommend the book, especially if you have any type of interest in math or cyptography. It is not the dull dry read you might be used to in other math books. It is an honest account and journey told by a sincere and bright young lady. I've already passed my copy along to someone else to enjoy.

Sarah Flannery is a most remarkable young woman. The story of how she approached her mathematics project and how she was able to discover the Cayley-Purser algorithm is fascinating.Instead of giving the Reader's Digest version of the book, I will just say that she wrote the book in the same manner in which she approached her work, with a lot of vim and vigor. One can not but get excited with her as she felt her way through the mathematics and learn as she did, step by step the methods of cryptography. Not being one who is familiar with crytography per se but an amateurish afficionado of Number Theory, I found her explanations of the pertinent mathematics charming, refreshing and stimulating. Her intermittent puzzles were fun and illustrative. I recommend this for anyone wishing to inspire curious youngsters with mathematics. The only quibble anyone could have with this book is the honesty and naivete exhibited by young Sarah, but then again, that is what is so attractive about this gem of a book that stands out amongst the jaded sea of mathematics book being cranked out by authors too cynical to be excited by the mathematical ideas they are writing about. Be forewarned however, you must be atleast a bit amused by mathematics or you won't get the maximum pleasure out of this book.

This is one heck of a good book. It is unusually well written for any book and exceptionally so for its genre. In Code is clear, informative and, as John Naughton (A Brief History of the Future) writes, it is "...engaging, almost playful."I hope I am a member of the Flannery's target audience. Although competent in basic mathematics and statistics, I know nothing about numbers theory and the other seemingly esoteric principles and concepts presented. Yet, for some time, I have been fascinated by information processing and cryptology. This book speaks to the reader as if (s)he were in a classroom with a gifted presenter as well as a gifted mathematician who, as we Americans say, "gets" the value of practical examples.Beyond the above, I am better able to practice my trade as a result of reading this book; that very seldom happens.I have an MA, am a member of MENSA and teach applied behavioral science in business settings. Among the subjects I address are problem solving and critical thinking. I am humbled by the use of puzzles to encourage thinking and inquiry beginning with Chapter 2. I wish I had David Flannery's gift of mentoring. I am revising my teaching to include as many individual and group challenging puzzles as I can get away with to accomplish what the Flannerys have done so admirably: teach in an applications-oriented, playful, genuinely enthusiatic and therefore memorable way.I take the word "gobsmackification" to mean something like "it hit me right in the chops."JBD, Folsom CA 8/4/2001

Number theory is the branch of mathematics that deals with counting numbers, 1, 2, 3... Sarah Flannery, born in 1982, entered that world because her father was a mathematician. What happened to Sarah is that she entered the number theory and cryptology world at age 16 with a science project that was new and original, and was a challenge to the way prime numbers were being used in the most popular of encryption systems. She has written _In Code: A Mathematical Journey_ (Workman Publishing) about how this happened, and its aftermath (or After Math, as a final section of the book is called). It is a delight. It is a book of mathematics, it is true, but it is also an inspiring look at a girl who had an exemplary upbringing and a strong streak of intellectual curiosity. Central to Sarah's story is the blackboard in the dining room of her home. She grew up in the shadow of Blarney Castle, she and her four brothers raised by an independent-thinking pair of parents. At meals, the blackboard would be the focal point for discussion of puzzles. She gives plenty of these for the reader to work on. Some are familiar, like, "Given a five-liter jar and a three-liter jar and an unlimited supply of water, how do you measure out four liters exactly?" Some got into more difficult concepts: "How might you determine the average earnings of a group of people in a room (at a class reunion, perhaps) without any individual's divulging his or her salary?" This second puzzle gives a clue into getting information and hiding information, a theme throughout the book. (All the puzzles are left for the reader to work on, and such work will repay effort in understanding the book, but answers are given.) Sarah repeatedly and sweetly apologizes for digging deep into number theory; before explaining matrices, she writes, "I promise that from then on there will be no more explicit mathematics, only light explanations of mathematical ideas." The main mathematical parts of the book are restricted to two chapters which she invites those who just can't stand the math to skim, and then there are appendices available for those who want to learn more. Sarah's project explained how the most famous current encoding system works, but before she was done, she had invented one of her own. She explains both systems and a lot of number theory along the way. She tells about her interactions with the judges for the competition, and the pressures that eventually resulted in her winning a silver trophy, a cash prize, fame, travel, and interactions with the media. Her lively descriptions of what happened after the newspapers got hold of the story of the genius girl are among the most amusing parts of the book; she and her family turned down a contract with Pepsi, but she did help in an article about herself which appeared in the Spice Girls pop magazine. Here is a book full of mathematical ideas that are worth knowing about, and a bright, funny, modest young woman to lead us throu