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In Code: A Mathematical Journey

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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 through them; Sarah denies that she is a genius, saying that she has met geniuses and that she does not have the spark that distinguishes genius from mere intelligence. Maybe so, but she is a likable author, and it is a delight to hear her describe with affection her parents who obviously know what they are doing. But perhaps the most inspiring part of the book is how well the mathematical community came together to nurture this newcomer. Time and again, experts who worked in the cryptology field were eager to help out. When it seemed that her new code system was patentable and might even make her a millionaire, Sarah got advice even from the mathematicians who might have shared in the bounty that, as one wrote her, "Mathematics should be above such mercenary nonsense!" Mathematical ideas should be freely shared by all, she agreed. It turns out that her system eventually proved vulnerable to attack, thus not quite as secure as the first system, but it doesn't matter. Sarah's book can easily be enjoyed by those who don't like math at all, and would be especially good reading for young people. It is full of happy discoveries in math, and discoveries about people, and it is wonderfully optimistic.

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 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.

Prior to my daughters graduation and a vacation planned to Hawaii I picked this book up to read on the plane; not realizing how this book is about a father-daughter relationship. Sarah tells a fascinating story on how she was drawn to the topic of public key cryptography. There is some basic introductory mathematics that explains the mechanism behind public key crytography but nothing overly complicated. Sarah provides the point of view from a young adults perspective in very clear way. You soon realize that she has a solid understanding of the concepts involved. Great family photos of Mom,Dad and the kids helps get a better feel for her family life; this idea had to come from Dad. After reading this book all parents may want to consider having a blackboard installed in the kitchen. I await the next book hopefully written by her Dad on mathematical puzzles.

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.

I first became interested in cryptography in 2004 after I studied and taught the subject in an academic summer camp. We used "The Code Book" by Simon Singh as our text (which also happpens to be an excellent introduction to the history and methods of cryptography). After the course ended, I went searching for a book that I had heard mentioned in mathematical circles but never actually read myself. This book was "In Code." I finally got my hands on it during my Christmas vacation 2004, and I blazed through it in about two weeks!

As a graduate student in mathematics, the thing that excited me most about this book was Miss Flannery's account of her mathematical research. I had the privilege of doing a research project as an undergraduate math major. I have not come across a better description than hers about what it is like to be so consumed by a problem that you find yourself thinking about it and working on it almost constantly.

This book would be useful in inspiring high school and undergraduate students to study mathematics and to pursue mathematical research projects. If this 16-year-old girl from Ireland can do it, then surely they can do it - as long as they have an experienced mathematician/teacher to help them and encourage them along the way, just as David Flannery did for his daughter.

Sarah Flannery is a young girl who overcame all the odds and won international recognition at a young age through her amazing research in cryptography. This book, In Code, is not really about her research project (although I can see how some would be misled by the title). Instead, it serves as a charming account of her childhood and young adult life: some of the puzzles and problems she worked on, the things she was thinking while working on her research project, her reaction to success, and more. After finishing the book I felt as if I'd known Sarah Flannery personally.

I found the riddles and puzzles sprinkled throughout the book to be very entertaining, and I learned a few things about mathematics I didn't already know while reading. The problems each served to show that even things that seem difficult can be very simple if you change your way of thinking. For me, the toughest part of working through the puzzles was resisting the urge to peek at the answers in the back of the book.

What I most liked about this book is the positive role model it provides for aspiring young mathemticians, particularly girls (who have historically been underrepresented in the field.)

Overall, I highly recommend this book to everyone who has any appreciation for a good puzzle. This book would also be good for parents of young children and older children who are interested in mathematics.

What can I say which hasn't been said already by my fellow reviewers! This is a heart-warming, mind-forming read of the first kind! I am writing this review as I prepare to read it for the second time in two years. This time I intend to solve ALL the puzzles and math problems, in a separate notebook. As a software programmer and math and cryptography aficionado, I have read Simon Singh's and Bruce Schneier's books, but I have never actually carried out any of the practical problems thereof other than in my head, skipping over most of the material I don't understand. Sarah Flannery's book has the advantage of being accessible and nicely graduated. To say nothing of the admirable human experience interspaced with the more intellectual stuff.

I am giving this book away to all my nieces as they come of age 16! I am hoping they will obtain as much pleasure as I have from reading this uplifting, well-written story.

Rob Hardy's review does the best job of capturing this book. Although it does have a fair bit of technical detail that anyone can understand if they have the patience, the real charm of the book is Sara's enthusiasm, her descriptions of epiphanies, her reaction to contest stresses and contest judges, her bouts with keeping herself human. For someone interested in education or the growth of a young intelligence, this book is a wonderful refreshing look at what can happen.

Flannery is the young Irish girl who made international news at the age of 16, when her high-school science fair project - a new cryptographic system which she had developed during a high school work term - was featured on the front page of the Times. I think much of this book contains some fairly heavy math, although it's difficult for me to tell. (I have a Master's degree in this very subject, so I was already familiar with everything she discussed, but others may find it heavy going.)

However, IMO, Chapter 2 alone is worth the price of the book, as it contains a list of Sarah's favourite math puzzles and gives invaluable insight into how her father, a mathematics professor, managed to instil such a phenomenal love of math and science in his children.

If you have young children, and you want to inspire them to be successful later in life, you really owe it to yourself - if not to your kids - to read this book.

See also "Math Power: How to Help Your Child Love Math, Even If You Don't" by Patricia Clark Kenschaft (unfortunately, this book is out of print, but it would be an excellent companion book to this one)