In Code: A Mathematical Journey [Paperback]

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.

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.