In Code: A Mathematical Journey

  • Sarah Flannery &
  • David Flannery
Profile Books: 2000. 292 pp. £14.99

Sarah Flannery is a teenager in County Cork, Ireland. She is also the creator of a coding scheme for information transmission that dramatically extends our ideas of how best to compress information. How could a completely typical Irish teenager astound the world of mathematics in this way? In Code is a first-hand account of the answer.

Sarah's father, mathematics teacher David Flannery, plays the Henry Higgins to Sarah's Eliza Doolittle. The Flannery household, rather ordinary by most standards, is quite unusual in one way: the presence of a large blackboard in the kitchen, on which Flannery senior would write challenging mathematical puzzles for his children to ponder. So, from the time she was a toddler, Sarah was continually exposed to logical thought processes and the thrill of discovery. That's one piece of the answer to her success, a mathematically friendly home environment where the fact that she is a child and a woman played no role in discouraging her from developing a native talent for mathematical thinking.

As Sarah's story continues, we find her taking educational enrichment courses taught by her father at the local college. By the account given in the book, these courses are rather extraordinary in the way they challenge the students to think through the logic behind various mathematical problems. Thus, the principles involved in finding answers are arrived at in a kind of Socratic process of dialogue and discovery.

During the development of her novel coding scheme, Sarah takes the reader through a sequence of science competitions, first in Ireland, then abroad, at each stage of which her project wins a major prize. The ultimate project is a code that improves upon the standard RSA coding scheme used around the world to compress and send information. Sarah's scheme, the technical details of which are not presented in this book, provides an alternative that is considerably faster than the RSA procedure, and thus has the potential to send information far more efficiently — and cheaply — than previously thought possible.

The success of Sarah's coding method in science fairs around the world brings her fame, minor fortune and lots of publicity — including a front-page write-up in The Times of London. It also brings innumerable offers from entrepreneurs, software houses and others of that ilk, who promise riches beyond her wildest imagination if she will enter into a commercial arrangement with them to further develop and market her work. To her credit, Sarah refuses all these blandishments, and tells the world that she intends to present her work publicly, essentially giving the code away for free.

But there is a fly in the ointment. As mathematicians scrutinize Sarah's work, they discover a security flaw in the scheme. While the flaw in no way invalidates the mathematical basis of the code, it does prevent it from being used as a public-key cryptosystem. This, in turn, destroys the code's commercial value. Sic gloria transit mundi. Sarah remains undaunted by this development, and we read of her admirable aplomb in shrugging off the tarnishing of her achievement by this blemish. ‘Who cares?’ she seems to say. Much mathematical work is less than perfect. But it is still regarded as a contribution to progress.

In Code is a wonderfully moving story. While at times it reads a bit too much like a gushy teenager's diary (which it is), the book contains a wealth of interesting information on mathematical puzzles, coding methods, elementary number theory and algebra. It is also well worth noting, however, that it can be profitably read by anyone; no knowledge of mathematics, codes, number theory or anything else is needed. In fact, the book does an exemplary job of walking the reader through a set of graded puzzles aimed at developing mathematical intuition, followed by a first-rate, gentle introduction to codes, deciphering and cryptosystems. So don't be put off by the fear that this is a book on some mathematical genius that you won't understand. It is just the opposite; it's a book about the thrill of the mathematical chase, and how it is a game that anyone can play.

The book also gives a fascinating account of how a gifted teacher like Sarah's father, David, can help nurture and develop the mind of a very bright — but far from genius-level — teenager such as his daughter, and inspire that mind to creative heights one would believe possible only of bona fide geniuses. Sarah's story should serve as an inspiration to all young people, especially young women, who might be contemplating a life in mathematics. I recommend it highly as summer reading not only for teenagers, but for anyone interested in the human spirit and its boundless capacity for innovation and imagination.