This is an inspiring book, telling the story of a young woman's introduction to, and enamourment with, of all things, mathematics. In an era where enthusiasm for the sciences is often seen as "uncool", it is delightfully encouraging to read the story of a family, and in particular the author herself, who understand both the value and the pleasure of such interests.
The book balances two quite separate elements. On the one hand there's the story of how Sarah became interested in mathematics, did an interesting science project, and got a lot of attention when as a seventeen year old Irish girl she nearly invented a powerful new cryptographic system. On the other hand there's a very clear introduction to the mathematics underlying modern cryptography, presented using a range of interesting examples, puzzles and clear explanations.
After an introduction to Sarah, her family, and the intellectual training methods of her parents, the first two thirds of the book focus mainly on the mathematical background, interspersed with regular anecdotes explaining how Sarah came to understand and use different skills and areas of knowledge. If you want an introduction to this area of mathematics you could do a lot worse than this book.
The last third of the book focuses on how she did her science project, and what happened when she won a major prize in the annual Irish Young Scientist competition, including how she and her family dealt with quite unexpected fame and media attention. What is interesting is how seriously the Irish establishment and media seem to take these things, and puts to shame the British indifference to this sort of achievement.
Finally a couple of appendixes present answers to the puzzles, and a few key pieces of mathematical background in more detail.
The book is co-written by Sarah's father David. He's a mathematics lecturer, and on the evidence of both the explanations in the book, and the way he inspired his children it appears he's a very good one. Between the father's very strong skills in presenting mathematics, and the daughter's refreshing simplicity and honesty about all that's happened to her, they make a very powerful team.
I would definitely recommend this book to any youngster interested in the sciences, or any sort of academic endeavour. I'd also recommend it to older readers, an encouraging proof that such interests have not been entirely abandoned.