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.

In the first three quarters of the book Sarah describes how she became interested in Mathematics via her father's puzzles. She then takes the reader through the absolute basics of the maths behind her project, without going too much into the details of the work she did itself.

The final section of the book is about the competitions she entered (and won), and the aftermath which ensued when she became an international celebrity following the news of her breakthrough.

Sarah's youthful enthusiasm for maths comes through in practically every sentence, as does her humility regarding her own achievements.

Although it's not a very technical work, there's quite a lot of maths in the book at a very basic level, which might not suit every reader.

The book does not describe the algorithm, nor what Sarah did with it to generate so much hype, and the fact that the system was found NOT to be suitable for public key cryptography is almost glossed over.

If you are interested in personal side of the story, then the book is touching and engaging. However, if like me, you buy it to find out more about the "Cayley-Purser" algorithm and Sarah's technical involvement in its development, you will be disappointed.