In Code: A Mathematical Journey

by David Flannery

In January 1999, Sarah Flannery, a sports-loving teenager from Blarney in County Cork, Ireland, was awarded Ireland's Young Scientist of the Year for her extraordinary research and discoveries in Internet cryptography. The following day, her story began appearing in Irish papers and soon after was splashed across the front page of the London Times, complete with a photo of Sarah and a caption calling her "brilliant." Just sixteen, she was a mathematician with an international reputation. IN CODE is a heartwarming story that will have readers cheering Sarah on. Originally published in England and cowritten with her mathematician father, David Flannery, IN CODE is "a wonderfully moving story about the thrill of the mathematical chase" (Nature) and "a paean to intellectual adventure" (Times Educational Supplement). A memoir in mathematics, it is all about how a girl next door, nurtured by her family, moved from the simple math puzzles that were the staple of dinnertime conversation to prime numbers, the Sieve of Eratosthenes, Fermat's Little Theorem, googols-and finally into her breathtaking algorithm. Parallel with each step is a modest girl's own self-discovery-her values, her burning curiosity, the joy of persistence, and, above all, her love for her family.

Genres: Nonfiction, Mathematics, Science, Biography, Memoir, Biography Memoir, Programming

341 pages, Paperback

First published March 20, 2000

Reviews

[David Rubenstein · Rating 4 out of 5]

This is a fun little book by a young woman who found some degree of fame in the field of cryptography. Growing up in Ireland, Sarah Flannery was constantly exposed to mathematics; her father, a mathematician, gave math and logic puzzles to her and her brothers. As a high school student, Sarah took a "transition" year off during high school, and worked for a cryptography company. She learned how to code algorithms in the Mathematica computer language. At the company, she was supervised by some gifted mathematicians, who gave her some difficult, challenging projects. She did well, and presented a very good science fair project at her high school. Her project was good enough to make it to the national fair, and then to an international fair.

Then Sarah decided she wanted to continue on, and do some original research. With the help of a mathematician mentor, she invented a new "trap door" algorithm that was much faster than the state-of-the-art algorithms. She presented her improved science fair project, and won at the national and international fairs. She had quite a big exposure, as the media caught on to her discovery.

In between her autobiographical narration, Sarah provides some fun mathematical puzzles. I loved the puzzle about the insurance salesman. Also, she guides the reader through elementary number theory, giving the reader enough understanding to grasp the essentials of modern-day cryptography.

[William Schram · Rating 4 out of 5]

In Code: A Mathematical Journey is a book on cryptography written by a young woman named Sarah Flannery. It chronicles the story of how she won a competition in her home country of Ireland and came to the United States to represent her country and won international fame. Sadly, I don’t remember this happening since I was 13 in 1999 and didn’t read the news.

The book is divided into chapters which isn’t surprising. It opens by discussing her family and how they gave her the unique opportunity to achieve what she did. She was raised on puzzles and brain teasers, supplying some of them in the process. I have heard of all of them. There is the farmer with the rickety old boat, the two jars problem, the Monty Hall problem, and several others. She provides the answers, but you are encouraged to try them on your own.

Miss Flannery begins with prime numbers, which are deceptive in how they behave. First off, prime numbers are numbers that are only divisible by one and the number itself. The fact that there is an infinite number of them was a solution known to the ancients by way of Euclid. He reasoned it out by claiming that a number was the prime of the greatest possible magnitude which leads to a contradiction. So we have an infinite number of primes, but few ways to determine whether a number is prime. There are several algorithms for it, but they are prohibitive in how long they take to crack.

So she entered the equivalent of a science fair with her project on RSA Public Key Cryptography. For a while, that was how internet messages were kept safe and so on. I don’t know if they still use that method though. The groundbreaking idea with RSA is that one of the keys is made public. The basic idea is that it is easy to multiply a number together, but difficult to factor that same number. Miss Flannery likens it to separating a mixture of white and black paint back into white and black paint.

The book is fascinating in the parts with mathematics. She provides a bibliography and notes with an index. The appendices list the program code she used for the competitions in Mathematica, which is a program to do mathematics in. The book is really well done, and I appreciate the time taken to write it by all involved.

[Ralph · Rating 4 out of 5]

3.5 out of 5 - Recommended
The story of Sarah Flannery, who at age sixteen, was awarded Ireland's Young Scientist of the Year for her visionary research and discoveries in the field of Internet cryptography.

[Creighton · Rating 4 out of 5]

A great way for laymen to get introduced to the basic ideas of cryptography and discrete mathematics. She writes in an easy to understand way

[Hattie · Rating 5 out of 5]

Second book in the series of ‘books that randomly appeared in my childhood bedroom written by incredibly precocious teenagers’.

This was really engaging and well explained, also quite funny. Not just the maths itself (and marvelling at her grasp of it), but also hearing about the experiences of winning an international competition and the resulting media/industry attention, as well as the dilemma of publishing vs patenting.

‘She has a fine voice, and whenever I see her and my brother Michael playing guitar and singing together I make sure Dad knows how much I hate him for the fact that I have inherited his crow-like voice.’

On cryptic crosswords: ‘He mastered this art in a few weeks after many exasperating efforts, tenaciously examining the published solutions on the following day. Now he instructs my mother in how to decipher their mysteries, which my father, who refuses even to try them, describes as the outpourings of a warped mind.’

‘Writing this book was torture’

‘Our particular thanks must go to Peter Carson of Profile Books. It was he who extended the invitation to write this book. We cursed him privately many times for so doing.’

[Chris Miller · Rating 4 out of 5]

I had tried to read Kahn's Codebreaking many years ago but was only able to get a third of the was through. I am going to have to try it again after reading this. Flannery won two major science competitions in the late 1990s, and this book is her and her father's account of how that happened. In order to describe her project, she presents a considerable amount of necessary math and cypher information necessary to comprehend the issues she is addressing. She does this in a readable and useful way, so that the reader has an inkling, even if complete comprehension is lacking. In fact, I found the explanatory material more compelling than her narrative of the competitions. She includes her project and several expansions of material in the appendices. Anyone who has a child (relative or friend) who might like to challenge them for science fairs or History Day or the like should have them take a look at this for her attitude and strategies. Neat book.

[Stefano Ottolenghi · Rating 5 out of 5]

This is an astounding book for several reasons. To start, it was written by a 17-ish years old tennager, which is remarkable given the style and clarity. But then, the way concepts are presented is just very good. I knew everything she was talking about, but her own explanations increased my understanding of the topics. She has that great ingenuity and enthusiasm that justify the belief that great work is done before 25 years old, and also the idea that teenagers should be involved in way more complex and challenging stuff compared to what we feed them nowadays. The role her father had for her is another thing to draw example from.

[Liam O'Keeffe · Rating 5 out of 5]

Sarah flannery says in her book that she is not a genius but she is. Her book introduces the reader to basic cryptography. It explains the Caesar cipher and rsa. She implemented an algorithm that was faster than rsa but it had a flaw which meant it could not be used for public key cryptography. It’s called the Cayley-purser algorithm. It’s not covered in the book but you can read about it on Wikipedia. God bless

[Andre · Rating 4 out of 5]

Wanted to read this since it was first published and finally picked up a second hand copy in a bookshop/cafe in Kells, Ireland (so a "Book of Kells") and I thoroughly enjoyed finding and reading it. Dr Purser was one of my lecturers (at Trinity College Dublin where the Book of Kells is today). But that was about a decade before the book's story which I think still makes for a good read today.

[Jodie · Rating 3 out of 5]

This would be a good book for younger kids who are interested in number theory/cryptography. For me, it was an inspiring story but a bit childishly written and too simplistic given that I've already taken a class on the subject. (It's really much more about math rather than code, despite the title)

[Sam · Rating 5 out of 5]

This is a charming and fascinating book!

[Rob Hudson · Rating 3 out of 5]

This was a fun story. I especially like the more math detailed chapters on number theory and cryptography basis.

[Russ Mathers · Rating 4 out of 5]

Good book. It got a little technical on the math and I glossed over that part. Very impressive young lady!

[Sarah Kate · Rating 4 out of 5]

Very interesting view into both Sarah's work and personal life.

[Ucp · Rating 5 out of 5]

An amazing story about Cryptography, puzzles and Math.

[Danielle Adams · Rating 3 out of 5]

The math was pretty heavy but fun story overall.

[Robin Coopersmith · Rating 3 out of 5]

Uplifting story and interesting math. 3 stars because it's written more like a conversation than a book. Very colloquial, and the story could be told without so many details and words.

[Jessica · Rating 4 out of 5]

Written by a 16-year-old Irish girl who made a name for herself by doing research on cryptographic systems for an academic project, culminating in her inventing and testing out a new cryptographic algorithm. The book promises to teach some of the math involved without getting too complicated, and even tells the math-wary reader what chapters are skippable if you just want the story and not the math. The book is definitely enjoyable and engaging, although the math gets a little slow in the middle. I went into this not knowing much about cryptography and came out of it feeling like I did have some understanding of the subject. Some of the trivia she provides is also quite interesting, like the math behind ISBNs (they encode information such as the publishing house and end with an error-checking digit which, due to the length of the ISBN, requires it to be base-11, which is why the last digit of an ISBN can be 0-9 or X for 10). Straddling the middle section about math and cryptography are two sections about Sarah, her family, and her experiences presenting her research nationally and internationally, and it's interesting to see both how her family fueled her curiousity and helped keep her in check as the press was lauding her as a "genius" and trying to get her to patent her algorithm so she could "make millions."

[Kailie Mae · Rating 2 out of 5]

I have an unrelenting passion for math. You may therefore think that would have inclined my admiration for this book, though what an erroneous assumption that would be; I did not like it in the least. I did find the actual mathematical parts to be intriguing and, for the most part, well-explained. In fact, I actually really enjoyed, admired, even, the various puzzles Sarah included in this book. However, to me, she came across as very snobby and placed herself on a high, revering pedestal. What I mean is this: the book is written very conversationally. She makes it seem like someone is reading her book because they don't know any math at all and are trying to learn. Perhaps it was just my perception of things, but in the end it grew my distaste for the book so much I could hardly force myself to finish reading it. The book's purpose is confusing; I couldn't tell if she was trying to explain the math behind her work or if she was trying to tell a story. If an attempt to do both, this book failed. If you can look past these shortcomings and blunts, and I know several have and can, then you may be able to obtain some actual benefit from In Code: A Mathematical Journey. I, however, could not. I give props to Miss Flannery, though. She is a woman of true intellect and good intentions. I simply just did not enjoy her book.

[Andrewcharles420 · Rating 2 out of 5]

I really liked the mathematics described in the book, and thought the author did a great job explaining them! The story was inspirational, but I sometimes found the biographical parts of the book plodding and pedantic. My thought is that this book was aimed for a younger, anglo-centric audience.

I suppose the writing advice, "write like your parents are dead", was intended for fiction, and could hardly have worked in a book co-written with her father, but it seemed like a lot of the words in the biographical part of the book were praising her parents/family. It's nice to be thoughtful, respectful, and grateful, but I get it. And I got it. And it was well understood long before it wore off. It gave an underlying theme to the book to always obey and respect your parents/elders, which, though I don't disagree with, I don't think was the purpose of the book.

I would have liked to have seen more mathematical details! If this could be rewritten into a short course book retracing the path the author took from grade school mathematics to academic cryptography studies, I'd be very interested in picking it up again. I would recommend this to mathematically-inclined youngsters, especially if they're of an age to start an independent project and enter competitions themselves.

[Steven jb · Rating 4 out of 5]

I enjoyed this book as both a coming of age story, a success story, a story about cryptology, and mathematics. The story is about Sarah Flannery, a sixteen year old Irish woman, who created a fascinating method of encoding messages using mathematical principles. She won many awards and received many awards for her work, but it is the insight into her thoughts and feelings during the process that is most fascinating. Sarah is confronted by the excesses and silliness of the press and people during her success, and the reader is able to understand how success can undermine a person. Sarah and her family do quite well. The first third of the book illustrates Sarah's upbringing by her mathematician dad and down to earth family, and she provides several fun mathematical puzzles. The second third of the book goes through some basic mathematical principles and it is well written. The reader can try to understand the math or not; the way the book is written, it is not necessary to labor through any math to enjoy the story. The last third of the book is the story of her math project, her learning of more advanced math, and success. I highly recommend this book.

[Scarlett Sims · Rating 4 out of 5]

As a teenager, Sarah Flannery won a few international science competitions with a project about an encryption algorithm. Though it turned out that the algorithm couldn't be used for public key encryption, she got quite a lot of attention for her achievements. Her memoir details her early exposure to math, the ideas that are the basis for her award-winning project, and her personal feelings about the contests and their after-math.

The book contains explanations of some of the basic mathematical principles she used. She says you can skip those parts, but I would recommend not. People find math intimidating for whatever reason but it's mostly just arithmetic presented in different ways so at least give it a try. It was interesting to read about someone who had achieved so much, however is in many ways just a normal girl. She gives entries from her journal about the days following her contest win, and her emotions are pretty typical of a teenager.

Math lovers should definitely check this out. Anyone interested in math education or the presence of women in math and science would probably also enjoy it.

[Tom · Rating 5 out of 5]

Yes, it's written by a teenager and it does read like it - all over-earnest and unsubtle - but it also reads like it's written by someone who is genuinely excited by the discoveries she's making and the adventures they send her on.

I may be wrong, but I would guess that if you have never done higher level mathematics this will be no more than fairly entertaining story. For those who have, it can be so much more. Not because there is much need to understand the maths in this book, but because you would need to know at first hand the joys of immersing yourself in mathematical investigation in order to really understand how she feels about the work. The section she gives over to the diary of the work she was doing really brought back some memories.

[Todd Allen · Rating 3 out of 5]

I was most interested in the puzzles, mathematical concepts and history of cryptography that were tactfully illustrated in the first nine-chapters. Crafted maturely was the recounting of Sarah’s pivotal upbringing as it was interspersed with the history and precedents of the mathematical underpinnings of cryptography. The latter chapters are mathematics free and recount the stages leading up to the 16-year-old’s European Young Scientist of the Year Award. Most notable to me was the humility intrinsic in the provisional nature of discoveries and the embodiment of this truth as witnessed by the protagonists.

[Katy · Rating 4 out of 5]

This was a fun, if dense read. She does a good job of laying out the math such that you can absorb as much as you want/can to get by enough to understand what she accomplished and what her project entailed, while leaving open the opportunity to dive deep into the math should you so choose. I walked a middle ground in that I read a large portion of the math stuff, but I did hit a wall where I finally decided to move along to the narrative...which was even better. Just fun to read about somebody having found such passion at such a young age and applying it so well.

[Carol · Rating 3 out of 5]

I didn't know it was possible to enjoy a book about mathematics. This first-person narrative about a teenager's experiences as she wins an international science/math competition is nicely written. She gives the reader to skip the really mathematical chapters which arent' necessary for enjoying the book. There's a section on the Caesar Cypher which I'll use when my soph's read Shakespeare this year.

[Avempace · Rating 3 out of 5]

A charming coming of age story of a young woman mathematician/cryptographer. The good news is that the math involved was clearly and persuasively communicated at a level that most would find comprehendible. Details of her family background and in particular her interaction with her father, himself an academician and a mathematician, were both appealing and endearing. Recommended to all budding young scientists and mathematicians, especially those girls and young women amongst them.

[Katie · Rating 5 out of 5]

This is a fascinating book about a really bright girl and her journey learning about number theory, cryptography, and a bunch of other math stuff. Very easy to understand. Very inspirational! She encountered setbacks and frustrations and came across as a very normal person. I thoroughly enjoyed this book!

[Logophile · Rating 3 out of 5]

I have to confess that I lost interest in the math, though I did learn a little about the one-way functions that make public-key cryptography work, which had formerly puzzled me. I found Sarah's personal experiences with the science contests more interesting, and I'd highly recommend this book to any young person with an aptitude in math or science.

[Aaron · Rating 4 out of 5]

I love reading math and science books - and this one continues to encourage me to explore those worlds. Not only did it remind me of some of my former math classes, but it inspired me to do a little more research on some topics that I might not have thought about otherwise. I was also surprised at the ending, I thought there was a little twist that I didn't expect. Great story, Sarah!