Fermat's Last Theorem became the Holy Grail of mathematics. Whole and colorful lives were devoted, and even sacrificed, to finding a proof. Leonhard Euler, the greatest mathematician of the eighteenth century, had to admit defeat. Sophie Germain took on the identity of a man to do research in a field forbidden to females, and made the most significant breakthrough of the nineteenth century. The dashing Evariste Galois scribbled down the results of his research deep into the night before venturing out to die in a duel in 1832. Yutaka Taniyama, whose insights would ultimately lead to the solution, tragically killed himself in 1958. On the other hand, Paul Wolfskehl, a famous German industrialist, claimed Fermat had saved him from suicide, and established a rich prize for the first person to prove the theorem. And then came Princeton professor Andrew Wiles, who had dreamed of proving Fermat's Last Theorem ever since he first read of it as a boy of ten in his local library. In 1993, some 356 years after Fermat's challenge, and after seven years of working in isolation and secrecy - "a kind of private and very personal battle I was engaged in" - Wiles stunned the world by announcing a proof, though his own journey would be far from over. Fermat's Enigma is the story of the epic quest to solve the greatest math problem of all time. A human drama of high dreams, intellectual brilliance, and extraordinary determination, it will bring the history and culture of mathematics into exciting focus for all who read it.
The achievement must be placed in historical context in order to better appreciate the amount of work and innovation it took to finally prove the theorem.
Both Singh and Amir Aczel wrote very good accounts of the process of solving the problem. They both did a good job of summarizing the history of the problem, they followed through with the building of the solution through each time consuming pain staking step. Indeed the solution is a literal accumulation of important results from many mathematical developments from over the past century. Each one of the steps illuminating the path toward the final proof. The solution encapsulates some of the most innovative solutions to mathematical problems that are seemingly unrelated to Fermat's Last Theorem.
It seems to me that Singh did a more thorough job of explaining the proof. The pace was a bit more leisurely and collegial. Aczel's account seemed more rushed, less considered, and had more of a rush to publish flavor. Not that is was a bad account.
I think that Singh had a more thorough understanding of the history of the problem because he took more time to set up the problem in its historical context. His explanations were also more detailed and better thought out for us amateur mathematician, who understand the fundamentals but not the details of rigourous proof.
Regardless, it was a treat to read and gave me a rush of discovery that usually comes with finishing a good murder mystery rather than an account of a mathematical achievement.
Cambridge mathematician Andrew Wiles announced a solution for Fermat's last theorem in 1993 but after a flaw was discovered in the proof, Wiles had to work for another year--he had already laboured in solitude for seven years--to establish that he had solved the 350-year-old problem.
But it's much more than that, since the final proof of Fermat's Theorem involves so many other math concepts. This book starts and ends with Fermat, but in the middle it is more like a grand tour of all the mathematical developments that make the proof even possible. It's interesting to read about all the different dead ends and other productive findings (that had tangentially made it a little more possible to solve Fermat, but whose main contribution was in some other area). Also, reading about Galois's amazing life always makes me giddy. I mean, I've read about him before, but his story is just so crazy--math genius turned revolutionary thrown in jail involved in affair ends in duel, scribbles out his last thoughts the night before he dies... amazing.
But don't expect to understand how the proof actually works by the end. The proof itself is over 100 pages, so there is no way a normal non-math genius can understand it. But you will get a general idea of the approach/trajectory/style of the final beast. Also, some of the math concepts leading up to it are quite easily comprehensible. I wouldn't recommend this book to a math whiz... it's more of a fun read for the layperson.
It would ultimately be more satisfying if the proof were a short elegant thing that didn't involve latest groundbreaking discoveries in math. But maybe the bright side is that we can still wonder about Fermat's original (alleged) proof that was never written down. It had to be different from Andrew Wile's proof; does it exist? Or was Fermat bluffing? Or did he make an error in his proof?
a diner was heard to be chargin'.
"I HAD to write there,"
exclaimed waiter Pierre,
"I couldn't find room in the margarine."
Ever since I recently stumbled upon the documentary called 'The Proof' I've become extremely interested (almost obsessed) in Wiles's proof of Fermat's last Theorem and have been searching for a good book that would provide me with a real, mathematical explanation of it (mainly the connection between modular forms and elliptic curves), because the documentary was rather simple and basic. Unfortunately, so was this book and my quest continues.
Nonetheless, this book is very interesting and well written, and shows you how many things that appear to be simple and almost intuitive can be incredibly complex (that's what's so beautiful about math). In situations like this, people always tend to give all the praise to people like Andrew Wiles, without realizing on how much work and discoveries made by other people his work relies on. And even though Wiles deserves all the fame and recognition he can get for his persistence and determination, it's nice to see all the other great mathematicians who greatly contributed being mentioned. Like old saying goes: nanos gigantium humeris insidentes, and if anything, by showing how complex the proof is, it leaves you wondering, did the Fermat really have the solution?
If you are only slightly interested in mathematics and were just curious about this certain topic and ideas on which the proof was based on, or are looking for a good place to start, I would definitively recommend this book. But to be fair, you can get all of that by watching previously mentioned documentary and it would cost you much less time. On the other hand, if you want something more complex and mathematical, you won't get it here.
The story is full of odd characters, many of them obsessive. Most of them not likeable (which adds to the story). The story of Andrew Wiles, the man who finally cracked Fermat's Last Theorem, is quite good, and is the reason this book was written, but is really only a small part of this tale. It is written as part of the overall history, not just a major part of it.
While the book is about the path to Fermat's Last Theorem, but because so many new ideas came about from the path of solving it, this book can be seen as a brief history of math. Highly recommended if you like pop-science type books and mathmatics, but without all the hard stuff.
I'll admit it, I wasn't really looking forward to this book. I did consider skipping it, I really would have if I wasn't so obsessive compulsive that I really have to read all of the books in the set (in numerical order). But I read the back and decided to give it the benefit of the doubt, I mean, surely I was just feeling unenthusiastic because of the subject matter; maths and I have never really gotten along very well.
I'm the girl who once got a grand score of 26% in a maths test (and was going to be refused entry into the GCSE maths class). I managed to overcome this, scored a 1 at Standard Grade (thank you Scottish education system) and then decided to quit while I'm ahead. Ironically, since giving up maths, I've become far more interested in it. I like discovering little mathematical tricks and quirks; my doodles at work often incorporate visual representations of the fibonacci sequence (yup, I'm a geek).
So I decided that actually, I might just fall in love with this book. Plus the blurb on the back said that you didn't need to be good at maths to read it. It really sounded like something I could get into. Plus, the day I started reading it was the day that the news was focusing on the fact that numeracy standards have slipped and many people can't do basic maths problems. It meant I could sit feeling smug and intellectual while I was watching it. History, maths, a centuries old puzzle; by the time I started reading it, I'd really talked it up in my mind.
Unfortunately, after all that, it was a bit of a let-down.
Despite the assertion that you didn't need to be a whizz at maths to read the book, you kind of did. To begin with I was kind of expecting the book to be a bit like those The Knowledge books (the general knowledge versions of the Horrible Histories series). It seemed to have a bit of a sense of humour and there were photos and diagrams (all reproduced very well I have to note, considering it was all black and white).
But I felt like I was missing huge chunks of the plot, there were aspects of mathematics which were explained in the minutest of detail, while other bits which were important to the solution on the Theorem were sort of glossed over. I don't think I ever truly understood the concept of the 'proof' anyway. Plus, you knew the outcome from the very start, it was going to be solved. I wonder if there could have been a better way of structuring it, considering the fact that the events of the book were highly publicised at the time it would have been tricky.
There were other bits of the history of the Theorem that I was a bit more interested in, and there was so little of the book which was actually devoted to Andrew Wiles' role in the discovery of the solution that I would have quite happily read about all the other people, rather than him. I'd quite like to know more about some of the other's involvement.
I did get through this book quite quickly, though it was partly because I just wanted to get to the end. I kept on hoping that I would get to a point where I would really enjoy it and everything would come together, but it never really happened. I'm sure someone more mathematican than me would enjoy the book more but it certainly hasn't inspired me to track down more maths-themed reading material!