Never thought I would use the words "Romance" "Suspense" "Thriller" and the History of Mathematics in the same sentence. Great book and worth reading. It is a gripping account of the events leading to the solving of one of the greatest puzzles in Mathematics.

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"Mathematical theorems rely on a logical process and once proven are true until the end of time," says Simon Singh, on page 21 of this impressive exposition of scientific method and the history of mathematics.

The author points out, under the rubric "Absolute Proof," that there is a difference between the "hard science" of mathematics and the guesswork, maybe, and make-believe of the "pseudo-sciences" (sociology, anthropology, linguistics, psychology and others). Singh goes on to say that the proofs acceptable in these pseudo-sciences "rely on observation and perception, both of which are fallible and provide only approximations to the truth."

Simon Singh has a Ph.D. in particle physics from Cambridge University. He worked for the BBC where he co-produced and directed their documentary film Fermat's Last Theorem, which is at the heart of the PBS/BBC/NOVA production The Proof, outlining Princeton professor Andrew Wiles' solution to Fermat's 400 year old problem. (I tried to purchase Fermat's Last Theorem directly from the BBC, when I could not get it from Amazon.com, but BBC prices are too steep for a poor "Yank")

Fermat's Enigma is the story of Frenchman, Pierre de Fermat, who happens to be one of the greatest mathematicians of all time. It is the story of the world's 400-year-long effort to solve a problem he discussed, later to become the "Holy Grail of Mathematics." The dust jacket says it is 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."

Every innocent school child, with an IQ greater that his shoe-size, is familiar with the Pythagorean theorem, which states that, in a right-triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The mystery of Fermat's last theorem is directly rooted in Pythagoras and ancient Greece.

Here's the problem under consideration by Fermat: x(to the power "n") + y(to the power "n") = z(to the power "n") where "n" is any number greater than 2. Can it be proved?

The equation represents an infinite series of equations each with a different value for "n". An infinite number of equations can never be solved, therefore it has always been impossible to prove that the underlying equation has no solution; i.e. there is no value for "n" which would make the equation balance.

This is exactly what the genius Frenchman, Pierre de Fermat, claimed to have done, almost 400 years ago, when he noted in the margins of Diophantus' Arithmetica: "I have discovered a truly marvelous proof which this margin is too narrow to contain." Thus was created a mystery and a problem not solved until Andrew Wiles came along.

"Wiles proof of the Last Theorem is not the same as Fermat's," Singh says on page 283. Fermat noted in the margin of his Arithmetica that his proof could not fit in the space available. "Wiles 100 pages of dense mathematics certainly fulfills this criteria," Singh continues, "but, surely the Frenchman did not invent modular forms, the Taniyama-Shimura conjecture, Galois groups and the Kolyvagin-Flach method centuries before anyone else.

So, if Fermat did not use Wiles' method and the tools available to Wiles, what did the Frenchman use? What was Fermat's actual proof and how did he arrive at his result? Wiles arrived at his own proof, his own way, and officially, Wiles has solved Fermat's Last Theorem.

While it appears that nobody knows for sure, exactly what Fermat did, or how he did it, I believe that [one person] knows, but remains incommunicado, like Lawrence of Arabia and Gordon of Khartoum. Fermat's mystery will have to wait just a little longer.

A beautifully written book that traces the development of classical number theory in a way that its "humaness", if you will, makes clear that even the most abstract of thinkers in this most abstract of all human endeavors, is very human, indeed. Particularly to my liking is the author's covering of the important women in mathematics, especially his excellent coverage of the contributions of French mathematician, Sophie Germain. That she had to work and publish under an assumed masculine name says a lot about the way we were; perhaps the way we still are in some instances. But finally revealing her identity to the great Guass, and receiving his praise for her work is simply delightful to read.

I cannot recommend this work too highly. A masterly performance that will reward the reader with at least a small appreciation of the power, the beauty of the human mind.

En este libro, el autor hace un recorrido histórico desde los orígenes de la criptografía hasta medios de encripción basados en computadoras cuánticas. Este libro enfoca la seguridad de los algoritmos desde un punto de vista practico sin necesidad de mucha parafernalia matemática. Si Ud. quiere disftutar de un texto general, técnico en ocasiones pero entendible en su totalidad, éste es el libro que debe adquirir. Por el contrario, si Ud. es una persona versada en el tema y desea profundizar sus conocimientos, debe optar por comprar libros de teoría de números y de álgebra abstracta, ya que éstas son la base de los algoritmos computacionales explicados en este libro. Excepcional !!!

"The Code Book: The Evolution of Secrecy from Mary Queen of Scots to Quantum Cryptography" by Simon Singh is a wonderful book about the history of code-making and code-breaking. What is most impressive about Singh is he is able to take the most complicated mathematical information (in my opinion) and explain it in layman's terms. Another more suitable name for "The Code Book could be Code-Making and Code-Breaking for Dummies: A Historical Perspective". Singh covers the history of encryption, tracing its evolution throughout time and outlining the impact cryptography and cryptanalysis has had on the world. World War II, the Enigma machine and how the fate of the world rested upon whether or not secret knowledge would fall into enemy hands, is discussed in great detail. From Singh's perspective, it would seem that the outcome of all military battles could be pre-determined by who had employed better cryptanalysis, as the most powerful weapon, is secrecy. Personally, what interested me most about "The Code Book" is its discussion about the Navajo Code Talkers, hieroglyphics, Linear B, and quantum cryptography. I also thoroughly enjoyed the author's humor and wit, ability to break things down so that a non-technological mind could grasp some of the most complicated of codes and his affinity for making the personalities who discovered the codes as well as the personalities who broke the codes, come to life. I would highly recommend "The Code Book" to anyone who is interested in cryptography, cryptanalysis, security, telecommunications, math, science, history or simply a good read.

Simon Singh can describe tails of drama, history, and common mathematical sense into a great book. While most people take cryptography for granted, Singh provides historical and simple examples to illustrate it's importance to mathematics and history. He details it's use in wars, especially World War 2, and commerce. He even delves into the political ramifications of strong versus weak encryption when discussing PGP.

Singh also provides easy to understand ways on how encryption works and even more intriguing, how to break it. He shows how all various encryption algorithms are done, and then how code breakers can decipher them, both in practical and historical consequences.

In the end, he even provides a challenge for would be decipherers out there. Granted, it's already been solved, it's still education and exciting that he offered a considerable amount of money for this challenge....

All in all, it's a fascinating book that will capture anyone's imagination, even if they hate history or math.

THE CODE BOOK is a beatuful overview of the history of cryptography. The book takes the reader from the simple ciphers of history (this is where Mary Queen of Scots comes in, but I thought that story was fairly far in the background), through the fairly radical improvements of the rennaisance, and truly shines in the discussion of the WWII Enigma machine and the truly amazing response of the English decoding aparatus. It appears that much material only recently became declassified, allowing Singh to discuss Enigma and the English code-breaking operation. Finally, Singh gets to the efforts to produce computer cryptography and the recent innovations that culminate in the "public key" encryption and the controversy over the PGP (pretty good privacy) program. This book was so exciting that I could not put it down. It is easy to read--no math in the text and plenty of appendicces with the formulas--yet reveals so much. On top of the beautiful exposition on cryptography, Singh also visits the public policy conflicts between national security and privacy. Not that those have any easy answers, but the conflict is very palpable.

Reading this book gave me my start in my self study of cryptography, its science and its history. While I will not pretend to be anywhere near an expert on the subject, I found this book very insightful. It is an easy read, and not tedious in any way. It is meant as a "science for non-scientists" type book, and more of a history than anything else. (I have only managed to solve the first two cryptologic challenges at the end of this book, but am diligently working on the rest in my spare time.)

The Code Book is a delightful treatment of the subject of cryptography. It is a nice combination of history, science, warfare and politics.

The author uses interesting historical events as background to narrate the different phases of what might be called the mainstream developments of cryptography and cryptanalysis. It is a captivating presentation.

The book started off with the story of Queen Mary of Scotland, and went on to cover the Caesar cipher, Vigenère cipher, the famous Enigma, the super-secret Colossus, and the modern day computer based encryption and decryption developments. The author also threw in a couple of interesting "sideline" stories, such as the Beale cipher, the Rosetta Stone, and the Navajo "code talkers" who played a key role in the Pacific theater during WWII.

My teenage son used to complain that most of the difficult subjects he learned in school would never have any use in real life. I gave him a copy of this book. The book is a compelling story of how science, engineering, mathematics, computer, linguistics, psychology are all critical pieces of this all-important game.

There are more technical treatises on this subject, and there are more lengthy and nuanced historical accounts on military intelligence as well. But this book is undoubtedly the best introduction to this uniquely fascinating subject.

I have always been fascinated by codes and Singh has put together a comprehensive book on the history of codes. Having read many books on codes, Singh was still able to enthrall me with some historical stories that I had not come across. It's not just technical stuff, but is written with the novice in mind as well. But the book holds enough technical information to keep the enthusiast interested as well. The version I bought has a crypt contest in the back, which I enjoyed working on - I was only able to solve the first 3 or so puzzles, but it was a lot of fun.

Great read.I was highly impressed by the fluency of the book. The author has tackled the insides of a very difficult and incomprehendable field not only in a manner that it come to grips with the lay persons but also in a way that he has happened to show the adventures and the joy of doing mathematics! Which is a feat in itself. Every now and then he takes us to the history of Mathematics and it's fore-bearers in such a way that it comes entwined with the history of mankind. I loved it the way he has successfully showed in the end that how the story of Fermat's Theorem has it's roots from the time of Pythagora's and how eventually Andrew Wiles takes the route of the mathematics from that of Greeks to Euler,to Euclid to Gauss and all the way to Shamura and Tanyaman to this day in the 90's; he makes one full circle, in solving this most difficult problem of mathematics.Bravo! However I did find one peice of historical narration out of place in the book which I'd like to point out over here, because if I don't, this review would not be of justice. The author while describing the granduer of the famous library of Alexandria has quoted that the library was brought down to it's demise first by the christians and then later by the Muslim conquerer Hazrath Umer Farooq in the 7th century AD. However the American Historian Hitti in his famous book "The Arabs:A short History" has dealt with this myth in his words:"The story that by Caliph's order Amr for six long months fed the numerous bath furnaces of the city with the volumes of the Alexandrian library incidentally, makes a good fiction but bad history.The great library was burned as early as 48 BC by Julius Ceaser. A later one reffered to as the Daughter Library,was destroyed about AD 389 by the Roman Emporer Theodosius.At the time of the Arab conquest, no library of importance existed in Alexandria and no contemporary writer ever brought the charge against Amr or Umer.(Pg70). So I really don't know where the author got his source of inform! ation on this matter, and I think I'd be justified to ask him that in the name of History the author should correct himself in the later editions of this book.

The author seeks to describe the events that led to the proof of Fermat's theorem and succeeds amply. Not only is the book informative, its very very enjoyable. The book does not require a math background. In fact the author takes care to properly introduce any math term or concept he uses.

Fermat was a great mathematician. In one of his notebooks he stated an equation and mentioned that the margin was too short for the proof of the statement. Later mathematicians found it impossible to prove this math statement. So hard was the problem that it became one of the most popular problems in mathematics and remained unsolved for centuries! Recently, a math professor from Princeton proved this theorem after a marathon effort.

The book introduces the reader to a lot of key mathematicians and interesting anecdotes associated with them. The best aspect of the book is that it presents events spanning centuries, in a manner that fits them together as parts of a solution to a single problem. Its not a sequential narration of events, instead its a coherent presentation of what was done over the years and how it contributed to the final assault.

Simon Singh's Fermat's Enigma is a very elegant book that accomplishes several difficult tasks: it acts as a brief history of number theory, explains the culture of the world of mathematicians, and acts as a window looking into the personal struggle of Andrew Wiles as he spends seven years attempting to solve a 350 year old riddle. This book is very accessible for non-mathematicians, and is the type of book that can inspire a young person who is mathematically inclined to become a mathematician -- similar to how Andrew Wiles himself became a mathematician. I particularly liked the portraits of the famous mathematicians who contributed to the proof over the period of time involved: Euler, Galois, Taniyama, Shimura, etc. The book is very nicely written; one never finds the book to be jarring or difficult to read. In its small format it is over 300 pages long, but it reads very quickly (less than 5 hours for me). The appendices contain some very elegant, simple explanat! ions of mathematical proofs. The manner in which the subject is made accessible is a testimony to the author's literary as well as technical skill -- something this easy to read must have been exceptionally difficult to write. Well worth reading, very high on my personal list.

Excellent book that takes the reader through one of Mathematics' most fascinating stories. This is not about whether you were good or bad in math at school, or are interested in Math, rather its about appreciating what makes Mathematics one of the most powerful things on Earth and why its appealing to so many. The author does a great job of giving a simple and historical explanation to the evolution of mathematics. This is an enjoyable read for someone who knows nothing about Math (thats me!).

For all the mathematical colleagues, this book has a minimum amount of notation, maybe little more than you can find in Treasure Island. It is a nice readable book, though, if you read it curled up on your couch with a cup of tea at hand, and nothing on mind.

If you are not a math or science major, you would ask me: why should I read this book? I would answer: because math appeals to a large number of people, and, you got to admit it, in this period of time people must know something about it. This theorem, in addition, had puzzled great mathematicians (even geniuses) for more than three and a half centuries. I think this means that it had passed around so many mathematical schools and fields.

The book starts with some exploration of Greek mathematics, being the base of modern thinking. Here we must see something about the Pythagorean Theorem, because it inspired the Fermat's Last theorem. The author speaks about a nice incident about a Pythagorean being killed for believing that there existed some numbers other than the Rationals (They were called Irrarionals later, even though they are as rational to the modern mathematics as any other numbers, say the quaternions).

He moves then to speak about Fermat, the French mathematician. He mentions that Fermat did not in fact write a proof for his theorem due to the limitation of the margins of his copy of Diaphintine's "Arithmetica,"! this caused the whole mathematical community to suffer 385 years to construct a plausible proof.

After that, we see how Euler proved the case when n = 3. Then Sophie Germain prove it, inspired by Euler, for the Germain prime numbers (which are some special prime numbers). This eliminated most of the cases, yet there still are infinitely many cases to check. The book does not go into technicalities, but you can enjoy reading about the backgrounds of some of brightest mathematicians of the 19th century.

Then comes some account on cryptography, as being the direct application of Number Theory, followed by the story of how Andrew Wiles, the most famous mathematician of our time, came to prove this theorem.

It proved to be even a harder task. It involved some modern up-to-date mathematics ... some fields of Number Theory called: "Elleptic Curves" and "Modular Forms."

Finally, I would like to say that I read this book when I was at my junior year in the department of mathematics at the University of Missouri-Columbia, I DID NOT NEED MUCH MATH TO UNDERSTAND IT. It, as a matter of fact, inspired me to continue my grad studies in the subject of Number Theory; unfortunately my real mathematical interests won the quarrel and I had to settle with Geometry.

I think any person with some understanding of the notion of mathematics may be very able to enjoy it as much as I did. If you want an introduction to this "mysterious" discipline, this book would provide you the best read.