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54 of 55 people found the following review helpful
5.0 out of 5 stars An engrossing page turner for the mathematically inclined
Wow! I just finished this one and was sad to see it end. The writing is so compelling that I had to stay up to finish it in one sitting. If you are not familiar with Fermat's Last Theorem and why it is such a "big deal", let me just tantalize you by saying that it is basically a "generalized" version of the Pythagorean theorem (the one involving...
Published on May 15, 2000 by LackOfDiscipline

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14 of 16 people found the following review helpful
3.0 out of 5 stars A riproaring romp through the history of maths
Pierre de Fermat was a state official in seventeenth century France. Forbidden from fraternizing with the locals (whom he might meet in the course of business) he resorted to a solitary hobby -- mathematics. His talent was prodigious, but he was notorious for leaving only sketches of the proofs of his conjectures for others to complete. Over the centuries, all his...
Published on September 15, 1998


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54 of 55 people found the following review helpful
5.0 out of 5 stars An engrossing page turner for the mathematically inclined, May 15, 2000
By 
LackOfDiscipline (FLAGSTAFF, AZ USA) - See all my reviews
This review is from: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (Paperback)
Wow! I just finished this one and was sad to see it end. The writing is so compelling that I had to stay up to finish it in one sitting. If you are not familiar with Fermat's Last Theorem and why it is such a "big deal", let me just tantalize you by saying that it is basically a "generalized" version of the Pythagorean theorem (the one involving right triangles, which you have surely seen if you have ever taken trigonometry in high school), although it asserts that higher forms of the Pythagorean-style equation are unsolvable.
Singh gives an exquisitely detailed history of the problem going all the way back to its ancient Greek roots (i.e. Pythagoras), proceeds through numerous failed attempts to solve Fermat's challenging theorem by the great mathematicians that succeeded him, and finally concludes with the (initially uncertain) triumph of Andrew Wiles, who posessed the genius to prove the Taniyama-Shimura conjecture (which implies the truth of FLT) and solidify a previously precarious bridge to vast new mathematical wonderlands.
If you enjoyed mathematics at some point in your life and think that interest may still be lingering within you, then you may want to get this one fast - your curiousity and admiration will be revived. One of the best mathematical popularizations around, and an historic scientific/intellectual achievement supremely documented.
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72 of 75 people found the following review helpful
5.0 out of 5 stars A fantastic trip through mathematics and history, November 18, 2000
This review is from: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (Paperback)
After enjoying Singh's "The Code Book" I picked up a copy of Fermat's Enigma. The problem itself was somewhat interesting to me, but I hoped Singh presentation of the story would be as good as "The Code Book". I wasn't disappointed. The solution to the problem is wrapped in a compelling story that takes you through the history of mathematics, starting before Fermat's time. Along the way Singh takes time to point out both the highlights and tragedies of mathematics, while weaving in elements of Andrew Wiles' life.
While the math behind the final solution to be problem may be out of reach for most people, Singh successfully communicates the essence of the mathematics used. The book is not complex or saturated with equations and is accessible to just about anyone. For those more interested in the mathematics, Singh includes a complete set of appendices containing problems and proofs from each era of mathematics he discusses.
All in all, a great read. Highly recommended.
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37 of 37 people found the following review helpful
5.0 out of 5 stars Superb combination of historical progress and modern drama., May 22, 2000
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This review is from: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (Paperback)
As an undergraduate math major in the late 1970's, I remember how my algebra professor used to chuckle that anyone who solved the Fermat conjecture would get an "A" in his course. (Some of us got A's anyway.) So I had to pick up a copy of this book when I saw it, and I couldn't put it down until I finished it.
Singh does a wonderful job of intertwining the history of Andrew Wiles' life-long fascination with the Fermat conjecture with the history of attempts to solve the problem through the centuries. The necessity for Euler to introduce complex variables into his solution for the case n = 3 gives the first indication that Fermat was probably toying with (ultimately) many generations of mathematicians who would never find a proof that could "fit neatly in the margin" of a page. While it takes a fairly broad background in mathematics to appreciate the book, one does not need to be a specialist in algebraic number theory to follow Singh's historical development of the progress toward final solution.
The description of Wiles' attempt to keep his work secret, and of the inadequacy of his first attempt at proof, reads like a first-rate cliffhanger. A splendid read.
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25 of 27 people found the following review helpful
5.0 out of 5 stars Think of the book as a great mystery�, August 2, 2000
For if you are to approach this book as a work that will lead you to an understanding of a theorem that took 350 years to solve, you might miss a great tale. As others have stated, High School Math will suffice, and for those who may be a bit rusty in Math in any event, the book is still very much worthwhile. The book mentions that some of the Math is understood by perhaps 5 people in the world. If high-level Math concepts were required to enjoy this book, the Author could just have made half a dozen copies.
A notation in a margin started 350 years of effort to solve, or rather prove a theorem that Pierre de Fermat described thusly "I have discovered a truly marvelous proof, which this margin is too narrow to contain". I recently read a comment by Stephen Jay Gould that Mr. Fermat may not have known the proof. His suggestion was that no amount of space allotted by any margin would allow for the proof. I certainly am not qualified to question either individual, but the space eventually used for the proof 356 years later by Professor Andrew Wiles of Princeton may answer the query for you.
Math is often put forth to show something that is universally true, a discipline that transcends language, Nations, and their Cultures. Math "is" and always will be, it allows for no opinion, it works or it does not. This book exposes the reader to a lifetime fascination for Professor Wiles, as well as the 7 years of near isolation it took to solve the mystery. If I understood the text, there were actually requirements needed for the proof that the mechanics for expressing those thoughts with Math did not exist, for Professor Wiles or anyone else. He could not invent truths, but he, and many who worked on this theorem for centuries were required to create new tools, prove the new tools were indeed valid themselves, and then use them to further their quest for the ultimate answer.
The book is also a Historical work of the science and those that labored for the better part of 4 centuries for the answer. It is a remarkable achievement, and it makes for a great use of one's reading time. As for the Author Mr. Simon Singh, he must be given tremendous thanks for his ability to bring this story to a wide audience that otherwise would have had no access to the famous enigma of Mr. Fermat.
Fascinating!
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14 of 14 people found the following review helpful
5.0 out of 5 stars A captivating tale of human perseverance and achievement, December 30, 1999
By A Customer
This review is from: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (Paperback)
Simon Singh manages to hold the reader in constant suspense, from his description of the origins of modern day mathemathics in Ancient Greece, to Wiles' eventual triumph in solving one of the World's most lasting mathematical enigmas - Fermat's Last Theorem.
The statement of Fermat's Last Theorem appears so simple, yet it survived rigorous scrutiny and remained unsolved for hundreds of years. Enter Andrew Wiles, the timid mathematician who became so engrossed in tryng to solve the problem that he lived in hermit-like conditions for seven years.
Singh seemingly enters into the very soul of Wiles, vivedly describing his secret seven year quest, the elation at solving Fermat's Last Theorem, the sheer horror of discovering an error and the eventual triumph of finally succeeding.
The reader is left with an undisputed admiration for the character of Wiles and it is guaranteed that this book will leave a lasting impression.
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11 of 11 people found the following review helpful
5.0 out of 5 stars An excellent account of the solving of the puzzle, January 17, 2001
This review is from: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (Paperback)
When Andrew Wile came through with his proof in 1993, I was flabbergasted. In my undergraduate and graduate days, this was it, THE prize in mathematics. The fact that there are two popular accounts on this topic is a tribute to how special an achievement proving Fermat's Last Theorem has become. Prior to to the solution, there is at least one book for the layman that Eric T. Bell had written that illustrates the difficulty of the problem.
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.
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11 of 11 people found the following review helpful
5.0 out of 5 stars don't worry if you're a dud at maths!, December 29, 2000
This review is from: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (Paperback)
Being barely able to balance a chequebook myself I approached this book with some caution - but Singh's other recent work "The Code Book", had really excited my interest and I wanted to read more of his work. That this one was about applied mathematics and complex formulas was a pretty daunting subject to tackle but I relied on the fact that Singh seems to be able to tell a historical story as well as simply explain quite complex technical issues. I was not at all disappointed. Singh weaves together hundreds of small and seemingly insignificant incidents to tell a great, and at times very suspenseful story. He seems to have a knack for finding simple explanations, diagrams and examples to gradually build this picture. Not that I feel I will be enrolling in any advanced maths courses anytime soon, about page 160 I found the technical going really tough, but by the then the human element of the story had me absolutely gripped and I wanted to read it to the end. It also helps that there is a little humour in it to help the less than able reader on the way so at one stage one mathematician is quoted as saying, "I was completely astonished because it had never occurred to me to add the extra gamma-zero of (M) structure, simple as it sounds." Yeah right!
To tease us all Singh has included a number of, as yet, unproved equations at the end of the book. So if you feel really inspired......
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14 of 15 people found the following review helpful
5.0 out of 5 stars Excellent Introduction to Fermat's Last Theorem - Great Drama, Great Mathematics, January 18, 2006
This review is from: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (Paperback)
I glanced through the pages, noted the absence of equations and proofs, and deemed Fermat's Enigma as just one more fluffy book on a widely publicized technical topic. I was absolutely wrong. Fermat's Enigma is a superb introduction to the "epic quest to solve the world's greatest mathematical problem".

Fermat's Enigma is not a mathematics book, but a book about mathematics. Andrew Wiles' proof, more than 100-pages in length, is quite formidable, and not readily mastered by mathematicians. Nonetheless, Singh does a credible job of explaining the nature of the theorem, the obstacles encountered over the past 350 years, and the breakthroughs that made the proof possible. Not only will it appeal to general readers, but I suspect that undergraduate math majors would find it advisable to read Fermat's Enigma before tackling more advanced works.

This short book begins well and improves with each subsequent chapter. It offers drama, the fascinating story of the brilliant, confident, obsessive, and secretive Andrew Wiles. It is history, the story of a monumental struggle by great mathematicians during the past three centuries to prove an apparently straight-forward conjecture. And it is mathematics.

Singh begins with more familiar topics like the Pythagorean theorem, the infinity of primes, and complex numbers. His clear, lucid explanations soon target elliptic curves (equations), L-series, modular forms, M series, and the critically important Taniyama-Shimura conjecture. He superbly explains two important kinds of mathematical proofs: proof by contradiction and proof by induction. He even explains Galois group theory, differential geometry, and the Kolyvagin- Flach method of solving elliptic equations with such ease that I felt that I was working alongside Andrew Wiles in his Herculean effort.

Singh's narrative account is an emotional roller coaster. I was excited when the young Japanese mathematicians Yutaka Taniyama and Goro Shimura posed their unexpected conjecture linking elliptic curves with modular forms. I applauded Gerhard Frey's remarkable insight: proof of the Taniyama-Shimura conjecture would ensure that Fermat's last theorem was true. I cheered when Barry Mazur over a cup of cappuccino suggested to Ken Ribet that the way forward would be to add some gamma-zero of (M) structure. (It mattered not that I didn't understand why or how.)

On the downside I shared Andrew Wiles' anxiety as he continued his desperate efforts to overcome a fatal flaw uncovered by journal reviewers. The pressure on him to publish his proof, even though not finished, was unbearable. He (we) needed more time. I shared his despondency as time was running out and failure seemed likely. The suspense, even though I knew the outcome, was intense. I was more relieved than happy when Wiles suddenly saw his way clear. I was too tired to cheer.

Fermat's Enigma is an exceptional book.
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9 of 9 people found the following review helpful
5.0 out of 5 stars A Very Nice Non-Mathematical Introduction, April 20, 2003
This review is from: Fermat's Last Theorem (Paperback)
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.
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11 of 12 people found the following review helpful
5.0 out of 5 stars Singh and Lynch's Fermat's Enigma, August 12, 2000
This review is from: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (Paperback)
Pierre De Fermat was in my opinion the greatest mathematician of all time except possibly for Pythagoras. We are still discovering astonishing things about him. He lived in the 1600s, mostly before Newton (with a slight overlap), but he invented/discovered large parts of the calculus before Newton. He invented analytic geometric before Descartes (Descartes was so furious at his secretiveness that he spent much of his life trying to ruin Fermat's career as a government lawyer/official in France). With Pascal, he invented probability theory. He invented modern number theory, which is key to cryptography among other things. The search for the proof of Fermat's Last Theorem resulted in the founding of several major branches of advanced algebra and number theory. He discovered major results in physics including optics before Newton and in fact in my opinion may have anticipated parts of Einstein's special theory of relativity because of his interest in optics (where he correctly found that light slows down in water, contrary to Descartes' findings) and the similarity of the quadratic(square) expression in Fermat's Last Theorem to the vital beta or 1/beta factor in the Lorentz contraction of special relativity. Fermat was roughly 300-350 years ahead of his time, and the only scientist who was more ahead of him appears to have Leonardo Da Vinci of the Renaissance who may have been 400 or so years ahead of his time. Even Einstein was only a few years ahead of his time because the mathematics apparatus was already in place when Einstein reinterpreted it from a physics viewpoint. McInerny's review is very good, but don't be surprised if somebody discovers a much shorter proof than Wiles' based on the reinterpretation of the word "margin" to mean difference in variables/numbers. Go out and buy this book.
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