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1 of 1 people found the following review helpful
5.0 out of 5 stars Enter the world of the mathematician.
Pierre de Fermat, a seventeenth century French mathematician, challenged his colleagues and perhaps future generations of mathematicians to prove the following formula: a^n + b^n = c^n will be false for n > 2. Fermat wrote in the margins of his notebook that he had proven the assertion, but he did not outline it.
Singh's book chronicles the development of...
Published on April 1 2000 by Walter Chang

versus
3.0 out of 5 stars Concerning Simon Singh's Exploration of Fermat's Last Proble
The author does an admirable review and explanation of Fermat's Last Problem, but only up to a certain point. He should have tried to get Andrew Wiles to be more explicit about about the details of his proof and if Wiles lacked the capacity to provide a sequence of simple unambiguous steps of explanation, there are certainly others who could have helped both Wiles and...
Published on Feb. 21 2000 by Paul Haines


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1 of 1 people found the following review helpful
5.0 out of 5 stars Enter the world of the mathematician., April 1 2000
By 
Walter Chang (Anaheim, Ca USA) - See all my reviews
(REAL NAME)   
Pierre de Fermat, a seventeenth century French mathematician, challenged his colleagues and perhaps future generations of mathematicians to prove the following formula: a^n + b^n = c^n will be false for n > 2. Fermat wrote in the margins of his notebook that he had proven the assertion, but he did not outline it.
Singh's book chronicles the development of mathematics from ancient Greece to the 1990s.
Singh begins with a discussion of Pythagoras and his famous theorem for calculating right triangles. It is the Pythagorean formula that is the basis for Fermat's equation.
Singh then discusses the many famous mathematicians that had attempted to reproduce Fermat's proof. Although they were able to prove the formula's validity for specific values of n, no one had succeeded in proving it for infinite values of n. Without this proof of universality, there had existed the possibility that some value will disprove Fermat's assertion.
Singh then focuses his attention on Andrew Wiles, the man who would succeed where others had failed. After studying the futile attempts of his predecessors, Wiles decides to employ twentieth century mathematics. With developments from other colleagues in other areas of mathematics, Wiles embarks on a personal and secretive mission to resolve this enduring problem and a contemporary mathematical challenge.
Fermat's Enigma is a nontechnical exploration of the mathematics and mathematicians from ancient Greece to the twentieth century. It requires knowledge of only high school mathematics.
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1 of 1 people found the following review helpful
4.0 out of 5 stars Amazing Mathematical Saga, June 11 2002
By 
D. Kapoor (Australia) - See all my reviews
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Singh and Lynch have successfully presented one of the most abstract subjects in a simple to understand language. For those who put down a Maths book by looking at the complex equations: Fear Not, this one does not go too deep into equations and relies more on plain English to convey the point. I think that Appendixes could have been a bit more descriptive. Overall it was a fun read. I highly recommend this one for Mathematics appetite of Not-So-Mathematical.
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5.0 out of 5 stars A human drama unfolds ... in a mathematical world!, May 7 2002
This is a remarkable and engrossing human story about the search for the proof to the age old Fermat's last theorem. A story which tells the tale of one man's unflinching determination and single minded devotion to the cause of this proof. The events which unfold and the riveting account of Andrew Wiles journey to glory are told in this gripping tale by Simon Singh. Singh's master storytelling abilities are very well exemplified and will be appreciated by one and all. Those not inclined mathematically will also gain insights and concepts of mathematics and also get a peek at the lives of the mathematicians who are featured in this book.
Andrew Wiles read about this theorem when he was barely ten year old in a library while flipping through one of E.T. Bell's book. The rest as we know is history because this particular moment became a turning point in young Wiles life. This would force him to take a career in mathematics and lead a rigorous life in mathematics. Later he would be shutting and isolating himself from the outside world so that he could devote his complete attention to the task at hand - to solve this 17th century conjecture devised by the great Pierre Fermat. History saw this theorem remaining unsolved for 350 years, which eluded mathematicians like Euler, Sophie Germain, Lame, Kummer, Cauchy et al. but who nevertheless had their own bit of contribution to the proof in particular and mathematics in general.
Andrew Wiles mathematical proof of the century was not without its share of pitfalls. After announcing the proof of Fermat's Last Theorem in June 1993 with much fanfare and publicity, Wiles didn't have the wildest idea about what was in store for him... something which will almost make him accept defeat...
Though Prof. Wiles succeeded in his endeavor, his proof was based on post-Fermat mathematical ideas like the Taniyama-Shimura conjecture, Galois group theory, Iwasawa theory and the Kolyvagin-Flach method. Fermat on the other hand had claimed that he possessed the proof for the theorem which obviously was based on mathematics of his time...
A great read. Recommended for one and all.
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5.0 out of 5 stars MATHEMATICAL PROOFS ARE ABSOLUTE, March 24 2002
By 
M. A. Treu (Bordentown, NJ USA) - See all my reviews
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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.
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5.0 out of 5 stars A book to read, not study, Jan. 26 2002
By 
J. Mack "reviewer2" (Pacific, USA) - See all my reviews
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Simon Singh has written an interesting story that unfolds in narrative style, about the solution of a timeless mathematical riddle. Fermat was a judge in 17th century France who dabbled in mathematics. He conjectured that the Pythagorean theorem (a squared + b squared = c squared) is never true for any other whole number power (e.g. a cubed + b cubed would never equal c cubed in any case). Maddeningly to later mathematicians, Fermat boasted in the margin of a paper that he had the proof for his conjecture.
Singh briefly reviews some history of mathematics, backtracking to Pythagorus himself and then unfolds through the ages developments in the quest for mathematical proofs. The human face of the mathematicians adds drama--the book is essentially about real people and their intellectual pursuits, challenges and failures or successes.
In the early chapters, the story is easily comprehended. Later chapters delve a bit more into the math itself, but for the purpose of unfolding the basic story, not to teach the reader "how to".
The book trumpets the final success in proving Fermat's conjecture by Andrew Wiles, which was front page news at the New York Times. That any man succeeded is truly a marvel and this account allows each of us to appreciate and share in human nature which struggles and strives for answers.
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4.0 out of 5 stars A compelling account of mathematicians, Dec 10 2001
By 
Singh's book is not just about math or the history of Fermat's Last Theorem; it is an account of some of the greatest mathematicians of all time. It was interesting to read why some mathematicians love their discipline so much, and I appreciate that Singh told the life story of each mathematician involved with Fermat's Last Theorem. The mathematics within the text is so simple it seems as if anyone can do math, and it is interesting to see how many major developments were necessary before the infamous problem could even be solved. Sometimes it is a little difficult to remember all the mathematicians' names and contributions, but that's because there are so many people who contributed to the solving of Fermat's enigma. However, Singh compellingly recounts the saga behind the mystery, making this book a must read for anyone who is involved with math or just appreciates a fascinating, full-circle story. My only criticism is that the Epilogue does not adequately describe the full effects solving Fermat's Last Theorem has had on Andrew Wiles, but this book was written shortly after the theorem was solved. Perhaps Singh will write a follow-up book in which he explores more in-depth the ramifications this problem has had on Andrew Wiles, the math community, and mathematics as a discipline.
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5.0 out of 5 stars Fascinating history of a math enigma, Oct. 28 2001
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.
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4.0 out of 5 stars Fermat's Penultimate Theorem, Sept. 13 2001
By 
Amazon Customer "bwillson2" (San Diego, CA United States) - See all my reviews
I have to wonder, after reading Fermat's Enigma, whether his next-to-last theorem was perhaps a postulation of how many people he could get to sacrifice their lives by cryptically formulating a theorem, scribbled in the margin of a book.
Singh's look at this challenge takes a relatively populist approach by first giving something of a history of mathematics throughout the ages. As an engineer, some of the names are familiar to me (Fourier being the most notable). By seeing how seemingly every big name in mathematics either attempted or did work that was subsequently used in an attempt on a proof of Fermat, one gets a greater sense of the connectedness of theoretical mathematics. Furthermore, that which was once considered theoretical is often transformed into the practical.
Not being a theoretical mathematician myself, the latter-20th century names were more unfamiliar and the work more eclectic. Eventually, the book moves from the historical aspect into the personal quest of the man who eventually proved Fermat's last theorem.
If you believe that theoretical mathematics is a quest unto itself then the end of the story is satisfying as well.
The rest of us are left with the feeling that the final chapter has yet to be written. We have yet to see whether Fermat's name can be uttered with Fourier, Maxwell, Shannon, and others or whether we will have to be satisfied with Fermat as a story of curiosity, a quest--undertaken by many--to answer the gauntlet thrown down by a prankster.
In that sense, Fermat's "other" theorem has long since been proven.
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4.0 out of 5 stars Fermat's Penultimate Theorem, Sept. 13 2001
By 
Amazon Customer "bwillson2" (San Diego, CA United States) - See all my reviews
I have to wonder, after reading Fermat's Enigma, whether his next-to-last theorem was perhaps a postulation of how many people he could get to sacrifice their lives by cryptically formulating a theorem, scribbled in the margin of a book.
Singh's look at this challenge takes a relatively populist approach by first giving something of a history of mathematics throughout the ages. As an engineer, some of the names are familiar to me (Fourier being the most notable). By seeing how seemingly every big name in mathematics either attempted or did work that was subsequently used in an attempt on a proof of Fermat, one gets a greater sense of the connectedness of theoretical mathematics. Furthermore, that which was once considered theoretical is often transformed into the practical.
Not being a theoretical mathematician myself, the latter-20th century names were more unfamiliar and the work more eclectic. Eventually, the book moves from the historical aspect into the personal quest of the man who eventually proved Fermat's last theorem.
If you believe that theoretical mathematics is a quest unto itself then the end of the story is satisfying as well.
The rest of us are left with the feeling that the final chapter has yet to be written. We have yet to see whether Fermat's name can be uttered with Fourier, Maxwell, Shannon, and others or whether we will have to be satisfied with Fermat as a story of curiosity, a quest--undertaken by many--to answer the gauntlet thrown down by a prankster.
In that sense, Fermat's "other" theorem has long since been proven.
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5.0 out of 5 stars Suspense Packed, Couldn't put it down, Aug. 24 2001
By A Customer
I'm not a book commenter type, in fact its my first book comment, but I was just compelled to write how good I thought this was, especially for a math book. Even though I saw the movie on Wiles beforehand, I kept reading captivated to get to the end and see how it ended even though I saw the movie about Wiles proving Fermat's theorem. The book wasn't overwhelming in the math, in fact, the book was great just skimming the math and reading the really entertaining story of the history of math, to the Fermat notorious theorem, and what turns into the legend of Andrew Wiles by his limitless courage against what seemed impossible doing what so many have failed to do before him, proving Fermat's theorem forever. Its a great story overcomming adversity which will probably inspire you in your struggles, even in other sujects besides math, and even to life in general. If your thinking about getting it I would (and did) plus, the price is right. "Wiles the wiley, persistence of astonishment, your one of the greats now - Immortal for all time!"
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Fermat's Enigma
Fermat's Enigma by Simon Singh (Paperback - Sept. 14 1998)
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