xn + yn = zn, where n represents 3, 4, 5, ...no solution

"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."

With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

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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.

44 of 45 found the following review helpful:

An engrossing page turner for the mathematically inclinedMay 15, 2000
By LackOfDiscipline
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.

28 of 28 found the following review helpful:

Superb combination of historical progress and modern drama.May 22, 2000
By Allan D. Bennett
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.

13 of 13 found the following review helpful:

A captivating tale of human perseverance and achievementDec 31, 1999

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.

13 of 13 found the following review helpful:

Excellent Introduction to Fermat's Last Theorem - Great Drama, Great MathematicsJan 18, 2006
By Michael Wischmeyer
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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