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ByWalter Changon April 1, 2000

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.

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.

ByAmazon Customeron March 10, 2001

I may have to apologize for not as raving as other reviewers on this book by Simon Singh. To be fair to the book and thus the author, I do find a fairly fluent narration on the mathematicians who attempted or contributed to solve the Fermat's Last Theorem. Meanwhile, I personally don't find the writing style and the organization of the materials to be particularly appealing.

We never hold any slightest hope that a 285-page book (the paperback edition) would offer us a clear understanding on how the proof, that incorporates so much of the techniques in the modern number theory, is devised. The book basically steers itself all clear from the mathematics.

These below are what significantly push my rating of this book to a low range:

1. Too much on who the mathematicians were rather what they did to the proof. Approximately two-thirds of the book is on stories behind those mathematicians who one way or the other got involved in the Last Theorem. Those may be interesting from a historical perspective but are simply irrelevant to how we came to the proof.

2. The author starts quite early in the book to tout mathematical proof as an "absolute proof" that "[m]athematical theorems rely on this logical process and once proven are true until the end of time. Mathematical proofs are absolute." By contrast, "... the scientific theory can never be proved to the same absolute level of a mathematical theorem ... So-called scientific proof relies on observation and perception." An account on the differences between the two is beyond the scope here. Apparently, the author either doesn't know those are apples and oranges or, worse, attempts to elevate mathematical proof to an "absolute" level it might not need at all.

3. Throughout the book, the author has mentioned more than once how important logical proof is in a mathematical proof. At least he cites the two events with the first in Wolfskehl's finding of "a gap in the logic" by Kummer then the second in Katz's checking of Wiles' proof. Unfortunately, the author allows such a gap of logic in the proof of Pythagoras's Theorem shown in Appendix I: "... four identical right-angled triangles are combined with one tilted square to build a large square." The author only states so but fails to provide any proof that the inside four-sided shape formed by the four hypotenuses IS a square. (Certainly we do know it is and can plug the proof. Otherwise Pythagoras's Theorem won't hold.)

We never hold any slightest hope that a 285-page book (the paperback edition) would offer us a clear understanding on how the proof, that incorporates so much of the techniques in the modern number theory, is devised. The book basically steers itself all clear from the mathematics.

These below are what significantly push my rating of this book to a low range:

1. Too much on who the mathematicians were rather what they did to the proof. Approximately two-thirds of the book is on stories behind those mathematicians who one way or the other got involved in the Last Theorem. Those may be interesting from a historical perspective but are simply irrelevant to how we came to the proof.

2. The author starts quite early in the book to tout mathematical proof as an "absolute proof" that "[m]athematical theorems rely on this logical process and once proven are true until the end of time. Mathematical proofs are absolute." By contrast, "... the scientific theory can never be proved to the same absolute level of a mathematical theorem ... So-called scientific proof relies on observation and perception." An account on the differences between the two is beyond the scope here. Apparently, the author either doesn't know those are apples and oranges or, worse, attempts to elevate mathematical proof to an "absolute" level it might not need at all.

3. Throughout the book, the author has mentioned more than once how important logical proof is in a mathematical proof. At least he cites the two events with the first in Wolfskehl's finding of "a gap in the logic" by Kummer then the second in Katz's checking of Wiles' proof. Unfortunately, the author allows such a gap of logic in the proof of Pythagoras's Theorem shown in Appendix I: "... four identical right-angled triangles are combined with one tilted square to build a large square." The author only states so but fails to provide any proof that the inside four-sided shape formed by the four hypotenuses IS a square. (Certainly we do know it is and can plug the proof. Otherwise Pythagoras's Theorem won't hold.)

This is a non-fiction mathematical detective story. Very intriguing. I didn't find the book completely evenly paced all the way through. However, the author was good at boiling complex concepts down so that an engaged reader could follow the discussion (only occasionally I found myself wishing there was more detail and technical explanation). A very good exploration of a long-standing mathematical mystery. As someone not well versed in the history of mathematics but definitely interested, it held my attention and didn't let go.

ByTelstar-manon February 23, 2016

It's a great literature for anyone wishing to know more about the history and evolution of mathematics. Well done research.

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ByAnita Fleggon May 4, 2015

Way fun! I love math and reading about math history and puzzles, and this book had everything, including being very readable.

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BySpaceweaselson November 9, 2014

A great book on an important, if obscure, moment in the history of mathematics. The greatest talent Simon Singh has is to present complex concepts and an easy way to understand.

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I could not put this book down! In clear, lively, captivating prose the author recounts the story of Fermat's Last Theorem and its elusive mathematical proof. The period covered is essentially from the days of Fermat until the theorem's proof by Andrew Wiles in the mid 1990s. Along the way, the reader is treated to the various valiant efforts by brilliant mathematicians through the centuries towards establishing such a solid proof - all in vain before Dr. Wiles. The ups and downs in the history of this seemingly intangible proof are particularly well illustrated.

Throughout the book, the reader is exposed to various mathematical objects that mostly form part of number theory, as well as mathematical techniques that have been developed over time. Because the mathematics is so masterfully described, this book should be accessible to a wide audience.

This amazing book should appeal especially to mathematics/science enthusiasts but any interested general reader could follow it quite easily and enjoy it tremendously.

Throughout the book, the reader is exposed to various mathematical objects that mostly form part of number theory, as well as mathematical techniques that have been developed over time. Because the mathematics is so masterfully described, this book should be accessible to a wide audience.

This amazing book should appeal especially to mathematics/science enthusiasts but any interested general reader could follow it quite easily and enjoy it tremendously.

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ByHong Gaoon January 10, 2006

This is the best book I had read about mathematics in last few years. It's beautiful.

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ByBoscoon May 2, 2004

Simon Singh never fails. This is a great book like all of his others. You really can't go wrong.

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By-on June 20, 2003

Singh writes with great skill of suspense, with minimal of math equations to help readers navigate the path to solving the ultimate math riddle of all time by a lone genius..Profoundly absorbing and engaging! Readers will no doubt also find the appendices helpful and intriguing.

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ByA. Vasudevanon December 19, 2002

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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ByD. Kapooron June 11, 2002

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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