Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problemxn + 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 seventeenthcentury 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 Enigmabased on the author's awardwinning 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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http://www.sindark.com/2006/06/20/theoremsandconjectures/
As strongly evidenced by how I finished it in a few sessions within a single 24hour period, Simon Singh’s Fermat’s Last Theorem is an exciting book. When you are kept up for a good part of the night, reading a book about mathematics, you can generally tell that some very good writing has taken place. Alongside quick biographies of some of history’s greatest mathematicians  very odd characters, almost to a one  it includes a great deal of the kind of interesting historical and mathematical information that one might relate to an interested friend during a long walk.
xn + yn = zn
The idea that the above equation has no whole number solutions (ie. 1, 2, 3, 4, …) for x, y, and z when n is greater than two is the conjecture that Fermat’s Last Theorem supposedly proved. Of course, since Fermat didn’t actually include his reasoning in the brief marginal comment that made the ‘theorem’ famous, it could only be considered a conjecture until it was proven across the span of 100 pages by American mathematician Andrew Wiles in 1995.
While the above conjecture may not seem incredibly interesting or important on its own, it ties into whole branches of mathematics in ways that Singh describes in terms that even those lacking mathematical experience can appreciate. Even the more technical appendices should be accessible to anyone who has completed high school mathematics, not including calculus or any advanced statistics. A crucial point quite unknown to me before is that a proof of Fermat’s Last Theorem is also automatically a proof of the TaniyamaShimura conjecture (now called a theorem, also). Since mathematicians had been assuming the latter to be true for decades, Wiles’ proof of both was a really important contribution to the further development of number theory and mathematics in general.
Despite Singh’s ability to convey the importance of math, one overriding lesson of the book is not to become a mathematician: if you manage to live beyond the age of thirty, which seems to be surprisingly rare among the great ones, you will probably do no important work beyond that point. Mathematics, it seems, is a discipline where experience counts for less than the kind of energy and insight that are the territory of the young.
A better idea, for the mathematically interested, might be to read this book.
Review: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem
User Review  Clayton Bigsby  GoodreadsJust a wonderful read. Like with many books written about complex mysteries of science, the actual problems and challenges are far too complex to describe in any sensible manner to the average reader ... Read full review
Contents
The Riddler  35 
A Mathematical Disgrace  71 
Into Abstraction  121 
Copyright  
5 other sections not shown