This entry is on the book: Fermat's Last Theorem by Simon Singh.

Simon Singh’s book Fermat’s Last Theorem is an exciting one, even for those without a great deal of mathematical knowledge. The focus of the book is on Andrew Wiles' famed 1995 proof of this most famous of conjectures, but it also includes many engaging asides. 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 very closely related to a proof of the Taniyama-Shimura 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.

This post was adapted from an entry on my blog, at: http://www.sindark.com/2006/06/20/theorems-and-conjectures