Blurb

Fermat’s Last Theorem

By Simon Singh

This book tells “the story of a riddle that confounded the world’s greatest minds for 358 years”. In particular, it is about “how an Englishman, after years of secret toil and frustration, finally solved mathematics’ most challenging problem”. I was attracted by these two phrases printed on the back cover and immediately I guessed it must be a very complicated problem. To my surprise, it seems to be very simple. As it is known, Fermat’s Last Theorem stated that the equation xⁿ+yⁿ=zⁿ has no whole number solutions for n greater than 2. At first sight, people may think it’s just a simple extension of the well-known Pythagoras’ equation x²+y²=z². Mathematicians had already proven that there are an infinite number of Pyagorean triples (combinations of three whole numbers that perfectly fit Pythagoras’ equation). Fermat stated his “Last Theorem” in the margin of Arithmetica, he then wrote “I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain”. After his death, all his other observations were proved one by one, but this remains the last to be proven. Therefore, it is called the “Last” Theorem.

Over three and a half centuries, great mathematicians such as Euler, Germain, and Cauchy had tried to prove this theorem, but every attempt had ended in failure. Besides, this theorem also saved the life of a young German industrialist, Paul Wolfskehl, who missed the appointed time of suicide while busy working out the proof. After that, he rewrote his will to award a prize of 100,000 Marks (worth over 1,000,000 pounds in today’s money) to whomsoever could provide the correct proof. There was no breakthrough until Andrew Wiles, a ten-year old English boy, met the theorem in a library book. When he grew up, got his PhD from Cambridge and joined the Princeton University, he started to concentrate in proving this Theorem by “abandoned any work which was not directly relevant to proving Fermat’s Last Theorem and stopped attending the never-ending round of conferences and colloquia. Whenever possible he would avoid the distractions of being a faculty member by working at home where he could retreat his attic study.” In order to keep his work secret, “Wiles decided to publish his (other) research bit by bit, releasing another minor paper every six months or so.” His seven-year secret work lead to the publication of the proof in two papers, consisting of 130 pages in total, in Annals of Mathematics (May 1995). They were considered “the most thoroughly scrutinized mathematical manuscripts in history”. Eventually, Wiles collected the Wolfskehl Prize worth US$50,000 in 1997.

In this book, the author not only described the major attempts and the relevant events in proving Fermat’s Last Theorem, but also other interesting stories in the mathematical history, from the Pythagoras theorem proved in the sixth century B.C. to the RSA public key encryption technique developed in 1976. As the target audiences of this book are not mathematicians, strong mathematical background is not required.

K.W. Wong

[Notes: Prof. Andrew Wiles is the 2005 Shaw Laureate in Mathematical Sciences for his proof of Fermat’s Last Theorem.]