by Simon Singh.
5.0 out of 5 stars
A book that is likely to induce your interest in number theory
“Fermat’s Enigma” tells the story of how the riddle posed by “Amateur mathematician” Pierre Fermat in 1637 was finally proved by Andrew Wiles in 1995. After the failed attempts of three and a half centuries by the most gifted mathematicians worldwide, (even the Devil was rumored to have given up), it is not surprising that much human drama is inherent in such a story. Neither is it surprising that the mathematical tools crucial to the proof of Fermat’s last theorem are beyond the comprehension of anyone who is not an expert in number theory.
What is somewhat surprising is that the reader is treated to a clear explanation at the beginning of the book about the difference between a mathematical proof (absolute proof) and a scientific proof, with an example that is both simple and elegant, one which everybody can follow. Another pleasant surprise is that the reader learns a few interesting features about number theory. For example, it is nice to know that 220 and 284 are a pair of friendly numbers (the sum of the divisors of each is equal to the other number), and 26 is the only number that is between the square and the cube of integers. For those who like challenges, there are, in the appendices, not-so-easy proofs to follow, including the proof of Pythagoras theorem and Euclid’s Proof that there are an infinite number of Pythagorean triples.
The most interesting human drama is of course the intellectual journey of Andrew Wiles. Since childhood, solving Fermat’s last theorem had been Wiles’ dream. He devoted years of effort trying to achieve this goal in isolation. Most dramatically, after announcing that he had found the proof on June 23, 1993, a “slight problem” was detected, which rendered his proof incomplete. After several months of concentrated but unsuccessful effort to fix the problem, he almost gave up and prepared to admit defeat. Then one morning, September 19, 1994, an inspiration occurred to him which led to success, enabling him to deliver the promised birthday gift to his wife: the complete manuscript containing the proof. The gift was indeed delivered on her birthday, albeit one year later than he promised. The manuscript was published in Annals of Mathematics in May 1995.
In following Wiles’ journey, we learned about the lives of several other mathematicians, both ancient and recent. These include Diophantus, Euler, Sophia Germain, Cauchy, Galois, among others. We also learned the life and work of two Japanese mathematicians, Yutaka Taniyama and Goro Shimura, including the tragic suicide of Taniyama at the young age of 31. His financee followed him, also committing suicide, a few weeks later.
Among the principal tools in Wiles’ proof are: elliptical equations and modular forms, Iwasawa theory, Kolyvagin-Flach method, Taniyama-Shimura conjecture, Galois group theory. Although these terms sound more formidable than Greek is to me, they in no way lessen my enjoyment of this remarkable book. Indeed, the book has stimulated my interest in learning more about the wonders of number theory.
Audio Version in YouTube:
(Source: Wikipedia)
(Source: Wikipedia)
(Source: Wikipedia)
(Source: Wikipedia)
Comments