Fermat's Last Theorem [Paperback]

Written like a detective story where the answer is known, this book is easy to follow, and leads readers through a maze of ideas, concepts and subtleties that would be a disaster in the hands of a lesser writer. This is absorbing narrative, leading up to the lecture where Andrew Wiles presented his proof of the non-solution of the equation. However, the proof presented on 23rd June 1993 was the beginning of a nightmare for Wiles, as a serious logic error was subsequently discovered that took an all-consuming 15 months to rescue.

The story of how a very gifted mathematician devoted himself for seven secretive years to a question that others had given up on is only half the tale that Singh tells. It is a journey through some of the history of mathematics, with the solution to the amateur mathematician Fermat's problem being an accidental occurrence. Along the way there are very good insights into the differences between mathematical proofs and scientific proofs; the former must be indisputable, whereas scientific proofs are only ever probabilistically true, and do change as knowledge increases.

There is no need for a great interest in or knowledge of mathematics to enjoy the story, which itself draws the reader onwards. I k now nothing of the similarities between modular equations and elliptical equations, tied up within what became known as the Taniyama – Shimura conjecture, yet can appreciate the means by which Wiles was able to prove Fermat's theorem by establishing the mathematical truth of the latter.

Simon Singh started by investigating the story of Andrew Wiles and Fermat for a British television program. This book that he subsequently produced set new levels for the history of science as a popular writing genre. At the end, Singh goes further, and raises questions as to whether the discovery was worth it. If Wiles had not been able to rescue his proof, it is suggested that the effort would not have been in vain, as there were significant advances in mathematic knowledge obtained in the trying. Singh also discusses other difficult areas, and muses on whether some of these will be unprovable, or insoluble. Fermat's Last Theorem, having frustrated the best mathematical brains for over 350 years, is now established, and is not one of the 'unknowable truths of mathematics'!

In concluding, it is fitting to use the words with which Andrew Wiles concluded his 1993 lecture: "I think I'll stop here".

Peter Morgan Bath, UK (morganp@supanet.com)

In 1637 Pierre de Fermat, a French 'amateur' mathematician stated that there were no solutions to a pythagorean type expression using powers above the value of two. Tantalisingly he wrote in the margin that he had a 'marvellous demonstration' which the margin was too narrow to contain. This was to torment mathematicians for over three hundred years. Did Fermat have a proof? Could he possibly have had a proof? What was the proof?

Andrew wiles was a young boy when he encountered Fermat's riddle and decided there and then that he would be the one who would solve it. Singh takes us on this journey and we become embroiled in the riddle ourselves. The appendices demonstrate mathematical techniques so eloquently and succinctly that the reader suddenly thinks that he, the reader, must have immense, hitherto undiscovered mathematical talent. Not so. The talent is that of Simon Singh, a talent that kept me totally enthralled for several hours, untol the book was finished. I felt disappointed that it did not go on longer, but the story was told and the ending was sensational. Not to worry, I have just ordered 'The code book' and 'The big bang' both by Simon Singh, I know I will not be disappointed.

I admit I did already know some of the details given in this book, but the history and the description of the characters in the world of mathematics added an extra dimension (no pun intended!) and made it all the more fascinating. Names like Euler, Dirichlet, Cauchy, LaGrange ... before I read the book they had merely been names of equations, polynomials, boundary conditions and the like, but the author gave us some fascinating details of their lives, what type of people they were (I've gone off Cauchy now, and I so loved his polynomials) and even the interactions that went on among some of these famous names.

And I loved the description of Wiles's "Eureka" moment when he realises he's finally got the proof ... it must have been like solving the world's most difficult crossword clue!

I don't know whether to go straight back and read the whole thing again, or lend it to a friend and share the experience.

On reflection, my friends can buy their own copy.