Under The Microscope

FERMAT'S LAST THEOREM by Simon Singh; Fourth Estate Publications, 1997; 362 pp; $39.95 hardback

Reviewed by Russell Dear

"I have discovered a truly marvellous proof, which this margin is too narrow to contain...". With these provocative words Pierre de Fermat, the 17th century French mathematician known as the prince of amateurs, issued a challenge to future generations. A challenge which baffled some of the finest mathematical minds for over 350 years until a mild-mannered Englishman solved the problem in 1995.

The book reads more like a historical novel than a work of non-fiction. The author weaves a story spanning over two millenia -- from the theorem credited to Pythagoras in ancient Greece, to the seven years of dedicated effort by Andrew Wiles who became fascinated by the problem when he first read about it as a boy of ten in his local library.

On the way we hear about many of the mathematicians who have been associated with the theorem. There are forays down side alleys where we learn how attempts to solve Fermat led to formative work on the theories of recurrence relations and complex numbers. There are tragedies of epic proportions; the politically inclined Evariste Galois scribbling the results of his research the night before meeting his death in a duel, Sophie Germain taking the identity of a man to conduct research in a field forbidden to women, the brilliant Japanese mathematician Yutaka Taniyama killing himself in despair.

Through it all the author keeps the storyline rolling along towards the inevitable climax when, after years of toil and frustration, Andrew Wiles makes the exhiliarating breakthrough and publicly declares his solution.

However, even that is not the end of the story. Crashing disappointment soon follows when the proof is found to have a fault. Was it to be just another pseudo-proof of the theorem which has attracted more faulty "proofs" than any other in the history of mathematics? It took another two years for Andrew to correct the glitch and give the mathematical world what had eluded it for so long -- a truly foolproof solution to Fermat's last theorem.

I thoroughly enjoyed this book. Expecting the subject matter to be difficult, I was pleasantly surprised to find that the author held my attention without complicating the issue with mathematics at all. Only a very basic understanding of the subject is required to fully appreciate the breadth and wonder of the story. In 1996, author Simon Singh co-produced and directed for the Horizon TV series an award-winning documentary on Fermat's last theorem.

Russell Dear is a Mathematician living in Invercargill