Book Review: Fermat's Last Theorem by Simon Singh

(4th Estate: London, 1997)

This book is thick and about math.. though I was excited by the subject matter, I was still daunted by the proportions of the text. As it happens, the text is easily readable, and more easily digestible. Singh takes time to clarify the logic which he includes in the book very completely, which clarifications may be skimmed, allowing the reader who understands, or thinks she understands, to verify if necessary or move swiftly on. The subject of the book is, as the title suggests, the enigmatic theorem of Pierre de Fermat, which remained unsolved for over 350 years. While there are problems older and perhaps even ultimately insoluble (following Godel’s undecidability, which makes a prominent appearance midway through the book), Fermat’s conjecture and Andrew Wiles’ solution comprise maths from Pythagoras to the most modern number theory available in the 20th century. The scope of knowledge utilised, and its distillation, is, I think, perhaps the key to the excitement generated by the solution of this problem, more than the legendary intractability of the problem. As a result, Singh is able to develop the history of the relevant maths (and even some of their offshoots) from Pythagoras (with even a mention of his predecessor, Thales) down to Andrew Wiles joining the mathematics scene as a grad-student in the 1970’s, by occasional reference to the future development and ultimate usefulness of these historical maths in solving Fermat.

Some digressions are engrossing by themselves, such as the details of the life of Evariste Galois, a fierce French Republican who died mired in tragedy and political intrigue during the period of the resotration of the monarchy, aged 20 and having studied maths only 5 years but nevertheless producing work which, once tidied up by other mathematicians, turned out to be brilliant on its own merits, and more importantly generative of further brilliant maths in subsequent centuries. A multitude of such major and many other minor digressions into the unhinted at drama of the development of maths make for a further layer of enjoyment. The lives of mathematicians like Yatuka Taniyama (of the Taniyama-Shimura conjecture, proved by Wiles in order to prove Fermat) suggest that despite the ivory tower respectability of mathematics, mathematicians are far from immune to the human condition; Taniyama committed suicide on the eve of his wedding, his fiancee followed soon after. There are several appendices which, among other expounding explications from the main text, lay out Pythagoras’ proof for his eponymous theorem, Euclid’s proof of the irrationality of √2, an explanation of game theory, etc. This arrangement allows the reader to delve into as much or as little of the logical complexity of the argument (short of reproducing the proof), whilst enjoying the contribution of the complexity of the logic to the narrative itself.

This is an excellent book, comparing favourably, at least, with anything I’ve read by James Gleick (my math reading is still limited and untechnical). I look forward to reading Mr Singh’s work on cryptography (which also makes an appearance in Fermat).