When to Stop Counting
- Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem by Amir Aczel
Viking, 147 pp, £9.99, May 1997, ISBN 0 670 87638 0
Aheroic story: Andrew Wiles, a Cambridge mathematician living in the United States, emerges after seven years of self-incarceration and paranoid secrecy from his Princeton attic, clutching two hundred pages of hieroglyphics. He is triumphant. He has cracked the most famous problem in number theory: Fermat’s Last Theorem, which has eluded some of the finest efforts of mathematicians for over three hundred years. He is beside himself with anticipated glory, but holds off, maintaining secrecy until the right moment. Serendipitously, a conference on exactly the branch of number theory covering his work is to take place in Cambridge. Choosing an unrevealing title, he lectures on three consecutive days. In the final minute of the final hour, he is able to utter the magic claim that the puzzle of Fermat’s celebrated theorem is now solved. Shocked silence and then a standing ovation from his astonished international colleagues. In the ruthlessly competitive world of research mathematics, Wiles has pulled off one of the most dramatic successes anyone could hope for.
The full text of this book review is only available to subscribers of the London Review of Books.
Vol. 19 No. 24 · 11 December 1997
Mathematics is not the organised hypocrisy glimpsed in the background of Brian Rotman’s self-portrait, ‘a renegade blowing the whistle’ (LRB, 27 November). Broadly speaking, if you accept the existence of the whole numbers 1, 2, 3 … as a set, some rules for making new sets from old ones and the use of the syllogism in arguing about them, then you have accepted modern mathematics as ‘true’. The simple is indivisible from the complex. If Fermat’s Last Theorem is metaphysical, then so is Baby’s First.
The serious worries are lower down. Style and standards of proof constantly drift: we visualise wrongly, we dupe ourselves, we miss possibilities. What keeps the literature from pullulating with errors is that falsehood tends to lead to more falsehood and finally to the absurd, such as that 1=2, from which we retrace our steps. But incomplete proofs of true state· ments are a legitimate concern. Wiles’s first draft was not quite there; in the late Eighties, an initially promising assault on the Poincare conjecture was lost altogether.
Why bother then? Why believe there are truths about numbers? What Wiles was doing in the attic all those years was raising what Wordsworth calls
that interminable building reared
By observation of infinities
In objects where no brotherhood exists
to passive minds.
Vol. 20 No. 2 · 22 January 1998
One neglected reason for Andrew Wiles spending all those years wrestling Fermat’s Last Theorem to the attic floor (LRB, 27 November 1997) might be the excitement brought on by the resonance of the phrase itself: ‘Fermat’s Last Theorem’. A crucial part of such carefully shaped phrases is the use of the word ‘last’: there is, for instance, Trent’s Last Case (you can feel the tingly resonance there) or The Last of the Mohicans; in radio, Krapp’s Last Tape; in cinema, The Last Picture Show. (There are shaped phrases which carry a peculiar resonance and that don’t have ‘last’ in them, but there aren’t many – ‘trained by Jesuits’ and ‘the storming of the Winter Palace’.)
During World War Two a joke shop in Preston which had published Billy’s Weekly Liar for many years opportunistically trans – muted the organ into the Berlin Liar. The same shop sold matchbox coffins containing corps-es of miniature Hitlers. Opening the matchbox/coffin allowed Hitler’s penis to spring erect (the penises being made from snippets of the fine pink rubber tubing manufactured for bicycle tyre valves). These artefacts were labelled ‘Hitler’s Last Stand’. That the puzzle of Fermat’s Last Theorem was ‘solved’ by Wiles using 20th-century means has brought a sense of loss; hence the assertions that Fermat’s own solution (if it existed) must have been shorter and more elegant. The quest to re-create that solution (if it existed), and thus enable the thrill of the phrase to carry on through history, would require an imaginative leap into the past which all the mathematicians in all the gin joints in all the world couldn’t manage.