Fermat's vast legacy

July 4, 1997

JOHN OCKENDON and Rebecca Gower, reviewing the books by Anir Aczel and Simon Singh on Fermat's Last Theorem (THES, June ), have missed the point about Andrew Wiles's outstanding achievement. Although his proof of FLT won him great publicity and the Wolfskehl Prize, his greatest contribution to mathematics has been to prove a substantial part of the much subtler Shimura-Taniyama Conjecture, which links elliptic curves with modular forms (and which Ockendon and Gower completely ignore). FLT is a historically interesting challenge, the main importance of which lies in the techniques mathematicians have developed in trying to prove it.

Furthermore, to criticise Wiles, Aczel and Singh for concentrating on abstract mathematics at the expense of practical problems is like complaining that Picasso was not a house painter. In fact it is worse, since the most abstract topics in pure mathematics, from non-euclidean geometry to the prime number theorem, have a habit of surprising later generations with their unintended applicability. If the reviewers fear that popular books like these will tempt bright young readers away from what they regard as useful mathematics, they would do better to find and publicise similar intellectual achievements in their own area of industrial applied mathematics.

Gareth and Mary Jones

Mathematics department

University of Southampton

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