Fermat's last theorem is an old and easily stated theorem about numbers. Its proof involves an intricate jigsaw of number theory and geometry whose comprehension demands a combination of determination and technical ability with which only a tiny handful of mathematical geniuses are endowed.

Because of the phenomenal theoretical superstructure behind the proof of FLT, it is an impossible task to make even the gist of Andrew Wiles's highly publicised proof plausible to, say, an A-level mathematician. Hence neither of the authors of these two books can have a serious pedagogic goal. Indeed, Amir D. Aczel has set out to provide enjoyment, and his book is billed as a piece of investigative journalism, while Simon Singh's "thrilling tale of endurance, ingenuity and inspiration" is told from the perspective of a physicist.

The books both comprise compilations of snippets of nontechnical information interspersed with elementary mathematical observations. Neither of them is as technical as many books on recreational mathematics. Aczel has chosen to describe things historically and his early chapters read like a Sophie's World for mathematics. Singh lays more emphasis on Wiles's background and personal attributes, but he also includes some more serious mathematical discussions in a series of noncompulsory appendices. Each author weaves into his cameos the inevitably cryptic remarks concerning the real milestones in the proof of FLT, and their skill and lightness of touch has resulted in two books that are fun and accessible. But their really striking common attribute is hyperbole; FLT and its aficionados are elevated to superhuman levels in which Fermat is greater than Newton and his theorem is as profound as the invention of quantum theory or the discovery of DNA.

Beneath the glamour surrounding FLT lie many deeper questions that may trouble the reader. One concerns the important role of "Mordell's conjecture", which offers the easiest way to glimpse the astonishing fashion in which visualising surfaces in four dimensions can help to understand the purely algebraic statement of FLT; only Aczel gives it any prominence. Another worry is the role the computer has to play in the proof of results such as FLT, about which both authors are rather negative. They and their sources grudgingly confirm the computer's importance for the famous four-colour problem for maps. But the idea of using electronic evidence more generally is portrayed as unsporting, despite the inspiration that so many researchers (including FLT ones) have derived from computer outputs.

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It is impossible to resist taking this opportunity to assess the scientific impact of the proof of FLT, because neither of these books addresses the question of where the towering edifice really stands, so far as the interface between mathematics and science is concerned. At a time when the scientific value of mathematics is discerned by ever fewer nonspecialists, especially in the press, this omission is particularly vexing.

Aczel and Singh rightly contend that FLT is a great problem of consuming interest, even though it has in Aczel's words "no possible consequences in science, engineering or mathematics". But by further fuelling the euphoria surrounding the proof, these books may render a disservice to science. There are countless practically relevant, mathematically challenging unsolved problems to be found in people's workplaces these days. They are usually much more difficult to explain to the layman than FLT, but just look at the powerful brains and powerful computers being stretched trying to understand the mathematical structure of models ranging from option pricing to superalloy design, from tumour growth to predicting the homeless population. Alas, the more applied the problems become, the more they are interwoven with concepts which the human brain has difficulty making precise and the less attainable is the idea of proof (even FLT used to be plagued by the possibility of logical undecidability, as Singh discusses). But this does not mean that epochal breakthroughs are impossible, only that the breakthrough would probably take the form of a new mathematical theory rather than a proof of an old mathematical theorem.

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The danger is that bright young readers of these books, and their teachers, will too easily infer that all the action in mathematics lies in solving problems that are famous and easy to describe; and there is no shortage of such problems. It would be a shame if intending mathematicians were discouraged from other topics at a time when mathematics in all its forms desperately needs the talents of these young people.

Only a handful of researchers can succeed working in the utterly single-minded and uncollaborative style adopted by Wiles. For evidence simply consider the fate of the band of "Fermatist cranks" as defined and brilliantly portrayed by Underwood Dudley in his recent book Mathematical Cranks. Society is right to be awestruck by the achievements of those as exceptionally talented as Andrew Wiles. But it should not be encouraged to infer that Fermat's Last Theorem is all there is to modern mathematics.

John Ockendon is research director and Rebecca Gower is a research assistant, Centre for Industrial and Applied Mathematics, University of Oxford.