The recent spate of books about mathematics for general readers includes histories of pi, e, i, gamma, zero (two of these), the four-colour problem, the Riemann hypothesis (thrice), and (inevitably) the infinite. The novelist David Foster Wallace describes his "compact history of infinity" as "a piece of pop technical writing" intended to be "comprehensible to readers who do not have pro-grade technical backgrounds and expertise. To make the math beautiful - or at least to get the reader to see how someone might find it so".

Foster Wallace is clearly enthusiastic; he often talks about his maths teacher, who evidently made it all come alive, and, in his turn, Wallace wants to convey the excitement of these ideas. Who would not be disarmed by a maths book with a footnote that begins: "Shit. All right. The strict truth is more complicated than that. . . ."? No one can accuse Foster Wallace of being stuffy; his book is engagingly dishevelled. It comes across like the sustained manic rant of one of his comic fictional characters, someone who has buttonholed you and is pouring out a torrent of mathematical history and invective, punctuated by manifold digressions.

But despite some amusing moments, Everything and More is ultimately too disorganized and confusing. Foster Wallace is maddeningly circuitous and distractible, often picking up a topic then quickly dropping it. This makes it hard for him to reflect in any sustained or helpful way. For instance, he keeps coming back to Zeno and Aristotle, but so fitfully that the reader has little help thinking about their arguments against infinity in the light of modern maths.

Foster Wallace's goal is to decipher the work of Georg Cantor and Richard Dedekind, but he gets bogged down. He is serious and provides mini-summaries of calculus, which tend to be telegraphic; his intended readers need far more ample and carefully structured accounts. Worse, the mass of detail clogs up the text and inhibits overview or reflection. Foster Wallace shows his love for maths, but his book is too chaotic to show its beauty.

David Foster Wallace
EVERYTHING AND MORE
A compact history of infinity
344pp. Weidenfeld and Nicolson. Paperback, £8.99.
0 75381 882 5.

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