Work it out by numbers

Mathematicians have always had an ambiguous relationship with ordinary mortals. On the one hand they court and enjoy the idolatry their profession attracts, accepting the awe-struck "It's all Greek to me" as no more than their due. On the other hand they have laboured with the tenacity of Sisyphus to push the mathematical deadweight on an unsuspecting public, hoping to "popularise numbers". H.G. Wells and Bertrand Russell attempted it, Wells apostasising in sci-fi, Russell opting for the Mathematics-Made-Simple approach. Stephen Hawking struggled heroically with impossible material, providing us in the process with the ultimate paradox of a best-seller that nobody understood. The reverse of the coin, of course, is the public's continued fascination with the most arcane scientific theories.

However, in this book K.C. Cole, a distinguished science journalist, has put together a very readable product. There are no obscure theorems, no messing about with foreign alphabets. Most of it is in plain English, and although the concepts are often difficult, not to say bizarre, Ms Cole writes crisply about fuzzy things like top quarks, the molecular structure of cats and the behaviour of other people's money. The whole is served up with a soupcon of wit, and peppered with startling images with which to amaze your friends and subdue your enemies.

Did you know, for example, that the humble flea can pull 160,000 times its own body weight? That a sixty-foot giant would break his thigh-bones with every step? That if you could empty Waterloo Station and then distribute six specks of dust at random throughout it, the station would be more crowded with dust than the universe is with stars?

Mathematicians are comfortable with such measurements. What makes them edgy is the widespread belief in their infallibility. Ms Cole feels it necessary to defend them from the charge that they know the price of everything and the value of nothing.

"Asking questions of Nature," Ms Cole tells us, "is always somewhat treacherous because the answers you get depend on the questions you ask." We simply ask too much, gulled into believing that knowledge is without limitations. We accept the word of the man in the white coat when there is a distinct possibility he is an escaped lunatic in a clever disguise.

Not only do they get the answers wrong at times, but quite often they miss the question itself. Einstein's relativity paper, for example, almost didn't get published because there was only one person in all of Germany who was prepared to believe it. Andrew Wiles, who proved Fermat's last theorem a few years ago, had the greatest difficulty in finding people to validate his proof, simply because not enough people were capable of understanding it.

Ms Cole labours to convince us that mathematics is both a language and a process. She argues persuasively that as a language it is as good a description of the world around us as art or literature (and probably no better), and that the particular way of thinking involved in calculation is as central to our humanity as any other.

At the other end of things, mathematics is fundamentally a reductionist process. She quotes J.R. Newman: "What better way to get at the fundamentals of structure than by successive transformations to strip away the secondary properties?"

But the particular structures that are revealed by that process have a kind of lean beauty that has little to do with the eye of the beholder and everything to do with the mind. Even the most devoted connoisseur of numbers could not accuse Ms Cole's beloved theorems of opulence. The QED for most of us is that the absolute truth and beauty of mathematics are an acquired taste.

William Wall is a poet and short-story writer; his collection Mathematics & Other Poems was published last year

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