Just for a moment imagine having to work out "sums" using only words. Five hundred and fifty-eight multiplied by seventeen, for example is pretty basic arithmetic, but if my reaction is anything to go by, if you can't at least visualise columns of figures and the business of carrying over, a paralysis descends.
Yet that, in effect, was the situation in Europe up until about 1200 AD when the crafty system of using symbols to represent numbers arrived from the east, brought back from his travels by the enterprising Adelard of Bath. William of Malmesbury later described it as "dangerous Saracen magic".
Until then (and indeed for several centuries more, the dangerous Saracen magic taking a long time to catch on) anything beyond the simplest calculations that could be done on fingers or counting boards or by using an abacus was impossible for ordinary folk. Numbers were like adjectives and arose only in relation to things - goods, money, people etc. Zero - which after all can only be abstract - did not exist. Unlike the problem of longitude that bedevilled navigational thinking for centuries, it wasn't a question of discovering a means of calculating something that everyone knew was out there. Zero was a concept that needed to be invented by man in order to exist. There were words for "nothing", but not an arithmetical symbol. Yet, it turns out that, in mathematical terms, zero is a number more powerful than any other.
The story of zero, from its beginnings as a humble oval dent in a counting board covered with sand indicating the absence of a pebble counter, to its place as the central tool in the alchemy that is calculus, not to mention the pivot of the binary system that now rules our lives in the shape of computers, is unfolded in the fascinating, The Nothing That Is, by the equally fascinating Robert Kaplan. "If you look at zero you see nothing," he begins (chapter zero), "but look through it and you will see the world."
The first thing I did when we met at the Savoy Hotel in London, was to apologise that my maths education had ended when I was 16. Some of the later stages of his story (Newton and Fermatt, for example) had left me glassy-eyed, I admitted. Instead of looking peeved at having been sent a dunce, Kaplan's eyes lit up with obvious delight and he proceeded to elucidate in the most basic terms what I had missed.
His book is not for specialists, he insists, but for people exactly like me. The only criterion for understanding and enjoying mathematics, he believes, is curiosity and bushy-tailed enthusiasm. "My intention was for everyone to find out that mathematics is the most accessible and the most beautiful of the arts."
Even more importantly, perhaps, it informs everything that surrounds us. Computers speak in only zeros and ones. Stockbrokers anticipate peaks and troughs through calculus. All the sciences have been mathematicised to enable the processes to be pictured through graphs.
Kaplan's objective in writing The Nothing That Is, he says, was to reveal the secret which mathematicians have until now kept to themselves: "How wonderful it makes the day, how dazzling the revelations are after the hard work one puts in after creating these beautiful structures."
This flowery proselytising is hardly surprising coming from someone who earns his living teaching mathematics at Harvard. Except that Robert Kaplan is as far removed from any maths teacher I have encountered as pupil or parent as Flann O'Brien is from Anthony Trollope.
Indeed O'Brien, Kaplan tells me, is one of his favourite authors and is, indeed, quoted in the book. He rattles off titles of books and characters as enthusiastically and instinctively as he quotes from Shakespeare and Seamus Heaney, Archimedes and Leonardo da Vinci, Sylvia Plath and the more arcane Indian mystics.
Kaplan is a man for whom the word, polymath, might have been invented. To describe his educational career as bizarre - which he does - is an understatement. At the University of Chicago he studied, not maths, but Chinese and Sanskrit. "Philosophy is my major interest," he says, "and, since I don't trust translations, I wanted to read Chinese and Indian philosophy in the original." He graduated within the year having "learnt nothing," he says.
Having learned nothing legally, and got a degree for it, he then thought it only fair to go to Harvard illegally and learn something. Which he did for four years. Unfettered by constraints of faculty or course, he attended any class he wanted. Those he enjoyed he stayed with, eventually admitting his nonstatus to the individual teacher concerned. "The answer always was, `Ah, someone who really wants to take my course. How nice.' "
Even then, maths hardly figured. He studied German, philosphy, English literature and language. He already spoke Latin, Greek, French and, of course, Russian, the language spoken at home. His mother spoke eight languages. His father "made two fortunes and lost three" having emigrated to the US after the abortive revolution of 1905, during which he he had been exiled to Siberia where he shared a cell with Stalin. They didn't talk - Kaplan explains: "Stalin was a Bolshevik and my father was a Menshevik."
Kaplan must also be the only American to play cricket, spending every summer in Scotland where he plays for the American Grange Club. It was through cricket that he first fully savoured the significance of nought. First man out for a duck is not the same as the no-runs scored by the tenth man who wins a victory by just keeping the batting going.
Robert Kaplan came to maths only when he started teaching. "I believe in teaching what you don't know so you can learn it." Now he teaches foundation students at Harvard, his area of interest "the interface between philosophy and mathematics. What are these things we are dealing with in mathematics? Because it's not obvious."
Philosophy remains at the heart of Kaplan's interests. "I began to see more and more that the way into the questions I was interested in - what is the nature of the mind, what is the nature of the world, how do they relate - was through mathematics. Because you don't have to believe it, there's no faith involved. There's utter clear, beautiful reason. And it gives you structures. Material may change but the structure remains. That is what mathematics reveals."
For the past six years, Kaplan and his wife, Ellen (whom he met at Harvard all those years ago and whose line drawings illustrate the book), have been running something called the Math Circle, a once-a-week class for anyone of any age. His oldest student is 64, his youngest is five. They began with 29, now they have 145. No qualifications necessary. The students chose themselves, he says. "We pose problems that they then work on by themselves, with us in the room as a presence. They end up doing very serious, very complex mathematics: calculus by eight and 10-year-olds, because they're inventing it themselves. They don't know it's hard - they make up their own terminology and they wrestle with it. And, at the end of the class, they don't want to go home."
THE understanding of mathematics, Kaplan believes, is more important now than it ever has been. Yet it is being taught "more badly and more slowly than ever. There's been a dumbing down of math in the States. Calculators are largely responsible for math illiteracy because you're letting the machine do it for you as if it was better than your mind.
"But math is such fun. I think that a lot of the fun is taken out of math because of teachers who fear it, because it was taught to them in a hard and rigid way. A lot of them go into it, not through any love of the subject, but because there's good pay in teaching math and they think if you just learn these certain formulas, it'll be OK as long as the kids don't ask questions. And, if they ask questions, just say this is the way it's done."
Dismissing the maths mystique as being something dense, impenetrable and boring was also the impetus behind The Nothing That Is. The Math Circle was proving a great success but limited to those who took part.
"In 1997 I began to think, what's the way into this? A book. A book which is attractive, mysterious, interesting. A book about zero, especially with the millennium coming up. It seemed like the right kind of topic because of all the literary, philosophical, psychological associations. One can appeal to people who are nervous about mathematics in a non-mathematical way and lure them in." To a very large extent, he succeeds.
And, for those who are interested, the third millennium doesn't actually start until 2001. Why not? It's all to do with zero and you'll just have to read the book.
The Nothing That Is: A Natural History of Zero by Robert Kaplan, £12 in the UK
Notes on the text can be found at www.oup-usa.org/sc/0195128427/