John Barrow believes the public needs to know more about science - which is why he's published ten books on the subject and in March will deliver one of this year's Darwin College lectures.

Superstrings, the infinitesimal vibrations that are strong candidates for the most fundamental of fundamental entities, are believed to exist in more than three dimensions. The extra ones are somehow folded up very small inside the regular dimensions that give our everyday world its structure.

Elusive? Well, that is what happens to ordinary language when you try to describe something that only makes sense mathematically. One can write "grammatical" sentences, but their meaning is unclear - which makes superstrings just the kind of subject that fascinates John Barrow, a man as interested in using maths to understand the universe as in explaining it to the rest of us. Maybe an idea like this, with no obvious analogies, means we are thinking new thoughts, he suggests.

Take a look at Barrow's CV and you wonder if he might harbour a few of those extra dimensions himself. How else does he find the time? He lists almost 300 scientific papers and articles on cosmology and astrophysics. He has written ten popular books, for which reviewers have dubbed him the heir to James Jeans and Arthur Eddington, the two great pre-war British astronomer-writers. And he is an indefatigable speaker, having lectured on cosmology everywhere from 10 Downing Street to the Vatican. And he appears to do it all without breaking sweat.

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A trim, dapper man in his late 40s, and a former track athlete, he is doubtless a workaholic in private. But he has that knack of public relaxation. As he explains yet another curious feature of the universe, he reveals a voracious intellectual curiosity. The adjectives he uses most often are "new" and "interesting".

As well as wanting to see what is round the next cosmological corner - one preoccupation is whether the speed of light might have been different in the very early universe from the famously constant value we see today - he has long been fascinated by how it is that we come to know the universe at all.

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In a series of books starting with The Anthropic Cosmological Principle , Barrow has virtually created his own popular metascience genre. The volumes tackle issues such as how finely tuned the constants of nature have to be to deliver a universe hospitable to life, and how defining what we can never know about the cosmos may be as revealing as what we can know.

Often, the books include staples of popular science such as the Big Bang and chaos and complexity theories. But they are generally put in a much richer historical and philosophical context than other authors manage. Barrow is as likely to be found discussing debates between 17th-century theologians as recounting relativity or reprising quantum weirdness.

Despite this dizzying erudition, or maybe because of it, he never gets carried away. This may be why he remains merely well known rather than famous. Barrow has never declared that he expects to know the mind of God, like Stephen Hawking. As popular cosmologists go, he is Mr Level-headed.

So is cosmology about the meaning of life? "Not on a day-to-day basis," he says. "It's just connected with a lot of other things. Cosmology is nice because there are so many interfaces. If you want to be mathematical and explore general relativity you can be a mathematical cosmologist, if you want to be an astronomer and look through telescopes, you can do that. If you want to pontificate about the anthropic principle, or where galaxies come from, or whether the universe has an end, you can do that too."

A cosmologist, in fact, should be a bit of a generalist. This might be a sign that the subject is immature. "You never know from where the next important insight will come," Barrow says - but that is to his taste. He has been a generalist since he was a schoolboy in west London, when he wound up with A-levels in English, Greek, and religious knowledge, as well as maths and sciences. This was the result of an unusual education in which he attended school, but was privately tutored in the humanities.

At university the generalist plumped for mathematics. He had first been drawn to science after being given a chemistry set when he was ten, but his interest in chemistry lapsed a few years later because "I realised that all the things I was most interested in about chemistry were really physics." Chemistry was supplanted by astronomy and the revelation that "you could use very simple maths and physics to understand concepts such as stars and galaxies, and even the expanding universe". And so from a maths degree at Durham he went on to research in astrophysics with Dennis Sciama at Oxford.

Sciama was a prolific supervisor, who also guided the early careers of Hawking, Sir Roger Penrose and Sir Martin Rees.

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Barrow was not sure he would succeed in this daunting company, but within a couple of years he was publishing results on the isotropy of the universe - whether it is the same everywhere - and then on chaos theory and cosmology. He still remembers the excitement. "I think everyone's favourite is their first paper."

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He had two advantages at Oxford. One was that most of the other students were preoccupied with quantum gravity rather than physical cosmology. The other was he read more than anybody else, although he characteristically disclaims credit for this, saying: "It was probably just that I wasn't so busy. Library facilities in Oxford are excellent. It was easy to read a lot."

This wide reading also got him thinking about cosmology and particle physics, a conjunction that became fashionable a few years later. So he was well placed to make a career as an astronomer-cum-cosmologist, and to interpret cosmology to lay readers after Steven Weinberg's The First Three Minutes alerted the public to the idea that there really was a story of cosmic significance unfolding. "The questions in the story are nice in that they are easily intelligible: how old is the universe? How big is it? You try to talk to people about big questions in biochemistry or the interpretation of quantum mechanics and they don't translate so easily -you have to do a lot of work before you can get the idea across."

Long established at the University of Sussex, he was happy to go on exploring new twists in cosmology's unfolding tale and writing books that mixed the disciplines: his latest, The Book of Nothing , is, as its title suggests, about nothing - a concept we find indispensable, but that never occurred to some earlier cultures. The volume is an eclectic tour through cultural history, guided by the question: how did nothing become something?

He could have stayed at Sussex, but he was head-hunted to sell something less glamorous than cosmology - mathematics. A little over a year ago he became director of the Millennium Mathematics Project in Cambridge, where he also joined the university as research professor of mathematical sciences.

With the MMP, he is involved in developing study programmes for school children at Cambridge's Isaac Newton Institute, as well as trying to increase awareness of maths among adults. "The perception of mathematics and mathematical sciences in this country is rather poor. The average person doesn't know what a mathematician does. There is no conception of what is underwritten by mathematics."

This is partly a legacy of uninspired education in the past, but also, he notes, because maths is neglected by the media. "Maths is not often reported in the press. It is hard to do - not easy to find out what the stories are. There is not a great Nasa public relations organisation giving you the logarithm telescope or something."

He believes people need to see maths as problem-solving, and that means allowing them to find solutions as well as telling them about interesting problems. This matters especially for schools. "If you supply interesting new material over the web about Fermat's last theorem or fractals, it is alarming because all it does is open teachers up to all sorts of questions from their pupils that they cannot answer. You must have an interactive aspect."

But beyond this, the rubric of the project makes it one of the more interesting attempts to change our culture. But Barrow, as productive as he is, might need to find some more of those dimensions to work in if he is to carry on pleasing his readers as much as his official paymasters.

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John Barrow will deliver his Darwin College lecture on Outer Space at the Lady Mitchell Hall, Sidgwick Avenue, Cambridge, on March 2, 5.30pm. The Book of Nothing is published by Cape, ?16.99.