Lucy Hodges meets Paul Muldoon, the Heaney acolyte who wants to rearrange furniture in our heads.

Paul Muldoon looked a bit the worse for wear. He was on a poetry-reading tour of the United Kingdom, staying at Groucho's, the media person's club in Soho, after giving a reading the night before at the Lyttleton theatre. He was in between one-night stands, as it were. Next stop: Oxford. For an up-and-coming poet, winner of last year's T. S. Eliot prize for poetry, Muldoon, 44, is awfully modest. Quietly spoken, with a Northern Irish brogue, he exudes an amiable relaxedness. On stage at the Lyttleton, which he nicknamed "the Bigton" for its size, Muldoon wowed the audience with his sense of fun, the odd love poem and a chunk from his new book for children, The Last Thesaurus, which he calls a "ripping yarn".

One of the refreshing things about Muldoon is that he does not write much about The Troubles. Although he grew up in Northern Ireland, he has lived in America since 1987, working there as a professor at Princeton University. His book, Annals of Chile, which was praised to the heavens for its linguistic dexterity, its "shimmeringly perverse wordplay" that "constantly conjures linguistic vitality and fluidity", ranges in tone from knockabout comedy to profound grief. It contains his famous poem "The Sonogram" about his daughter, now three and a bit, as a foetus, and "The Oscar", which contains the immortal image: "Though she preceded him by a good ten years, my mother's skeleton has managed to worm its way back on top of the old man's, and once again has him under her thumb."

It is hard to label Muldoon. He wants to unsettle the reader, and does so with humour and razor-sharp observation. "There's this theory of writingIthat the end of art is peace," he explains. "And I don't believe in that at all. I believe in the exact opposite. The end of art is disquiet and discomfort and rearranging the furniture in your head." He is the son of a schoolteacher mother and a market gardener father and is a lapsed Catholic. He no longer has close connections in Northern Ireland, or a home there. Both his parents are dead, and neither his brother nor sister live in their native land. His wife, Jean Hanff Korenitz, is American, and his daughter, Dorothy, is growing up American. But Muldoon will not necessarily remain in the New World for ever. His roots, he says, will always be in Ireland.

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When did he decide he wanted to be a poet? "Well, I don't think I've ever really decided that," he says. "I don't really think of myself as a poet. I always shy away from the word 'poet' somehow. It seems like such a tall order, you know." Does he think it sounds pretentious? "Well, I think in many cases it is pretentious," he replies. "I try to write poems. I don't want to sound falsely modest or anything like that, but that is how I look at it." Of course, it sounds ridiculously modest, this notion that the poet Muldoon cannot call himself a poet. But that is Paul Muldoon for you, not wanting to be pompous, anxious that he should not represent himself as more than he is. Yet the answer worries him, too. "It's so hard to write a poem. One is only a poet for those few hours or minutes when one's writing, if even then, if one's lucky. Somehow to describe oneself as a poet means one's done it, you know, and I, at some level, feel I have never quite done it, you know, but always feel as though one of these days I might do it."

Whatever the case, Muldoon began to write poems a long time ago, when he was a schoolboy at St Patrick's College, a grammar school in County Armagh. At university he read English, squeezing in his studies between games of snooker and more poetry writing. He was not a good student, he says. Queen's, Belfast, had a very traditional English department, and he preferred to do other things. But he read some English, including his favourites, Robert Frost, John Donne and Edward Thomas. And his tutor, Seamus Heaney, was a great role model, making it possible "for someone from the middle of nowhere to believe they could write poems" and that someone would publish them.

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His first book of poetry came out while he was still at university. Afterwards, he carried on writing in the early mornings and at lunchtime, fitting in the verse around his job as a producer at BBC radio in Northern Ireland. Muldoon worked on arts programmes, eventually moving on to television work. Altogether, he was with the BBC for 13 years, but he finally quit to write poems full time when it hit him that television was a 24-hour occupation and the BBC was changing in ways he did not like. Also, his father died, which meant he did not need to be in the North any longer. So, he went south of the border, to Dingle in County Kerry, where he lived off a stipend provided under a scheme run by the Arts Council and the Irish government.

It was a brave thing to do - chucking in a safe job with a great British institution in favour of insecurity and living off his wits. But, of course, Muldoon made it. He applied for a fellowship at Cambridge, which he got. There followed a term at the University of East Anglia's creative writing programme, after which Muldoon left the country for America. Since then he has taught at Columbia University in New York, the University of California at Berkeley, the University of Massachusetts and, since 1990, at Princeton. Today he is director of the creative writing programme at Princeton. "The great thing about it is that it allows me to have some time to do my own work," he says.

His great desire, he says, is to produce writing that is accessible and available in the tradition of mainstream English lyric poetry. But it must be said that not all Muldoon's work is easy to read. Some is downright erudite, not to say opaque. For example, "Madoc: A mystery", a poem containing 247 chapters, about Coleridge and Southey's attempt to found a "Pantisocratic" community in 18th-century America, is hard work. Refracted through a mad history of western philosophy, each section is headed with the name of a philosopher, thinker or scientist. "It's a ripping yarn," says Muldoon. "But people find the framework of it a bit daunting."

John Carey, Merton professor of English literature at Oxford, has criticised Muldoon for being less than easy to understand, which miffs him somewhat. Certainly, his new book for children, which is about dinosaurs becoming extinct, is easy enough to grasp - as it should be. He came to write The Last Thesaurus by looking at the word "thesaurus" and letting his imagination run riot. He wrote it in a couple of days and never thought about which age group it might suit: "If anything I thought about it as a book which would appeal as much to parents as children." He is right. The vocabulary is advanced. One of Muldoon's aims is to suggest that there is a whole world of incredibly rich and exciting language out there, which has a past. At the end of the book-poem, he has penned another poem, "A Colossal Glossary", to explain all the difficult words in the first. Written in rhyming couplets, it exhibits all the verbal fireworks and inventiveness for which Muldoon is famed. It begins thus. "The aardvark's a kind of ant-eater, an 'earth-pig' in Dutch, while abracadabra is a charm much favoured by alchemists. As for that wine-coloured gem, the amethyst, a Greek would place it in his cup 'so as not to be drunk', a thought no foul-mouthed Anglo-Saxon ever thunk."

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Muldoon may have a talent to amuse, but in the end his work is much more ambitious. "Poems should change the world at some level," he says. "Each poem should change how you read the world."

The Last Thesaurus is illustrated by Rodney Rigby and published by Faber, price Pounds 8.99.