Having a god as a narrator gives you freedom to do anything, say anything'

It takes a certain chutzpah to write a novel narrated by a Greek god. But then, John Banville has always been in a class all his own. As the celebrated Irish novelist points out with the same understated brand of irony and playfulness that characterises his 15th novel, The Infinities, "not many people would be arrogant enough to try".

Long lauded as one of the most accomplished novelists of his generation, Banville is also famously charming and mischievous in conversation, but has always enjoyed more renown for writing "difficult" novels than for his humour.

Indeed, until his masterly 2005 novel about grief and memory, The Sea, won the Booker Prize, he was considered a difficult author who was read by only a few thousand devotees. He recalls with wry humour the moment when he told his publisher that The Infinities, which he began in 2004, before his Booker Prize win, was narrated by the Greek god Hermes. "His face fell, and he said, 'Oh yes John, another crowd pleaser?'"

Given, too, his reputation for writing novels centred around damaged, often bitter male protagonists of a certain age, it would perhaps have been no surprise to his publisher that The Infinities would also tell the story of a man on his death bed. Yet, The Infinities has left many a literary pundit lamenting its omission from this year's list of Booker Prize nominees.

Even Banville, who is long inured to the tag of "difficult", "weighty" or "plotless" - or all three - that tend to accompany his literary novels, is quick to concede that "there's a certain playfulness in this book that has probably been absent from recent ones. And I like it."

He quips: "Having a god as a narrator gives you freedom to do anything, say anything. But I do feel that there's a little more light, a lot more humour. None of which I really intended but when that happened, I was very pleased that it had."

Penned over the past four years, in and around the process of writing three detective novels under his pseudonym, Benjamin Black, The Infinities is a wickedly playful novel that seduces, dazzles and confounds in equal measure. Unfolding across a single summer's day, it sounds every conceivable note from bawdy through to tragic and comic as it tells the story of Adam Godley, a once great mathematical theorist delivered to death's door by a stroke caused by straining on the lavatory.

Having once grappled with concepts of infinity, Godley now lies comatose in a room at the very top of the house, halfway between heaven and earth.

Unknown to the various family members, including his second wife, Ursula, a closet drunk, his self-harming daughter Petra, and his guileless son Adam, the immortals, too, have gathered not only to observe, but to play.

Quiz Banville about its elusive, mischievous properties, the unmistakable sense of transcendence in its seams, and he reveals that "the first inklings of the novel was that wonderful line in Emerson where he says 'a man is a dog in ruins' and I rather think Hermes is sort of the opposite of that. He's a man in a state of transcendence because I suspect the whole farrago is going on inside old Adam's godless head. I don't know, but I wanted that ambiguity."

He is at pains to acknowledge Heinrich von Kleist, whose blending of classical drama with Shakespearean burlesque in his 1808 play Amphitryon was inspiration for the novel, and makes an eloquent case for a return to Paganism. "What I love about the Greek gods is that they're as greedy, small-minded and malignant as we are. They just happen to be gods and I think that's quite a good representation of reality because there is so much of the world that we cannot see or know.

"I think that religion at its best is a wonderfully poetic way of looking at reality, and I liked that notion of the dream world of the gods on one side and the so-called rational world of mathematics on the other. But then science nowadays is becoming much more poetic anyway."

His oft-stated aim is to write prose that resembles poetry. "What I want to convey is some sense of the other-worldliness of this world, the extraordinariness of the ordinary." In The Infinities he has undeniably hit a grace note, but is quick to tell you he's not among those lamenting its failure to make the list for this year's Booker Prize.

"Over the past six years, maybe only four, starting with me," he chuckles, "they've given it to some very odd books. Now it's back on track. It is an English prize," he reminds me minutes later, mischievously adding, "I can never understand why they let Irish people into it."

He chuckles at the mention of the controversy surrounding his own 2005 Booker Prize win, which was described by one eminent London critic as "... perhaps the most indefensible choice in the 36-year history of the contest".

"It amused me," says Banville. "It's good that there's controversy about the Booker, that's what keeps it so popular." But he does take issue with the frequent use of the term "cold" to describe his prose or his novels. "To me they're embarrassingly warm and overflowing with sentiment. But when you get a label, it sticks"

Nor does he see his novels as being particularly difficult. "Unlike many people supposedly catering for popular tastes, I don't despise my audience. I think anybody can read my books and I have frequent evidence that what they (the critics) consider to be anybody, does."

He relates how once when his wife was grocery shopping in Marks and Spencer, the checkout woman said: "Are you related to John Banville? Tell him The Sea is the most beautiful thing I've ever read." "And that," says Banville, "is the best review I've had in a long time."

• The Infinities is published by Picador, R195