Though likes to say that he writes in “a literary patois” he calls “Hiberno-English,” the Irish novelist and critic is, without question, one of the great living masters of English-language prose.

“The Infinities” – his 15th novel and first work of literary fiction since “The Sea,” which won the 2005 Man Booker Prize – is a dazzling example of that mastery, as well as of the formal daring and slyly erudite humor that make his novels among the most rewarding available to readers today.

In the years since his Booker triumph, Banville has published two superb detective stories under the pseudonym Benjamin Black. “The Infinities” is emphatically a Banville novel and one that surely will delight his many well-deserved admirers. Adam Godley, a world-altering mathematician, is dying. While in the midst of a difficult bowel movement – Banville is a wonderfully elegant chronicler of his characters’ earthier moments – he suffered a paralyzing stroke. Now, in the “sky room” of Arden, his country house, he awaits death. His utterly dysfunctional family – an alcoholic wife, a lumpish son, a daughter given to self-mutilation, a couple of anxiously problematic pseudo-servants and a wretched disciple-cum-aspiring biographer – have gathered at the great man’s bedside.

Banville fans may feel they’re – in one sense, at least – on familiar ground. Three of his previous novels have explored science and, particularly mathematics – “Doctor Copernicus” (1976), “Kepler” (1981) and “The Newton Letter” (1982) – and it’s clear that the ambiguous ground between quantitative certainty and aesthetic assertion preoccupies this writer in a particular way. The formal structure of his new novel is the key to its narrative exposition. Banville evokes and simultaneously subverts the classical unities – all the action takes place in a single day; there is progress from light into darkness. Indeed, the first and most obvious of the narrative conceits is that the old, Homeric gods are once more alive and the storytelling voice is that of Hermes, who begins his tale with this exposition:

“Of all the things we fashioned for them that they might be comforted, dawn is the one that works. When darkness sifts from the air like fine soft soot and light spreads slowly out of the east then all but the most wretched of humankind rally. It is a spectacle we immortals enjoy, this minor daily resurrection, often we will gather at the ramparts of the clouds and gaze down upon them, our little ones, as they bestir themselves to welcome the new day. What silence falls upon us then, the sad silence of our envy.”

Formally, “The Infinities” is – on one level, at least – a gloss on the German Romantic playwright Heinrich von Kleist’s retelling of the story of Amphitryon and, indeed, within the first few pages, a lustful Zeus has descended to take the form of the younger Adam Godley and has ravished his beautiful, young actress wife, recently cast in a production of Kleist’s play.

Banville’s narrative is salted with clues to his intentions, though historical and technological details are oddly off-kilter. The elder Adam is dying with all the apparatus of contemporary state-of-the art medicine deployed at his bedside, while outside a steam-powered train stops each morning near his country house. Adam the mathematician’s revolutionary contribution is the proof that Einstein et al. were hopelessly wrong and that an infinite number of parallel universes exist. Hence this novel’s world, in which the classical unities are fulfilled utterly by the continued existence and intervention of the old gods. Adam’s insight is a revelation which – in post-modern fashion – nonetheless brings him little satisfaction:

“The majority of them I despised. How they fawned and flattered when they saw at last the irrefragable rightness of what I had made. But then, did I not despise myself, also, myself and my work, my capitalized Work, of which I am supposed to be so vain? Oh, not that I think my achievement is less than anyone else’s … only it is not enough for me. You take the point. The world is always ready to be amazed, but the self, that lynx-eyed monitor, sees all the subterfuges, all the cut corners, and is not deceived.”