John Banville is a calculating craftsman. The Irish novelist’s 1998 “The Book of Evidence” was shortlisted for the Man Booker Prize and his 2005 novel “The Sea” won it. Critics have compared his dreamy, playful writing to that of Vladimir Nabokov and Virginia Woolf; Don DeLillo praised his work as “dangerous and clear-running.”

So if “The Infinities,” his twentieth novel, is somewhat disappointing, it should come as no surprise that Banville still chose the perfect title to describe his work. In this book, Banville smoothly brings together unbounded ideas and weaves them in mind-bending ways, much like a mathematician might with grand mathematical concepts. He opens new worlds and twists truths (if infinity encompasses everything, there can’t be more than one), but painted with such a broad brush, Banville’s novel comes across more theoretical than credible—an illusory exploration of reality and family too lofty to be moving.

The plot’s premise is fairly simple: Adam Godley, world-renowned Irish mathematician, is dying and his family has assembled at his country home to watch him go. It is no coincidence that Banville uses the name of Shakespeare’s magical forest for Godley’s estate—Arden— and the plot itself is soon complicated by the presence of the supernatural: Hermes, the Greek messenger of the gods, watches and narrates as the awfully-named Godleys eat, drink and live their mortal lives. Other gods also enjoy the human spectacle and occasionally intervene. As Adam lies immobile on his bed, Zeus seduces his daughter-in-law, Helena, disguised as her husband, also named Adam; the trickster god Pan meddles with the household as well.

On a structural level, this setup recalls the myth of Amphytryon, in which Zeus cuckolds an unsuspecting general by taking on his form. References to the myth run through the book—Helena is to play Amphytryon’s wife in an upcoming play and carries a ring with the character’s initial. This parallel story line adds texture to the book’s simple premise. As the Godley family flits and bickers, the gods too flirt with drama. “Oh, Dad,” Hermes frequently exclaims at Zeus’s escapades.

The unfolding plot becomes more and more complex. Godley’s mathematical work deals with parallel universes—and it turns out that the entire book takes place in one. Sweden, we learn, is always on the warpath; Godley’s own fame comes from his success in cold fusion, a process which only works in his world. One begins to wonder at the potential truth of the grandiose statements that Adam turns over while lying in a coma. “My equations spanned a multitude of universes yet they posited a single world of unity and ultimate order,” he recalls.

Banville has said that he wishes to give prose, “the kind of denseness and thickness poetry has.” Practically, this wish causes him to write in long, flowery sentences. He opens his novel with ornate description: “Of 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.” His soft rhythm and languid flow serve to uphold a hazy atmosphere throughout.

Other stylistic choices work less well. Banville frequently expresses emotion through repetition and rhetorical questions, and the forcefulness soon gets tiresome. “But I ask—am I haughty? Do I bridle? A little, I suppose. A little,” reads one of Hermes’ interior monologues. Banville’s moves are well-considered—minds, after all, are noisy places—but it seems unlikely that his characters would really end all their thoughts with vigorous punctuation.

This choice especially hinders the female characters of the book. Where Adam Godley’s thoughts, even in his coma, develop with nuance, the women of the book come across one-sided. Petra, Adam’s melancholy daughter, spends much of the book defined by her stone-like name; her mother rarely acts unless to pour herself a drink. This may be a reflection of the confined place of women within the Godley household. Women, it seems, didn’t have much place in Adam’s math-filled mind. “One I drove to drown herself, the other I drove to drink,” Adam recalls of his wives. But even as such, Banville’s portrayals of his female characters feel flimsy, and almost lazy.

Such unconvincing renderings of human life permeate the book, and they ultimately thwart Banville’s loftier ideas. Where Banville’s concept of parallel universes is enticing, his portrayal of more-grounded daily actions are unsubstantial to the point where one wonders if one should trust him at all. Banville paints the heavenly realm with ease, but he describes sex as “a repeated toing and froing on the edge of a precipice beyond which can be glimpsed a dark-green distance in a reeking mist and something shining out at them, a pulsing point of light, peremptory and intense.” Without a strong foundation in the human realm, Banville’s more conceptual ideas don’t stick.

—Staff writer Madeleine M. Schwartz can be reached at mschwart@fas.harvard.edu.