For 40 years Paul Muldoon’s rococo artfulness has been a standing rebuke to poetry’s more mundane and literal tendencies. Obsessively formalist, Muldoon’s linguistically omnivorous poems have, since The Annals of Chile (1994), used elaborate rhyme schemes to take on difficult material.

Muldoon’s new book continues in the same mode. Anyone interested in new writing will want to read One Thousand Things Worth Knowing, but, as ever, its weirdness cannot be overstated.

The book, like many of its poems and individual lines, often goes the long way around its subjects, then suddenly coheres. Many readers will have the feeling they have seen Muldoon do all this before, at exactly the same time that they get the feeling that no one has ever done anything like this ...

In “Cuba (2)”, Muldoon revisits his earlier poem, “Cuba”, and unspools a trip with his daughter to Havana in leisurely, enjoyably scattershot quatrains:

I’m hanging with my daughter in downtown Havana
She’s worried people think she’s my mail-order bride.
It might be the Anseo tattooed on her ankle.
It might be the tie-in with that poem of mine.

Later, he writes, “Hopped up though I am on caffeine / I’ve suffered all my life from post-traumatic fatigue” and the poem’s oddly underwater jaunt ends ominously:

“The Riviera’s pool is shaped like a coffin.
So much has been submerged here since the Bay of the Pigs.
Maybe that’s why the buildings are wrinkled?
Maybe that’s why the cars have fins?”

Unusually, though, the poems don’t always have their eye (or ear) in. When “Cuba (2)” raises its head above the parapet of its immediate context, it is unusually leaden-footed (“In Ireland we need to start now to untangle / the rhetoric of 2016”), while “Watchtower II, cherry-picks facts about green diesel smuggling and trails off: “It must be because steroids / are legal in the North but not the South the Brits like to eavesdrop / on our comings and goings. As for kerosene, / the fact that it’s cheaper in the North is enough to sicken/ our happiness. That and the upstarts / who try to horn in on our operation.”

Muldoon’s genius, and maybe this is true of all genius, is sui generis, but the pile-up of his signature effects can make for poems that read like stylistic exercises. The book can seem “over the hill” when it crams together his dramatic rhymes, non-sequitur factoids and fragmentary asides (which work so well in live performance), not to mind the obscure proper nouns and modal verbs (could, might, should and would). The opening lines of “Barrage Balloons, Buck Alec, Bird Flu and You” are typical:

After those first paintings at Art Research and Exchange
I would never again be able to go home, never mind home on the range.
The Swede who invented the Aga
had previously lost his sight to an explosion. The rain summoned by a blackbird’s raga
came sweeping over the Shankill, over the burning car
where Boston and Lowther were dumped, having been fingered in the bar ...

Drawing together more and more recherché areas of knowledge, Muldoon seems to be testing the limits of his forms’ capacity, as he looks for ways to offset or freshly register the terror and ache of mortality to which his best poems unsentimentally return.

Before he sews together the slashed throat of a chicken (“Her throat left my own throat raw”) in “Charles Emile Jacque: Poultry Among Trees” there is a typically wonderful swivelling between the hard facts of how things are, and dreams of another life:

Though I might have taken the blueprint of a shack
from Poultry Keeping for Dummies,
I’d fancied myself more of an Ovid in Tomis -
determined to wing it, to tack
together Jahangiri Mahal from a jumble
of 2x4 studs, malachite,
run-of-the mill planks, cedar shingles, more off-cuts
in New Jersey’s rough-and-tumble.

Ingenious, witty and metaphysical as his work has always been, it is impossible sometimes to shake off the feeling that Muldoon, pinballing his way through the weak ties of various unlikely Google searches, is the definitive 21st century poet.

The book’s opening and closing long poems, though, show the limit and the range of Muldoon’s method. Cuthbert and the Otters, written “In Memory of Seamus Heaney”, alludes to the Venerable Bede’s story of St Cuthbert’s secret night-time feeding of otters, witnessed by a monk who is sworn to silence by the saint.

The poem’s 27 stanzas rhyme, mirror-wise, first stanza with last, second with second-last and so, digressively, on. Sometimes it’s brilliant, sometimes allusive to Heaney and more of the time baffling.

If “Cuthbert and the Otters” does not seem to have “naturalized” its wild connections (although, as always with Muldoon, this reader may be missing something obvious and revealing about the poem’s set-up), the same cannot be said about “Dirty Data”, the book’s closing tour de force. Its 19 sonnets and interlaced rhymes (yet again) bring Muldoon back to childhood and his experience of the Troubles, seen this time through the prism of a potted biography of Lew Wallace, author of Ben Hur and a lawman who did a deal with Billy the Kid and served both the Mexican and US administrations.

Wallace’s border crossings are then overlaid with the life of his Irish translator, Seosamh Mac Grianna, and with the plot of Ben Hur.

If that sounds dizzying - we cannot tell if we are in Northern Ireland or the Mexican border or Judaea - the poem’s pay-off is that each of these elements seems to cohere: its different threads amalgamate so that it feels dense and suggestive, weighty and limber, effects magnified by Muldoon’s “out there” use of soundalike phrases: “Ben Hourihane / falls fuel of the new Roman turbine” and, when Pontius Pilate “lets that hanky fall, // it swerves as a morning.” It surely does.