John Banville’s territory is the memory novel, in which ageing narrators sift their treacherous recollections and weighty secrets. Although he has established a crime-writing pseudonym in the interim, The Infinities is Banville’s first novel under his own name since his Booker Prize-winning The Sea (2005). Although there is again an ageing – indeed, dying – man at the centre, the book offers a playful revision of his familiar territory, its tone one of sportive, bawdy metaphysics during a single midsummer day.

Adam is an elderly, world-renowned mathematician who has suffered a stroke in Arden, his Irish country house. His family and acolytes hover like ‘mourners-in-waiting’, while Adam lies like ‘a dead pharaoh’ in an ugly four-poster, curtains keeping out the light. This is not a happy family, though it’s