In his 1985 Jerusalem prize acceptance speech, Milan Kundera spoke about the novel’s ability to transcend binaries, using Tolstoy’s Anna Karenina to illustrate his point. “The novel is the imaginary paradise of individuals,” he said. “It is the territory where no one possesses the truth, neither Anna nor Karenin, but where everyone has the right to be understood, both Anna and Karenin.” In an age of certainty, the novel is the home of doubt, of ambiguity, of multiple truths.

Colum McCann has written something he calls a “hybrid novel,” in which the form’s mutability, its stance on both sides and neither, is used to address the entrenched positions of the Middle East. The title is taken from the mathematical term for an object of an “observably infinite number of sides”, a shape that serves as a model for a new way of thinking about a conflict that is too often reduced to simple, opposed positions.

It’s a strange time for a novel as full-hearted as Apeirogon. It feels as if the situation in the Middle East is always a reflection of its age. In the optimistic 90s we had the Oslo Accords and a real sense that some solution to the conflict could be found through diplomatic channels. Now each side has retreated into belligerent isolation, with Donald Trump gleefully fanning the flames of discord. But perhaps that’s the point – the desperation of the situation has brought forth a work of art whose beauty, intelligence and compassion may go some way to changing things. Is it absurd to suggest that a novel might succeed where generations of politicians have failed? Perhaps, but then Apeirogon is the kind of book that comes along only once in a generation.

You don’t read Apeirogon so much as feel it – the particular tragedies are lived out in an ever-present moment of loss

This is McCann’s seventh novel. In 2009, he published the wildly successful Let the Great World Spin, which won a National Book award and the Impac prize and was translated into 40 languages.

Apeirogon takes its inspiration from the real-life friendship between a Palestinian, Bassam Aramin, and an Israeli, Rami Elhanan: “An Israeli, against the occupation. A Palestinian, studying the Holocaust.” The men are united in their grief – they lost their daughters: Smadar, turned into “a scattered human jigsaw” at the age of 13 by a suicide bomber, and Abir, assassinated aged 10 by a trigger-happy member of the Israeli army. Both men join the Parents Circle, a group of the fellow-bereaved who unite in their sorrow to press for a peaceful resolution to the conflict: “This became their jobs: to tell the story of what had happened to their girls.”

Apeirogon is structured as 1,001 individual chapters, some as short as a sentence, some comprising Sebald-like photographs, some merely blank spaces (a reflection of one of the mathematical theorems that underlie the novel). The central chapters of the novel are deeply moving interviews with each of the protagonists: “elsewhere in this book,” McCann says in an author’s note, “Bassam and Rami have allowed me to shape and reshape their words and worlds”.

The number of chapters is a reference to the 1,001 Arabian Nights – “a ruse for life in the face of death”. The novel pivots on a single day in 2016, when the two men travel to a meeting of the Parents Circle in a Cremisan monastery in Beit Jala. The bereaved parents are there to do what we do as we read the book: “to listen to the stories of Bassam and Rami, and to find within their stories another story, a song of songs … remembering, while listening, all of those stories that are yet to be told.”

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You don’t read Apeirogon so much as feel it, as the particular tragedies of Bassam and Rami are lived out in an ever-present moment of loss. The deaths of Smadar and Abir are interlaced with a host of other tales that enter into a strange and powerful dialogue with the stories of these two girls who had barely begun to live yet. We read of Bassam’s epiphany in prison as a young man watching a documentary about the Holocaust; we read of the Israeli soldiers who came to build a playground in memory of Abir, despite the risk this posed to their lives; we read of the tragedy of divided geography and shared history; we wander off down seemingly unrelated tangents about François Mitterrand’s last meal, about the high-wire walker who crossed from Palestine to Israel, about a mad missionary, about birds, about Borges and Darwish and a vast chorus of others who comment, however obliquely, on the situation in Palestine.

For all its grief, Apeirogon is a novel that buoys the heart. The friendship of Bassam and Rami is a thing of great and sustaining beauty. There’s a picture of the two of them, asleep together on a train in Germany, travelling from one speaking engagement to the next. They lean against each another, Rami – the older man – supporting the smaller Bassam as he sleeps. This, the novel suggests, is the solution to the conflict: something as simple and easy as friendship, as the acknowledgement of a shared experience, as love. I kept thinking as I read it about all the ways that Apeirogon could have failed, about the ammunition it might have provided to all of those who claim that no one should write a novel that reaches beyond their own particular experience. It could have been maudlin, tawdry, exploitative, trite.

Instead, it’s a masterpiece, a novel that will change the world, and you don’t hear that very often.

• Apeirogon: A Novel by Colum McCann is published by Bloomsbury (£18.99). To order a copy go to guardianbookshop.com. Free UK p&p over £15