Boxing writers sometimes try to make comparisons across weight groups. They used to say, for example, that Floyd Mayweather was the best pound-for-pound fighter in the world. Saul Bellow for many years has had the reputation of the best page-for-page writer. Every paragraph has something that arrests you: an image, an insight, a line of dialogue, or a moral dilemma.

This is the kind of thing: ‘My brother picked me up by the trustful affections as one would lift up a rabbit by the ears.’ The sentences flow, both natural and vivid. Bellow can capture the moment’s peace of a commercial traveller, sitting in the garden of his lover’s rented apartment:

He breathed in the sugar of the pure morning.
He heard the long phrases of the birds.
No enemy wanted his life.

Or tell you how to eat an English muffin in a Chicago diner: ‘Torn not cut,’ a woman tells the waitress, so the edges burn a little and grow crunchy. I’m quoting from memory. If it’s the job of a writer to offer a usable shorthand for complex feelings and impressions — ‘the best that has been thought and said’ — then Bellow looks like the natural successor, only a few hundred years late, to Shakespeare.

But there’s also a kind of sting in such praise, and the stock of Bellow’s reputation has probably fallen since his death in 2005. The second volume of Zachary Leader’s brilliant biography begins where the last one ended, with the publication of Herzog in 1964, and Bellow at the height of his fame. His success was astonishing. ‘Within a month of publication, Herzog was number one on the bestseller list, supplanting John le Carré’s The Spy Who Came in From the Cold.’ This for a novel about a semi-employed academic who wrote a book about Romanticism and Christianity and spent much of his time firing off letters to other scholars about their work. There’s something odd, noble, but also disconcerting about a literary writer who reaches the top of the pops by sticking to his esoteric tunes. But ‘money kept rolling in’ — including $371,350 for the paperback rights to Augie March and Herzog. ‘Guys, I’m rich,’ Bellow told his friend Mitzi McClosky. He was riding a wave.

One of the oddities of Herzog is that he seems much older than he really is — and Bellow himself was still shy of 50 when the novel came out. Yet you can already see in both book and man the terms according to which he was in danger of becoming dated, or losing touch. On civil rights, on the war in Vietnam, on Israel, he found himself drifting away from the literary liberal consensus. During the various students protests at the University of Chicago in the 1960s, Bellow tended to take the administration line. He also showed up at President Johnson’s White House Festival of the Arts in the summer of 1965, which other writers, such as Philip Roth (a friend and follower) and Robert Lowell, boycotted to protest against the war in Vietnam. Bellow himself was hardly a champion of this war, but he thought, if the president invites you, you show your face.

And yet on other issues he refused, as he once put it in an interview with the critis Michiko Kakutani, ‘to line up’. Especially on civil rights, which got him frequently into trouble. Leader writes carefully and thoughtfully on tensions in Chicago between the Jewish and African-American communities. Bellow’s provocations fell roughly into three categories: the things he said because he had thought about and deeply studied the crisis of American cities, and the culture that came out of them, and wanted to utter hard truths; the things he said to get a reaction; and the things he said stupidly or worse. But it’s not always easy to tell them apart.

Bellow landed in hot water for a remark he made over the phone to James Atlas, who quoted it in a New York Times profile of Bellow’s friend and co-teacher Alan Bloom: ‘Who is the Tolstoy of the Zulus? The Proust of the Papuans?’ Leader remarks: ‘Few words by Bellow have done more to alienate liberal and academic opinion than these, or to banish his fiction from college syllabuses.’ Bellow himself tried to give an explanation for the remark, in an op-ed piece published in the Times: he was only trying to make a distinction between literate and pre-literate societies, of which he had been a student, as Leader points out, for much of his life. All of this gets complicated. In culture wars, everything is connected to everything else.

And yet sometimes it also isn’t, and writing fiction has a way of exposing any blind spots in our view of the world. When the black pickpocket in Mr Sammler’s Planet silently exposes his genitals to the old Jewish hero, it’s hard to see this as a complex account of a complex racial situation. (I don’t think the pickpocket gets a line of dialogue in the whole book.) And yet that’s exactly how the Times’s own review characterised it by giving him a voice: ‘Silently, underlining the message with his eyes only, the Negro says in effect: the contest is unequal. Give it up.’ (In a curious twist of fate, the reviewer, Anatole Broyard, was himself mixed race, and at least by some accounts ‘passed off’ as white for much of his life.) Mr Sammler’s Planet won a National Book Award in 1971, Bellow’s third.

For a writer who specialised in deep sympathies, Bellow could run short, not just in his fiction but in his life. He put his kids through the misery of several divorces and spent a decade of his life battling his third wife, Susan, in court, without much regard for the poison leaching from this legal conflict into the family groundwater. And yet Leader’s biography is an attempt to address another kind of failure of sympathy — of Bellow’s previous biographer, James Atlas, who knew his subject and let the work be coloured by his personal feelings (not to mention his own ambitions). Leader’s portrait manages to be both subtle and even-handed. Bellow could be a real jerk, but he could also be a decent colleague, a generous teacher, a conscientious reader, a lively father and a thoughtful friend.

And part of the pleasure of the biography is the light it shines on some of the work. Leader writes well about the books themselves — not just on their biographical sources but on their virtues and literary faults. Characters from Bellow’s life kept recurring in his fiction (even if, as his last wife, Janis Bellow, warns, ‘Biographers, beware; Saul wields a wand, not scissors’). But you also see the way his human failings show up in the work. His vivid depictions of women sometimes get in the way of more natural relations with them. And the characteristic Bellovian narrator, articulate but also a little goofy, dreamy and out of it, in need of what he calls ‘reality instructors’, is a front that conceals the determination of the author to get his own way. Bellow tended to imagine himself in his fiction as something related to but other than what he was. Instead of the famous, wealthy, world-travelling Nobel Prize-winning novelist, for example, he figured himself as an academic, or botanist, or musicologist, and the displacement partly accounts for something missing in his portraits of each: the decent mediocrity of ordinary lives.

But the biography also gives glimpses of Bellow’s extraordinary literary intelligence, shaping and seeing him through the mess of his own life. Bellow’s fourth marriage, to the Romanian mathematician Alexandra Ionescu Tulcea, failed partly, Leader writes (quoting one of the many interesting and subtle insights of the writer’s children), ‘because she was not going to take care of him… on a deep level the attachment was not strong enough’ to see him through the final stages. And in fact his last marriage — his fifth — to one of his former students, Janis Freedman, turns out to have been his happiest — and did the heavy labour that he needed it to do. Apart from anything else, their relationship made Ravelstein possible, his last great work, based on the life of Allan Bloom, published when Bellow was 85.

Leader’s two-volume biography is an astonishingly detailed and thoughtful record of an important life. American kids playing football in the street tell each other to ‘go long, go deep’, before hurling a pass downfield. Leader goes long and deep here, using Bellow as a kind of supersensitive canary to guide us down the mines of 20th-century culture wars. And whatever else you think of him, the guy could sing.