As he lay dying, Saul Bellow asked a friend: "Was I a man or a jerk?" The case for the prosecution would argue he had five marriages, four ending in divorce, numerous affairs, and was too self-absorbed to be much of a father. "He had a biblical Old World morality," said one woman who encountered him, "but his fly was entirely unzipped at all times."

Bellow was quick to take offence and got involved in endless rows with agents, publishers and often with his closest friends. In recent years, Bellow's novels were accused of being unfair to women. "What do women want?" his most famous character, Herzog, wonders. "They eat green salad and drink human blood." Some of his public pronouncements smacked of racism. "Who is the Tolstoy of the Zulus? The Proust of the Papuans? I'd be glad to read him," he once wrote. Some years ago, I produced a TV programme with Bellow and Martin Amis. Bellow had been one of my heroes for years but I found him cold and unlikeable.

And yet… Few modern writers have created more sympathetic characters, decent, humane, thoughtful, like Augie March, Charlie Citrine and Moses Herzog. They worry endlessly about what it is to be a good man, to lead a good life.

Bellow inspired two generations of younger writers, from Philip Roth whom he met in Chicago in the '50s to Martin Amis, Ian McEwan and Salman Rushdie. And perhaps above all, he spoke to Jewish readers like no one else, with his evocations of immigrant tenements in New York, fast-talking hustlers in post-war Chicago, his prose and dialogue crackling with Yiddish rhythms and cadences.

I first read Bellow's masterpiece, Herzog, for A Level long ago. We had battled through Jane Austen, Jane Eyre and all the other Janes and then came to our last set text. One of our teachers refused to teach it because it was not proper English. Even though I had never heard of Herzog or its author, Saul Bellow, I pricked up my ears. Then I read the first sentence: "If I am out of my mind, it's alright with me, thought Moses Herzog." I still have my old Penguin 1973 edition with the wonderful Ben Shahn drawing on the cover. The sentence is underlined in blue biro. That spring day I fell in love with Saul Bellow's writing.

I understand why women critics like Linda Grant worry about Bellow's misogyny. I see why non-white readers dislike his description of a black mugger in New York in Mr Sammler's Planet.

Bellow causes more offence than many great writers. However, there is something so smart, so modern, so moving, and so Jewish, about his writing that it speaks to me like no other novelist.

First, there's that voice. From The Adventures of Augie March in the early 1950s that voice stayed recognisably the same for half-a-century. Part Russian, part American and part Jewish it is the literary equivalent of the opening of Gershwin's Rhapsody in Blue.

From his Russian roots, he picked up a love of big ideas and a kind of soulfulness. Then from his childhood in Chicago, the younger brother of two larger-than-life machers, he found a verbal energy and love of street-language that sets him apart from any of his contemporaries.

Philip Roth once wrote that Bellow's novels gave voice to "the language you spoke and the stuff you heard, the American argot that you heard on the street." What other writer, wrote Martin Amis recently, "has such a reflexive grasp of the street, the machine, the law courts, the rackets?"

We first heard that voice in Augie March. Think of its opening sentence: "I am an American, Chicago born - Chicago that sombre city - and go at things as I have taught myself, free-style, and will make the record in my own way: first to knock, first admitted; sometimes an innocent knock, sometimes a not so innocent."

What is striking here, and in all his best writing, is the torrent of words, it just pours forth. "The book just came to me," Bellow wrote. "All I had to do was be there with buckets to catch it."

That opening sentence has it all: Chicago with its hustlers and tough guys. Then there are those opening words, "I am an American". Bellow has tapped into an American literary tradition that goes back to Tom Sawyer and Huck Finn, more Redskin than Paleface, youthful and energetic.

And then comes the Jewish component. The Yiddish words (remember that there were hardly any Jewish writers among the great American writers between the wars). Bellow translated Isaac Bashevis Singer's Gimpel the Fool. He translated T S Eliot into Yiddish.

It is true that he hardly wrote about the Holocaust until the late '60s and Israel barely features in his novels. However, Jewishness runs through Bellow's writing like mustard and mayo in a perfect pastrami sandwich: Old Testament morality, nostalgic evocations of the old immigrant world and, above all, the rhythms of his prose. My old teacher was right. It's not proper English. It's a language in which Russian Jewish immigrants meet mid-century Chicago, unlike anything modern literature had ever seen.

All of this starts in Augie March.Philip Roth, the best writer on Bellow, is good on the particular kind of Jewishness we find there. Bellow takes the sentimental nostalgia for what Irving Howe called "The World of Our Fathers", but then adds a shock of high-energy America. In Augie March, Roth said to Bellow in an interview, "you plugged into Jewish aggression and Jews as businessmen… That's what's at the heart of your book, which is the small-time lawyers, the owners of the middle-sized businesses, the conniving and cheating. You were not ashamed of Jewish aggression because you saw it as American aggression… It was Chicago aggression."

Perhaps this goes back to Bellow's childhood. Like most of his central characters, Bellow was the smart, bookish one, preoccupied with what he later called "the deeps". His brothers, though, were both tough, self-made men who started out in the coal business and became millionaires.

Bellow's books bring together men of the world like his brothers and people like Herzog with their head always in a book, worrying about big ideas about literature and philosophy. Heraclitus appears in the second sentence of Augie March, Herzog is named after a character from James Joyce and is writing a book about the Roots of Romanticism.

But in Augie March we soon meet Joe Kinsman, the undertaker's son and on page 5 of Herzog we hear about how Herzog's "sexual powers had been damaged by Madeleine." Romanticism and sexual damage, Heraclitus and Joe Kinsman. That mix of the high and the low, constantly churning together, is at the heart of the genius of Saul Bellow.

Roth is right to see the aggression in Bellow, both the man and the writing. Perhaps he's too aggressive for our PC culture. But aggression is just one component.

Bellow will make you laugh out loud - you cannot read his account of Augie's brother being taken off to an institution without a tear in your eye, and he brings the world of ideas to life like no one else.

So much goes on in Bellow, so many tones and moods rubbing against each other.

One hundred years after his birth in Lachine, Quebec, Saul Bellow remains one of the greatest writers of modern times.