Meeting Arthur Miller is awesome. He stands at the door in chinos and shirtsleeves, a huge figure in 20th-century American literature and - thanks to his second marriage to Marilyn Monroe - popular culture.

He is 78 years old. Are his powers waning; is he stooped, ailing, rambling? None of those things. His handshake is muscular (having been a passionate carpenter all his life, he has strong, working man's arms). His smile is wide and engaging, his eyes bright. He is deeply tanned, courteous, brisk.

He is in London for the final rehearsals of his new play, Broken Glass, which opens this week at the Royal National Theatre. This is no accident. David Thacker has become the leading director of Miller's work, and the National Theatre company its leading interpreters. The demise of serious drama on Broadway means that he is much more widely seen in this country than in his own. He and his third wife, the photographer Inge Morath, are staying in a hotel behind Marble Arch, in the same room that he has had on every visit for the past 20 years. The area has changed, he says, quite non-judgementally; more Arabs. Arthur Miller has always been interested in the plight of minorities, but his plays have not until now dealt much with anti-Semitism.

Broken Glass, however, set in 1938, tells the story of a woman seized with hysterical paralysis, which she ascribes to Hitler's treatment of the Jews in Germany. 'There's a magical element in the play, I might as well confess: a woman who by virtue of her own sensibility is affected by something going on 4,000 miles away. I knew that woman when I was a teenager; she, and the story, came out of my own past. But her plight is not specifically Jewish. It could apply to any group of people who feel endangered because of their identity - be they Armenian, Basques, Irish or Jewish.'

Miller's fame was established in 1947 with All My Sons, followed two years later by Death of a Salesman. Like everything that was to come, they dealt with central emotional and moral questions in American life - and his own. The Crucible, written in 1953, is an evocation of the Salem witch trials in Massachusetts and the religious hysteria that erupted in 1692. He wrote it at a time when anti-Communist hysteria and the egregious performance of Senator Joseph McCarthy's witch hunt as enacted through the Un-American Activities Committee gripped America. Those hearings involved Miller himself. After his marriage to Monroe in 1956, he was offered a chance to escape interrogation if his wife would agree to be photographed with the chairman of the Senate hearings, Francis Walter. She and Miller declined. He was subsequently tried on a charge of refusing to give the name of a writer suspected of being a Communist; indicted for contempt and convicted. A year later his conviction was overturned on appeal.

Arthur Miller was born in New York in 1915 and brought up in Harlem and Brooklyn. He grew up amid the street-life and language, music, poverty, struggle for respectability and violence of that city in the Twenties. Few people owned or read books; his own father was illiterate. He remembers vividly the impact of the crash of 1929 and the consequent struggle for survival. The savagery of New York is not new: in his autobiography, Timebends, Miller recalls being knocked down aged nine and robbed of his rollerskates. So nothing's changed?

'A great deal has changed. The city of New York, which was once, in my youth, the most progressive place in the United States, is losing population each year because people can't find a comfortable or even a reasonable way to live in it. Drugs are a devastation, a plague - like being attacked by malaria.' Miller is part of that exodus: 40 years ago he bought an estate in Connecticut, where he does most of his writing.

How important is his Jewishness to Miller?

'I see the whole Jewish ethos - that sense of living as a minority, sometimes persecuted, the victims of prejudice, but cliquish, too - that sense is shared by many other people. To me it's important only because I was born into a Jewish family and we had a certain amount of ritual, but nobody was all that bound up in it. I can't shred my identity and tell you which part of it derives from being Jewish. I guess I'm that mixed-up thing, an American.'

None of his wives was Jewish. Did this make for difficulties?

'My first wife's family was opposed to her marrying a Jew. People were much more conscious of it in those days, before the Second World War; they were more parochial. Anti-Semitism was quite dense in the United States, and Catholics in particular were very much influenced by the Irish clergy. That's pretty well gone now. Mary (his first wife) reverted to a kind of childish fear and a wish to please her extremely neurotic mother, who feared hell and damnation awaited her daughter for marrying me - although she hadn't been near a church in years, and never would again.'

Why did his second wife choose to convert to Judaism? Was it to please him or even his parents?

'Marilyn Monroe wanted to convert to Judaism, which seemed to me rather unnecessary. I had a good friend who was a young rabbi and he was eager to perform this ceremony, preceded by an hour's rather meaningless conversation, which was her 'instruction' in the Jewish faith. I think it was a sentimental thing on her part. She'd been brought up - if you can call it being brought up - she'd been exposed to this fundamentalist Christian rapture, which she came to hate I think, from the people who took care of her when she was a child.

'She wanted to belong to something; but it proved to be something that passed quite quickly, and I don't think it meant a damn thing. Marilyn could not belong anywhere, finally.'

Miller writes in Timebends with protective tenderness about his years with Monroe. They met and had an affair in the early Fifties, while she was still an unknown young actress. He divorced his first wife, Mary, and married Marilyn in London in 1956, to the enormous delight of the press ('The egghead and the hourglass' was a typical headline). She died exactly 32 years ago, one year after their divorce had become final.

'What I wrote was a reaction to a lot of people, including Norman Mailer, who tended to diminish her - this was before the mythology had taken over. The tendency was to denigrate her in any way possible. Nobody killed her, in my opinion - not literally killed her - but that sense she had of being a target was part of her dying, I think. This was in the days before the whole sexual display grew so much stronger.' Marilyn became both an icon of desire and an object of destructive rage. Yes, Miller confirms, plenty of people did want to kill her; certainly to see her destroyed.

There are two kinds of fame: the celebrity limelight, and lasting recognition. Is the second kind easier to live with?

'I'm no longer a person but some kind of an icon: I guess that's part of the whole phenomenon. I've managed the whole thing with a minimum of inconvenience, but it's still there.'

Back to his play. Why is Broken Glass being previewed here?

'I like to do my plays here, (a) because the National has generated a wonderful audience, and I'm not hearing every minute about the money involved in mounting a production - which seems to be all we talk about in New York; and (b) because there is a more conducive atmosphere for serious work in London.

'At dollars 50 to dollars 100 per seat, there's an extremely limited audience on Broadway, where the true audience has been driven away by high prices. The theatre there has passed crisis and is in a state of calamity. Every time I'm in London I see plays at the National or the RSC which I could never see done on that level at home.

'We're making it practically impossible for actors or new writers to make a living in the American theatre, while a handful of big musicals are making a mint. It won't stop me writing, but as a young writer it might have done.'

To whom does he now address his plays?

'Good question. I suppose I'm talking to myself. A certain number of people are interested - though the number interested in films is outrageously greater. To me, when it's good, the theatre is more exciting than anything else. But today, people's consciousness is awakened by TV and the movies, not by the theatre, and maybe that's permanent. I don't see any sign that it will change.'

Does it matter if the flickering screen has become the crucial art form?

'People will have lost a human contact. In the theatre you're looking at a human being, not a picture of one, and hearing his voice, not a recording. Theatre is the art of the present tense. The movie form is based on dreams, and so the movie arouses passivity: it happens to you. A play requires language, which takes an effort of listening and interpretation; consequently the effort becomes part of the enjoyment: but if you have an audience trained not to put out effort, it arouses impatience. Passivity always wins out because it's easier.'

What else, apart from writing, preoccupies him?

'I am very interested in politics and social development: the jumble of events around the Clinton administration is bothersome right now. If you look sharply at it, there is no personal scandal; there is adversary journalism. I don't think anything has been unearthed which is to his discredit. They put in a Republican investigator who comes up with nothing, and they go right on looking . . .

'But Clinton isn't the issue. The issue is whether we'll use the wealth we've got to make a more just society. I'm an optimist. In the long run we manage to improve matters - but people don't live in the long run; they live every day, and there's a lot of desperation in the country, and a deterioration in people's morale.

'Accompanying that is a serious deterioration in the very concept of being responsible for one's own life. In some ways that idea is almost incomprehensible to some of the young. It's partly because people are sometimes literally helpless to fend for themselves. De-industrialisation has invalidated tens of thousands of people who were formerly highly skilled.

'Take General Motors. It used to be mother and father to thousands of people who expected their children and grandchildren to take their places. Now, the idea of loyalty to a company is absurd. The idea that once cemented the country - that there was a connection between a man and his labour - has gone. Now you look out for yourself, hiring out your labour, unable to predict what will happen next week; and when we cannot predict the future we live in a state of extreme anxiety. A politician who chooses to work on that terror, the fear of the unknown, can always go some distance: though Ross Perot didn't get very far, did he?

'The country is in a long, unadulterated depression and, short of restructuring the economy, I see no end to it. It's a consequence of the end of the Cold War.'

What has improved?

'What is better, despite everything, is the race question. People have a consciousness and a new sensitivity, partly as a result of race riots, so that the United States may now be the first truly multi-ethnic society. We've got 40 members of Congress who are black - I remember a time when there weren't any.'

Despite the events he has seen in 78 years, despite his dismay at the spreading horror of tribalism (he means nationalism in its worst guise, as in Bosnia), despite the fact that his own country knows less about his work than Europeans do, Miller's demeanour is not that of a disappointed, let alone a defeated man. His creative vigour is remarkable; his speech and his physical presence are youthful and energetic. Despite everything, Arthur Miller remains an optimist. Icon, or guru, or great writer, or carpenter, Arthur Miller is amazing. No wonder she married him.

(Photograph omitted)