Arthur Miller had integrity. It is what gave his work its tensile strength

I first met Arthur Miller nearly 30 years ago, tracking from New York into a Connecticut where the woods were aflame. It was what is known as the leaf season when the maple trees turn to liquid colour. There were no hotel rooms to be had and I spent a night on a fold-down bed in the middle of a conference centre. It was the last time I had to do that. In all the years that followed I was welcomed into his home.

He was a carpenter and took as much pleasure in fashioning furniture from the wood as he did from creating plays from his words. He made the table from which he ate, consulting a professor of mathematics to get the angles right. What he wanted to create was a table at which 12 people could engage in the same conversation. Maybe that was how he saw the stage.

When an apple tree in which his daughter used to play blew down in a gale, as it did in his play All My Sons, he fashioned the wood into salad servers. He also loved machines. He would drive around in a Land Rover bought in England more than 40 years ago, mending it when it broke.

When he left university in 1938, he took with him a play that he hoped would be accepted by Broadway. The producers found it "too Jewish," even though they were Jewish themselves. Anti-Semitism in New York was, he explained, "fierce".

When he travelled south on behalf of the Library of Congress, to collect regional accents, he was threatened by a man with a shotgun who assumed that anyone connected with federal government must be Jewish. No wonder that, after the failure of his first play, The Man Who Had All the Luck, he should write a novel against anti-Semitism.

He was an American author who wrote against the American grain. So, beginning in wartime, he wrote a play about a manufacturer who sent defective parts to the Army Air Force. It was banned by the military in occupied Europe. At the beginning of one of the greatest booms in US historyhe wrote Death of a Salesman, about the human cost of the distortion of the American dream. When he might have kept his head down he wrote The Crucible. As a result, his passport was withdrawn and he had to make a trip to the House Un-American Activities Committee. When the Vietnam War broke out he was at one of the first teach-ins and flew to Paris for negotiations.

Yet it was the plays that mattered, plays in which the past was so often brought into the present because he was insistent that actions have consequences. He was not interested in guilt but in responsibility. In so many of his plays there comes a moment when the central characters call out their names, desperate to invest them with meaning, even as they are tempted to betray the integrity for which they reach. Miller had integrity. It is what gave his work and his life its tensile strength.

He wrote his first play in 1935. His most recent opened last year. His career lasted longer than those of Chekhov, Ibsen or Strindberg, alongside whom he can surely take his place. I think Finishing the Picture was genuinely his last work. For the first time there was no new play in prospect. And though that was a play begun in 1978 its title now has a special poignancy.

His characters, shaped for dramatic function, still bear the marks of their humanity as the furniture he builds carries the grain of the wood, with its striations of the passing years. In a poem, he talked of drawing time out of the air and shaping it into form. It described the wood he shaped with his hands but also his plays. In that poem he recalls the pleasure of "mornings in the woods/ Before I vanished into what I made," adding "I think I endure exactly as I disappear." So he does. So he will.

The author has written several books on Miller