"It's my first time in Venice," her son says. "And it feels like the emperor's new clothes: a weird dream state. But it's easy to live with because it doesn't happen that often. I don't go to premieres and stuff; I'd rather just go to my local movie theatre. Mum and I have been looking at each other all weekend asking: 'like, what's going on?' "
Damon has lost 25lbs since Saving Private Ryan in order to play Ripley, which also has the effect of lopping years off his age. At 28, he looks as though he ought still to be in short trousers. He is charmingly solicitous of his mother, even trying from time to time to bring her into our conversation. He still has the astonished air of someone who can't quite believe all this is happening to him. He told another interviewer he was knocking on wood so hard his knuckles were bleeding. If this is an act, it's a brilliant one, and has everybody fooled.
"The very first big photoshoot I ever did was with Bruce Weber," he says now. "I couldn't believe this guy was taking my picture, so when he told me to get in the bathtub, I just did. It's only now, looking back, that I realise, you don't have to do everything people tell you."
The feeding frenzy is due to Damon's apparent ubiquity: this year alone, he has played the leads in Gus Van Sant's Good Will Hunting, Francis Coppola's The Rainmaker and John Dahl's Rounders, as well as the small but crucial title role in Steven Spielberg's Saving Private Ryan. And somehow or other he has found the time to date a series of high-profile actresses: Claire Danes (his co-star in The Rainmaker), Minnie Driver (his co-star in Good Will Hunting) and, currently, Winona Ryder.
Then there is The Talented Mr Ripley directed by Anthony Minghella (his first film since The English Patient) and co-starring Gwyneth Paltrow and Cate Blanchett. And after that, Damon is already signed to play a young Texan drifter in an adaptation of Cormac McCarthy's All The Pretty Horses under the aegis of the actor-director Billy Bob Thornton. "I started The Rainmaker in August 1996 and I've been working consistently ever since. It's not like I had some grand plan; I keep getting offered jobs so good I can't say no. I have another year until I'm done And then I'm gonna take a nap."
Dahl sees a link between Damon and the characters he often plays: highly intelligent underachievers who are not altogether sure whether they want to chase after fame and fortune. "Good Will Hunting came out the first or second week we were shooting Rounders," Dahl recalls. "And nobody involved in our film realised it was going to be such a phenomenal success. But I remember going to the cinema to see it and thinking that there was one scene in which he was really terrific." This was the moment in which Damon's character, a maths genius who has dropped out of college to work as a janitor, confronts the psychiatrist, played by Robin Williams, who is attempting to convince him not to squander his gift. In a bid to bond with the recalcitrant rebel, Williams shows him a watercolour he has painted himself. Damon sneers at the picture, as though deliberately to alienate the one man who wants to redeem him.
"He was playing the golden boy, the guy with the talent, who's getting all this advice from all these other people and trying to figure out what to do. So it seemed like he was the right person for the part in my film too," says Dahl: in Rounders, Damon jacks in his law studies in order to return to his true love, gambling. "It's interesting that Matt is drawn to this kind of material. In a way it reflects who he is himself."
Damon describes his family as "hippies". His mother, a teacher, had progressive theories about education and wrote a book about toys arguing that they got kids hooked on consumerism and crippled their imagination. Her son remembers only being allowed to play with building blocks as a child. She supported his ambition to become an actor when he told her, rather grandly, that he had decided to "go professional" at the age of 16. He then took a detour into the Ivy League establishment after being accepted at Harvard to read for a degree in English. But after he began winning small roles, notably in Walter Hill's under-rated Western Geronimo, he never got around to graduating.
"Everyone told me Geronimo was going to be a huge, huge hit and the best thing I could do for my career would be to stay in Los Angeles and keep pounding the pavement, because when it opened everything was going to explode. It was a huge bomb and I found myself stuck in LA with no money."
This went on for a while: as recently as 1995 Damon was still getting rejected for bit parts. "I auditioned for Cutthroat Island and got turned down - and I'm not talking about the Matthew Modine [male lead] role. As a struggling actor you're not looking for parts that define you, you're just looking for work."
So instead he hooked up with his old friend, Ben Affleck, who, so the story goes, crashed on the couch at Damon's tiny apartment in a seedy district of West Hollywood. They lived on Ramen Pride (the American equivalent of pot noodles) while thrashing out a script which, they hoped, would give them both the showcase roles they deserved.
"Ben and I would write standing up, improvising and using a tape recorder. We'd play it out and play it out and then look at it all and say, 'OK, where's the story in here?' We're not real writers in the classic sense. Staring at a blank computer screen and a blinking cursor is like torture for me." His mum's belief in building blocks would appear to have worked, even if their working methods were slightly erratic - and it took them a full five years to get the project off the ground.
"I don't think Ben and I were ever really ruthless about selling our script, we were just determined and driven," he says. "It took so long to write it and trying to shop it around that a lot of our own identities were wrapped up in it. It took on a mythic importance for us." Their persistence paid off earlier this year when Good Will Hunting won them an Oscar for Best Screenplay (as well as a Best Supporting Actor award for Williams and two other nominations, including Best Actor for Damon).
"Selfishly, I remember thinking, 'there goes my small little poker film,' " says Dahl, who originally conceived Rounders as a low-budget, independent project in which Damon, an unknown newcomer, would be surrounded by more established actors such as John Malkovich, John Turturro, Edward Norton and Martin Landau. "But everyone was happy for Matt because he's such a great guy and has worked so hard to get where he has.
"It may be that Damon's niceness will, in the long term, inhibit his range as an actor. Here's what he has to say about Patricia Highsmith's celebrated sociopath: "We wanted Ripley's humanity to come across. In the book he's this awful, calculating person, but Anthony and I tried to have him not ever manipulate anybody and come from a position of pure honesty all the time. He believes what's happening and he believes the world he's indulging in."
But, meanwhile, Matt Damon is charming the media and the fans (he doesn't have time for lunch, but he does stop the publicity juggernaut to sign autographs for some little Italian girls) while his mum frowns and pronounces it all a "symptom of a really screwed up society".