But when he smiles that famous smile, with those almost perfectly straight teeth (up close, one bottom tooth is thankfully just out of alignment), his look transforms altogether, from serious and standoffish to carefree and engaged.When we sit down, he’s wearing a navy polo shirt, jeans, and a commemorative Fenway baseball cap.

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It was 1996’s Courage Under Fire that changed everything.

Damon was determined to get Hollywood’s attention, and his turn as Army Specialist Ilario, a tormented, heroin-addicted soldier (Damon shed a scary 40 pounds for the role) did the trick: Within the year, he was tabbed for the lead in Francis Ford Coppola’s The Rainmaker and the title role in Steven Spielberg’s Saving Private Ryan.

Everything changed again in 1997 when Good Will Hunting made him famous overnight.

Suddenly, he was an “it” boy, and not just because he had turned in a good performance (because he had), but because he had the weight of an Oscar for screenwriting behind him to force Hollywood to take his talent seriously.

The wry Matt who turned in a hilarious performance as a straight man pretending to be a gay man trying to win a spot on a choir trip to Europe on the television show Will & Grace. This summer, after Ocean’s Twelve wraps, he’ll begin filming the Steven Soderbergh–George Clooney-produced Syriana, in which he plays a man with a young child. “I hadn’t even thought of it,” he says quietly, reflecting.

The cheesy Matt who likes the Starland Vocal Band’s 1970s hit “Afternoon Delight” enough to weave mentions of it into interviews and onto movie soundtracks. Maybe it’s because he’s reached that biological hour — he’ll be 34 this October — or because his involvement with Barroso and her daughter has brought family into the everyday foreground. “It was just a role I liked in a movie that I loved. I think some people take kind of a cynical view of their careers, and they go, ‘Well, now I need to take the next step, and now I need to play a father.’ That didn’t occur to me.” Don’t be fooled into thinking that Damon’s career path and the roles he’s chosen are left to circumstance, however.

The Matt who did an unbilled cameo as a lead singer of a garage rock band in the teen throwaway Eurotrip. He says he has always wanted to be an actor and has pursued that goal with a singular resolve.

It’s a side of Damon’s personality that makes you want to be in on the joke. “When Matt was a freshman,” remembers Gerry Speca, Damon’s drama teacher at Cambridge Rindge & Latin School, “the first thing he said to me was ‘I’m going to be an actor.’ He was so focused and eager.” Damon shrugs off his success in characteristic nice-guy fashion.

CIA operative Jason Bourne doesn’t even know his own name.