Jennifer Connelly, the 31-year-old beauty who bared the intensity of her talent in Requiem for a Dream, then won both an Oscar and a Golden Globe for her portrayal of Alicia Nash in A Beautiful Mind, will be appearing next as Betty Ross in director Ang Lee's The Hulk. Probing for clues to this extremely private New Yorker, Michael Shnayerson gets Connelly's explanation for why she chose to play opposite a green monster, and discovers what she learned from her previous co-star Russell Crowe, as well as the personal quest that has made her success so ironic.

The lobby of Hollywood's Chateau Marmont is dark even at midday, more like a cloister, with its stone walls and stylized Moorish gloom, than a hotel. At night its sconces are turned so low that when one of the world's most beautiful women wafts in, impossibly thin and garbed in black, she's almost invisible. Which in her private life is exactly as she wants to remain.

On-screen, Jennifer Connelly is fiercely, unforgettably visible, so much so that last spring's Oscar and Golden Globe awards for her intense performance as Alicia Nash in A Beautiful Mind are mere recognitions of the obvious: she's about as good as they get. Not only is she a new star, she's a new look. Who was the last leading lady with long, straight, nearly black hair and unmistakably patrician features? Audrey Hepburn, perhaps? Part of Connelly's appeal is that she looks less like an actress than she does a young corporate lawyer at a top Manhattan firm, razor-smart, ambitious, tightly wound: perfect in pinstripes, with a sleek attache case.

In person. Connelly is both warmer and more remote than her image, cordial but wary. "Good luck," says a woman who has worked on two films with her, and the warning is apt. Connelly is loath to talk about herself, grimly protective of her privacy, the brows over her wonderful winter-green eyes furrowed more often than not. Once in a while, however, she does throw out intriguing clues, each one making it in creasingly clear that Connelly is not your average actress.

Take the matter of what she's wearing. The real Jennifer Connelly is never in pin stripes --couldn't be further from them. Tonight she has on her standard outfit: a black, loose-flowing sweater, blue jeans tight enough to show off a micro-size waist, and black, sharply pointed Manolo Blahniks.

Every day when she gets up, she tries on four or five different changes of clothes. Almost always she ends up with what she's got on now. Not the same sweater and jeans, just the same general outfit. Though, if necessary, she can wear the same clothes again and again. She did that once on a trek through Tibet. That time, she says casually as we settle in for a private dinner in Room 16 off the Chateau Marmont's lobby, she also went three and a half weeks without a shower.

Three and a half weeks without a shower?

"What would I like?" Connelly ponders the room-service menu seriously, as she seems to ponder everything else. Finally she decides on a small green salad and a Diet Coke. It's not that she doesn't like to eat, she says. It's that she had lunch earlier in the day. "I just put on weight!" she protests when the suggestion is made that people sometimes eat both lunch and dinner. "I'm feeling earthy and proud of myself!"

At 31, Connelly is feeling proud in a more profound way, and quite rightly, after a quirky, start-and-stop career marked by roles that still make her cringe. There are children, now grown, who remember her fondly from the Muppet film Labyrinth, which she made in 1986, at the age of 15. Doubtless there are onetime teens who never forgot her as the sex kitten of Career Opportunities (1991), with Frank Whaley. And somewhere must lurk a fan of Connelly's portrayal of Chilean writer Isabel Allende opposite Antonio Banderas in the insignificant Of Love and Shadows (1994). But Connelly shudders at the mention of those films.

For her, the first keeper came two years ago with Waking the Dead, based on Scott Spencer's 1986 novel, about a political candidate so haunted by memories of a dead girlfriend that he comes to feel she's still alive. Initially, director Keith Gordon saw no point in auditioning Connelly. "I didn't think of her as a serious actress," he admits. But Connelly's agent -- and close friend -- Risa Shapiro, of International Creative Management, persuaded the director to view a 1996 independent film called Far Harbor, in which Connelly's character had a monologue about the death of her child. "I turned to my wife," Gordon recalls, "and said. 'Am I crazy or is she really good?"'

Gordon's wife, Rachel, agreed, and so the director called his prospective male star, Billy Crudup, who had worked with Connelly in Inventing the Abbotts (1997). "And he said, 'No one knows how really good she is."' Gordon was soon among the converted, and so was Scott Spencer. "The way she would listen to the main character was exactly the way I always thought he'd be listened to by her," Spencer says, "There was a subtlety and depth even to her gaze that captured more of the relationship than I ever could have hoped for."

Connelly, like her character, had awakened. Then came the shocking Requiem for a Dream (2000), a nightmarish depiction of drug addiction, based on Hubert Selby Jr.'s 1978 novel of the same name, in which Connelly and Jared Leto play lovers whose craving for heroin destroys them. "I like to stick the camera into an actor's face and bring the eyes to the audience," says director Darren Aronofsky, who cast Connelly after an audition so intense that she threw a chair across the room. "She was really fearless in letting me get in there." Ultimately, Connelly's character performs in a brutal sex show for the entertainment of leering businessmen in exchange for drugs -- a scene difficult to watch, but much more so to play. "There was no sex, of course. but there was ... interaction," Aronofsky says. "All professional, but unbelievably emotional and intense. We don't really talk about what went on that night."

When he saw Requiem for a Dream, director Ron Howard noticed that the actress he'd cast in a supporting role in Inventing the Abbotts was coming into her own. He also noticed that she bore a strong resemblance to the young Alicia Nash, wife of the schizophrenic physicist John Nash, about whom Sylvia Nasar had written the 1998 biography A Beautiful Mind, which Howard was preparing to adapt as a movie.

One reason Connelly took unfortunate roles when she was younger, she says, is that she let herself think they were more than they were. "Like I was reading a lot of Harold Pinter when I did Career Opportunities," she says, "and I thought, It's kind of like The Dumb Waiter." So one might reasonably assume she chose to follow A Beautiful Mind by starring in The Hulk because ... the comic-book re-creation seemed likely to be a blockbuster on the order of Spider-Man that would make her a ton of money? "Actually," she says earnestly, "this is a five-character family psychodrama."

At least this time her director is the reason for such pronouncements. The Hulk as standard comic-book fare would have held little interest for her, Connelly avers. The Hulk as directed by Ang Lee of The Ice Storm (1997) and Crouching Tiger Hidden Dragon (2000) was a whole other proposition. "Ang brought such lyricism to those movies," Connelly says. "I just wanted to be around him." And when he started talking Greek tragedy and telling her of his walks through the California desert in search of rocks with just the right texture for the Hulk to crush, Connelly was hooked.

Lee says he does discern the bones of Greek drama in the Fantastic Four -- the series in which the Hulk appears -- and has been a fan long enough to have put a reference to the comic-book quartet in The Ice Storm. To Lee, the Hulk represents the dark side of our nature. "I feel the power of the Hulk, the excitement of the unknown," he muses. He's "the things we're afraid of, though they're ultimately exciting."

Connelly signed on before the Oscar nominations, so Lee -- and Universal Studios -- doubtless got a good deal. But she has no regrets. Well, perhaps just one. In filming first around Berkeley, California, where the story is based, then on Universal's back lot in Los Angeles, she has had to speak an awful lot of her lines to a cardboard-cutout Hulk head on a stick. Like most superheroes, the Hulk has a human alter ego: Bruce Banner, played by Eric Bana (Chopper). But whenever he's transformed into his superhero self, a computer-animated Hulk takes over the screen. The cardboard head is Hulk-high, to give Connelly her "eye lines." "I'm looking at pieces of pink tape on the cutout head, " she says with a grin. "There's nothing there! I've never done that before -- it's a little humiliating."

"The first day it was a bit of a problem having her talk to the Hulk head," Ang Lee admits. "But within a week, she had a scene with the Hulk where she looks at him with real feeling, and all the emotion was there." Connelly, says Lee, was always his first choice. "Her intensity appealed to me. And she's gorgeous to look at. You can't ask much more than that."

"I think we've all been cast for our angst abilities," says Bana, who's come to admire Connelly cool professionalism. "It's quite an angst-ridden script."

Almost as soon as she read the Hulk script, Connelly had changes to propose for her character, Betty Ross. Both in the comics and in the script, Betty is a scientist who works in the same university lab as Bruce Banner and begins to suspect that Banner's experiments are affecting him strangely.

What she doesn't realize is that her own father, an army general, knows something about those experiments. James Shamus, the screenwriter, had sketched a relationship between father and daughter, but Connelly was underwhelmed. "The issues that she had with her father," she says. "were kind of stock issues that you'd have with your father if he's in the military and you're a liberal scientist."

Connelly and Shamus worked together to create nuances in her character, inspired, they agree, by the poet Anne Carson, in particular by her poem Flatman (1st draft), about living in a flat, superficial world. "The material of the movie is so colorful, but flat, boxed in, cut off from anything real," Connelly explains. "And then in it is this character who's trying to find something human, and sacred, trying to sort out her past and her memories."

Shamus says he gave her one of Carson's books after Connelly's remark, in another interview, that she admired the poet Wallace Stevens. "Carson's themes shed light on the nature of pop culture [and] violence," he says. But, for Shamus, sharing poetry was just part of the larger pleasure of working with an unusually quick-witted and literate actress. "The thing about Jennifer -- and it was a prerequisite for the role -- is that she's just plain smart," he says. "So it's not hard to believe that her character has a Ph.D. in genetics." If his words got changed in the process, that's all right by him. "Process," he says. "is what makes cheese -- and movies."

Whether or not popcorn munchers find anything sacred in Betty Ross when The Hulk lurches onto screens next June, Connelly has the muscle now to make her characters her own. Clearly, her co-star in A Beautiful Mind showed her something about how to flex it.

"He asks a lot of questions," Connelly observes of the infamously less-than-easy-to- work-with Russell Crowe, "and he really applies himself. He puts a lot into what he does."

The two met first for a reading at Ron Howard's office in New York. "When he first walked in I thought he was ... energetic," says Connelly, picking her words carefully. "You feel him come into the room. He's very alive. He had hurt his shoulder and he was talking about that. He's kind of charismatic and interesting to watch. Kind of strongly seated in himself." Not, she concedes, overly polite. "Then we started doing scenes together, and by the end he was really polite. He was walking me to the elevator and saying, 'Let my driver take you home.' Very sweet and attentive."

Together, Connelly says, she and Crowe challenged the script at every turn, always struggling to establish the Nashes' relationship as profoundly as they could. Often, that meant paring down the speeches. "Like toward the end of the movie there's a scene where we wonder if she's left him," Connelly recalls of Alicia's marriage to John Nash. "after the whole baby-in-the-bathtub business. The scene in the bedroom where I'm kneeling in front of him was originally a really long spiel. It just didn't seem appropriate at the time [her to be] saying. 'We have to get out of your mind, and what we need to do is re-introduce you to the physical world.' It seemed more appropriate to do that through touch rather than through dialogue."

To the inevitable musings about whether the two co-stars had fallen in love oftscreen, Connelly has a terse and emphatic response. "I have a boyfriend," she declares "[I] was not on the market." When she made the film, that would have been Josh Charles, a tall, comic actor in movies (Dead Poets Society) and television (Sports Night). By last spring, however, Connelly was being sighted with another actor, Paul Bettany. When the romance had actually begun was a subject of some curiosity, as Connelly had clearly met the 31-year-old British actor while filming A Beautiful Mind. Bettany plays the tall, lean, curly-blond-haired English scholar who turns out to be an imaginary friend in Nash's schizophrenic mind. This is not, however, a matter that Connelly is inclined to clarify.

"He's a remarkable person." she says through beautifully tensed lips. "Just a really good, kind, beautiful person, and I'm really happy to be spending time with him right now." She admits that he's got "a really cute accent," and she laughs when she thinks of it. "He makes everything sound so much fancier when he says it than when I say it. Really annoying." But that's all one can pry from her. "I think it's about really nice things for really good reasons," she says. "But I don't want to talk about it, O.K.?"

Abruptly, Connelly untangles her long legs, stands up on the upholstered chair she's been sitting in, and unfastens the high latch of the tall, leaded window beside her.

"I suddenly really want to smoke," she exclaims. "I'm going to smoke out the window because you're pestering me so much with the boyfriend thing."

Bettany is at least the third actor with whom Connelly has been involved. The first was Billy Campbell -- her first serious romance, when she was 20 and he was about 30. The two met while filming The Rocketeer in 1991. (Campbell went on to star in television's Once and Again.) Connelly said publicly that they were engaged; they remained an off-and-on couple for about five years, but never did marry. She prefers not to talk about Campbell or Charles, either.

Connelly exhales furiously. "I didn't smoke at all today," she says. She's propped now on top of the chair, a long blue-jeaned leg on each of its arms, still in nondisclosure mode. "I can go days at a time without it and be really repulsed by it."

Aside from that occasional smoke, Connelly seems much too disciplined to have any vices. But this she vigorously denies. "I love this quote- who wrote this? 'The skeleton of habit alone upholds the human frame.' I think it was Blake. I have tons of bad habits... A lot of them are just bad ways of looking at things and thinking." She pauses, then beams. "I bite my nails! I massacre my nails." She holds out one beautiful finger. "This one's my favorite."

It looks gorgeously unbitten.

"I filed them for you!" she says, and cracks up. "And then I tell you! I give my self away. I filed them so you wouldn't think I was a freak, and then I told you!"

The word "freak" is another clue, along with the sweater-and-jeans uniform, the showerless trek in Tibet, the reading of Blake and Stevens and Carson, that Connelly harbors a private cool. A quester's cool, of standing apart from the material world, pushing away its lures, feeling instead a kinship with those who look for deeper sense -- in poetry or mysticism, or mountaineering. The irony of Connelly's success, and perhaps one reason, along with innate shyness, that she's so uncomfortable in interviews, is that the stardom it's brought her is so ... uncool. It makes her an icon of the very pop culture she's tried to eschew.

As a quester, Connelly has done her share of Kerouac-esque cross-country drive "numerous times," she confirms. "I like the movement of being on the road, and being away from phones." More dramatic -- and emblematic -- are her climbs. Along with trekking in Tibet, Connelly has gone mountaineering all over the western United States. Often that has involved rock climbing with crampons, ice axes, and ropes. She did a number of tough climbs in the Red Rocks, outside Las Vegas. She climbed Mount Shasta, in California, crossing a glacier in the process. In a climber's rite of passage, she did an eastern ridge of the Grand Tetons in one push.

"We started at midnight," she recalls, "hiking into the headlands. By the time the sun came up, we were starting the more technical climb. We did a straight push up, and then back down. From when we started until when we got down, it was 19 hours. I was so exhausted on the way down, I'd sit and tell them they should just leave me there."

Her partner in most of those climbs was David Dugan with whom she was romantically involved for a few years in the mid 1990s. Dugan was the exception: a photographer not an actor. In 1997 he and Connelly had a son, whom they named Kai. "Kai" means "ocean" in Hawaiian; Dugan had lived in Hawaii for some time. "He came out looking so not like a Liam or whatever else we'd thought of," says Connelly. "He was so dark and exquisite and almond-eyed that those names didn't work. So we put a few names in a bag, and I pulled out Kai four times in a row."

Dugan today works with an advertising agency in New York. He and Connelly raise Kai together, which works best when Connelly is back home at her apartment in Lower Manhattan. Her decision not to marry Dugan was, she bristles, "kind of deeply personal." But she does allow that "if I got married I would rather not get divorced. And I didn't arrive at that place where I felt that was the choice."

One can read that simply as another sign of Connelly's independent streak. But as a key to understanding her, it may not be irrelevant that in 2000, after nearly 30 years of marriage, her parents got divorced. Both parents seem to have played formative roles, positively or not, in Connelly's career.

Connelly declines to make her parents available for an interview -- or her friends, for that matter -- so inferences must be drawn. From the scattered facts, Connelly's father, Gerard, appears a study in contradictions: an Irishman who worked in Manhattan's garment industry, a father who chose to settle his family among the genteel 19th-century town houses of Brooklyn Heights but longed for another life among the artisans and hippies of Woodstock, New York.

"It never did make any sense to me that my dad worked in the garment industry, to tell you the truth," says Connelly. "He's not particularly materialistic; he's one of the few guys who could wear head-to-toe Armani and still look like a wreck."

Gerard moved his family to Woodstock twice, when Jennifer was born and then again when she was in second grade for about four years. There he bought a restaurant and expanded it into something called Tinker Square. Connelly recalls it as "a Woodstock version of a shopping mall, with a little shoemaker, little stained-glass maker, and then upstairs a gallery where they had art classes. And my mom had an antiques store in there." But Connelly's mother, Eileen, seems to have preferred the city to upstate. Her daughter remembers her in high heels in Woodstock -- an anomaly among the Birkenstocks. When Jennifer was 10, the family moved back to Brooklyn Heights. Gerard returned to the garment industry, and Jennifer, at her mother's instigation, started going on auditions.

"I have a bit of a block on how it all [her acting career] happened, to tell you the truth," Connelly says. "I'm not intentionally obscuring it, honestly. I remember what I did, for the most part, but I don't know why. I had no aspirations, I had no movie posters in my room, I wasn't a movie buff; I liked Evel Knievel and animals, and I kind of liked science. And English."

Somehow, Jennifer found herself going to auditions after school at the private St. Ann's in Brooklyn Heights. Sometimes the work she landed was fun: at 11 she made her film debut in Sergio Leone's Once upon a Time in America, playing Elizabeth Mc Govern's character as a little girl in flashbacks because she had a McGovern-like nose. Sometimes the work was just drudgery, as when she posed for department-store catalogues and print advertisements. "I'd be the geeky little girl in leotards on the Danskin package," she says with disdain.

Connelly didn't just make the rounds a few times a month. She did it, she recalls, every day. Her mother was the one who accompanied her. Not, Connelly says after a pause, in an overbearing way. "I don't know that if I'd really complained about it that anyone would have forced me to do it. Sort of in retrospect I think, Why did I ever do that? It's such a strange thing for a kid to be doing. But I don't remember coming home from school and crying and saying, 'I don't want to do this,' and my mother making me go."

Mostly, Connelly says, she wanted to make everyone happy, "to take care of everyone" -- an interesting choice of words. She managed to do well enough at St. Ann's, even while making a few movies in high school (Labyrinth, Some Girls), to get into Yale. There, she threw herself into her studies with an almost obsessive zeal, both out of shyness and, she says, because it was her first chance to be a full-time student. Mostly, she stayed in her tower dorm room, writing papers for English lit while wrapped in a blanket to ward off the cold that seeped through the cracks of the walls and the floor.

"I'd read a book three times, until the pages were covered with yellow Post-its that had ideas scribbled on them, and more Post-its stuck on my walls. But I had the best time just thinking about things."

Despite this rather Nash-like behavior, Connelly did break off from her schoolwork long enough to make The Hot Spot in 1990 for actor turned director Dennis Hopper, who cast the 19-year-old in her first adult lead role after auditioning "everyone in Hollywood." The story is a sexual intrigue, with Don Johnson as a Texas drifter caught between two worlds. Connelly has a nude scene in the movie, which also delves into a lesbian relationship her character had when she was younger. "Jennifer had no problem with the nudity," says Hopper. "I thought she was very brave. It's a really gutsy performance."

While at Yale, Connelly also made the forgettable Career Opportunities for writer-producer John Hughes, in which she plays a small-town beauty hiding out in a department store who falls in love with the teenage night watchman. That was the one she thought seemed like a Pinter play. "Cut to release of the film," Connelly recalls, "and there's this big cardboard cutout of me on this mechanical rocking horse at the New Haven movie theater, and the cutout is rocking, and my favorite English professor tells me, 'Hey, I saw you at the theater!' I was completely mortified."

Oddly, considering her academic diligence, Connelly dropped out of Yale after her sophomore year. "I completely fried myself," she says simply. She transferred to Stanford'different architecture, she explains, different climate -- and lived, on and off, with Billy Campbell. At the end of her junior year she left college altogether. She hadn't committed to acting, exactly. The work just seemed to come, enough of it that staying in college no longer made any sense. And so unfolded her early 20s: a few roles, enough money, a lot of drives and climbs. A lark, in short, for which she has no regrets, but which finally seemed pointless.

"I went through a kind of personal crisis: 'What am I doing and why am I here?"' Connelly explains, back in her chair, green salad still untouched two hours after its arrival. Then Connelly had her son, and that, more than anything else, changed her. "I thought, Now I really know what I want." What she'd searched for was what she'd had inside her all along but filled to recognize. She wanted to act -- but no longer for her parents' sake, or because she could get the work. She wanted to act because, she realized, if she went for the right roles and gave them her best, she could do it well.

After Connelly's parents parted, her father moved once again up to Woodstock, her mother to Big Sur, California, to become a craniosacral therapist. ("she attempted to do it once to me, and I couldn't handle it," says Connelly.) Her mother has remarried; her father has not.

Connelly's father was in the car with her on the ride over to the Oscar ceremony last spring. She recalls feeling dizzy and tired, and oddly relaxed, which is how she gets when she's stressed. She made everyone in the car listen again and again to Joni Mitchell's "A Case of You," one of her all-time favorite songs -- and one of the all-time great love songs. She'd written a speech in case she won, and assumed there'd be a lectern on which to rest the "enormous piece of paper" on which she'd written it. When she sat down, beside Cameron Diaz, whom she likes a lot, Connelly was horrified to realize there was no lectern to speak of. "So I was thinking: Is it obnoxious to learn the speech before I go up? Or is it obnoxious not to learn it?" And hoping she'd lose so she wouldn't have to go up at all.

Connelly's speech struck more than a few Oscar watchers as surprisingly low-key -- almost dour. Partly it was that intensity of hers, partly just shyness. A number of industry observers had another reaction. What had happened to those once ample breasts? Had Connelly had plastic surgery to reduce them? Connelly's publicist Cari Ross says no. "It's absolutely not true -- swear on my life. She simply lost weight, and when she did she apparently lost weight in her breasts as well. She's put on weight since the Oscars, and you can see in pictures taken since then that they're sort of back."

That night, when Connelly went home, she put her gold statuette on a table. "And Kai introduced him to Action Man," she says. "They got a little thing going."

In the ensuing weeks, as she plunged into The Hulk, she found her life hadn't changed in any perceptible way. "It wasn't like 'Ooh, now I feel validated,"' she says. "That's just not the way my head works. And does it actually mean I'm the best supporting actress? Does it mean I'm better than Helen Mirren [who was nominated for Gosford Park]? It doesn't quite work that way."

The day after our dinner at the Chateau Marmont, Connelly does a scene for The Hulk dressed in pretty much her standard offscreen uniform of sweater and jeans. Actor Sam Elliott, playing her father, asks his daughter not to act on her suspicions, but rather to give him time. As take follows take, Ang Lee presides gently, almost diffidently -- in his wide-brimmed straw hat, he looks more like a botanist than a director -- but he clearly commands great respect from the dozens of actors and techies gathered outside a San Francisco-style house on Universal's back lot. In the breaks, Connelly rides the two blocks to her trailer in a chauffeured Cadillac Escalade -- quite a change from her cross-country road trips.

Inside the trailer, Connelly turns on the iPod that's become a staple of her existence, and the favorite tunes of a discerning quester come out: old ones, from John Lennon and Van Morrison, Tom Waits and John Hiatt; recent ones, from Norah Jones and the Pogues. On one wall is a small bulletin board with snapshots of Paul Bettany horsing around with Kai. On another is a large mirror, almost completely covered by a taped-up child's drawing. Connelly used to wince when she caught sight of herself in mirrors. Now she just covers them up.

It's true, Connelly says on reflection, that the Oscar hasn't changed her life. And yet, after years of ups and downs, and questioning, and often making herself feel bad, the fact is she has felt better since winning it. "To tell the truth," she says, "I am so ridiculously happy right now. I always had at least one corner of my life that wasn't working and was causing me pain. And I don't really feel that now. Everything feels good."

A sharp knock on the door. "Two minutes." And then, vastly relieved the interview is over, Jennifer Connelly goes back to work.