"Science!" Jeff Goldblum exclaims, holding up a finger and surveying the crowd that has packed into Rockwell Table & Stage in Los Angeles to see him perform with his band, the Mildred Snitzer Orchestra. "Does anyone here work in, in, in the sciences?"

For Goldblum, who's not a scientist but plays one in summer blockbusters — an MIT-educated, alien-hacking satellite tech in Independence Day; a mathematician and chaos theorist in Jurassic Park — this quest for knowledge is a parental imperative. "I have a 3-year-old and a 1-year-old," he announces in his distinctive diction that is occasionally peppered with an oddly mellifluous stammer. "I want to pass on something besides my half-baked ideas."

A young woman waves her arm and beams when Goldblum approaches, microphone in hand. "Now, you have some fun facts about science," he asks her, "because you're involved in the sciences of some kind?"

When the woman, a native of Australia, affirms that she's an astrophysicist at Caltech, Goldblum's eyes light up. "You look for planets around other stars," he says, nodding. "You've found, you, you keep finding things, don't you?"

"Well," she says, "my fun fact was going to be that we know of 3,793 planets right now around other stars, and we're adding five more at 10 a.m. tomorrow."

VIDEO: Jazzy Jeff Goldblum Answers Your Style Questions

"Hey, that's breaking news," he says. Rising to his full 6 foot 4, he shows off the full scope of his appropriately snazzy outfit: slim-fitting black-and-white tiger-striped pants from Isabel Marant and a silk Prada shirt printed with a panoply of zoo animals as well as unicorns and dinosaurs. "At 10 a.m. tomorrow there's gonna be how many more? Five more? And are any of them going to be named after, um, your experience tonight?"

He raises his brows, points at himself, and spins, hamming for the crowd. Informed by the Aussie astrophysicist that, alas, there will be no new planet named Goldblum Prime, he shrugs and flashes a broad grin.

At 66, Goldblum is secure in his place in the pop-culture firmament. He's an icon of idiosyncrasy with near-universal appeal, a habitual hugger and selfie-posing teddy bear whose shtick might seem contrived if it were really a shtick. But there is no PR plan or social-media strategy behind his random acts of coolness. When he sees a Hollywood-star tour bus, he's been known to roll down his car window and greet tourists. If you happen to run into him at a supermarket, an airport, or a restaurant, he will say hi warmly. If you chat, he will ask your name and later remember it, first and last. And he will delight in the details of your life, no matter how curious or commonplace.

"I am interested in people — I tell you that," Goldblum says when we meet a couple of days after the show at the Mint, a music club across town. "I'm naturally ... um, um ... gregarious, I guess is the word."

This is evident between sets at the Rockwell as he chats and poses for photos with nearly every audience member. The show is sold out, as it has been every Wednesday since Goldblum and his band took up residency almost six years ago. What started with Goldblum on a portable keyboard and his friend Peter Weller on trumpet busking on the Sunset Strip has evolved organically over time, as Goldblum has, into a phenomenon with growing appeal. Through the years, celebrities like Jim Carrey and Bob Odenkirk have sat in with the band, and everyone from Dick Van Dyke and Allison Janney to Halle Berry and Charlotte Gainsbourg has taken in the show. This night there is a mix of hipsters, Hollywood execs, young single women, and couples on dates. More variety show than straight-up concert, the bits range from "Would you rather?" to quizzes on misquoted movie lines to the dietary and urinary habits of polar bears. Mixed in are standards by Charles Mingus, Sonny Rollins, Herbie Hancock, and the like — all played cold on the piano by Goldblum. "I never know the set list. I told John to purposely make me unaware," he says, referring to his pal John Mastro, the band's manager-producer. If it all feels like an exercise in improvisation, it is — a chance to let Goldblum's eclectic interests and innate charm come through. "I really like this sort of happening, this sort of hangout that we have," Goldblum says about the weekly revue.

It was the promise to preserve that vibe that persuaded him to record Jeff Goldblum and the Mildred Snitzer Orchestra's first album, The Capitol Studios Sessions, which was released in November. But there is no risk of Goldblum's moonlighting in music ever eclipsing his career in movies and TV. "I was never careerist or strategic," he says of his jazzy gig. "I never wanted to get anything out of this except just the fun of doing it. Acting was another thing, although my way of doing this has bled over, happily, into what I'm doing in acting." He adds, "I feel I'm doing my best stuff and am on the threshold of even better stuff than I've ever done."

If anything, Goldblum has been continually revealing his talent. As his career took him from small parts in the Robert Altman classic Nashville and Woody Allen's Annie Hall to his breakthrough roles in the '80s in The Big Chill and The Fly to the more recent mix of mainstream blockbusters and arthouse fare like Wes Anderson's films (The Life Aquatic with Steve Zissou, The Grand Budapest Hotel, Isle of Dogs), Goldblum has earned acclaim and a certain deference from directors. These days he will occasionally be asked to play it straight. "Some people will say, 'A little less of the recognizable familiar Goldblum stuff' — and I'm thrilled to do that," he says. Just as often, however, filmmakers seek out his signature style and request an extra helping of his je ne sais quoi.

That special sauce extends to his fashion choices as well. As a child, Goldblum loved going back to school because it meant shopping for new clothes. The first time he wore a suit, a neighborhood kid teased him. "He saw me, and he said, 'Jeff Goldblum, you look … you're as sharp as a matzo ball,' and I said, I said, 'No, Bobby, I'm smooth.' " Later, inspired by Sammy Davis Jr.'s spin on Carnaby Street fashion, Goldblum demanded a small version of the Nehru jacket ensemble he saw in a department store, with a turtleneck and a medallion. "I said, 'I want that whole outfit,' and I got it."

Once Goldblum became an actor, the lines between his personal and professional dressing blurred. He enjoys collaborating with costume designers and made dressing a part of his method. "Working from the inside out was part of the deal. But so was from the outside in." He mined inspiration from the aesthetic and physical sensation of the clothes, even "finding the right pair of shoes that made you walk or feel a certain way."

Today, there is a simpler reason his closets are stocked with suits by Tom Ford, Saint Laurent, Dior, and Balenciaga plus Acne jeans in every shade: "I'm crazy, but I really like it. I don't know why." Goldblum hired a stylist named Andrew T. Vottero about five years ago, around the time he married Emilie Livingston, a dancer and contortionist who competed in rhythmic gymnastics at the 2000 Olympics. "I just needed somebody to talk to about my enthusiasm in this area without wearing out my wife," he says with a laugh. "Because there's only so much she can endure."

His jazz show, then hosted at Café Was in Hollywood, even played a part in his courtship of Livingston. Only a few days after meeting her at the gym, a smitten Goldblum coaxed her out of the audience and onto his piano top to reenact Michelle Pfeiffer's seductive rendition of "Makin' Whoopee" from The Fabulous Baker Boys. For Goldblum, who was previously married to Patricia Gaul and Geena Davis, this third union appears to be the charm. One telltale sign is that he became a father, for the first time, in his 60s.

"Through the day I'll have moments with the kids when I'm ecstatic," he says. "Being with Emilie and Charlie Ocean and River Joe is more nourishing and transformational and fantastical than ever. So, yes, I would say mark me down for 'I'm happy.' I'm happier than ever."

His buoyant countenance belies Goldblum's deep involvement in social causes, with leanings that aren't hard to divine. "I'm fervent about my proclivities, politically," he says, "and it's no secret that Emilie and I campaigned for Hillary Clinton in Ohio." Since the 2016 election he has remained active and engaged. "I've watched the unfolding goings-on with alarm, concern, and passion toward what I can do to keep the ball rolling toward a better place."

He's also been struck by the power of the #MeToo movement. "Who hasn't? Who isn't aware of the challenge of gender discrimination and persecution?" he says. "I'm a particularly fervent champion of women's empowerment." And yet he loves attention and lavishes it on his fans, and he knows his curiosity could be mistaken for a different kind of interest. "I am a flirt, in a way. But I'm aware," he says. "I'm hypersensitive to anybody's boundaries and their sensitivities, and I try not to ever violate them."

This is something he thinks about as he's raising two boys. "You know, I've devoted my life to poetry and art via imagination," he says. "I'd love to see them paint and make things up and play, but if I could offer them anything, it would be the wisdom of factual scientific investigation."

He muses for a moment, then shakes his head and chuckles, as if he's realizing that some things will always defy his understanding. "I've always been joyful for no reason, in fact."

Photographed by Beau Grealy. Styling: Andrew T. Vottero. Grooming: David Cox.

For more stories like this, pick up the January issue of InStyle, available on newsstands, on Amazon, and for digital download Dec. 7.