IN THE ’80S teen flick Weird Science, two nerdy guys conjure up a beautiful woman who makes them instantly cool. On a fall day in New York’s SoHo, it seems as if two young men at the do-it-yourself invention store littleBits have done just that when a svelte, black-clad 23-year-old suddenly joins them at a back table. She tinkers with pieces of electrical circuitry and strikes up a discussion of computer microchips. “It goes back to binary code,” she says. “Or chemistry,” one guy interjects, asking, “Was it silicon and then germanium?” “Silicon was the later evolution for transistors,” she says.

As he recommends that she read The Idea Factory, a book about research facility Bell Labs, it’s unclear if he knows he is speaking to the model Karlie Kloss . Yet her 3.4 million Instagram followers and fans of her personal YouTube channel, Klossy, know that today she could just as easily be making apple crumble with her friend Taylor Swift as working on a Vogue shoot with photographer Mario Testino. Paparazzi lie in wait for her to leave the store—“There’s no getting used to that,” says the St. Louis, Missouri, native, striding across West Broadway. As she nibbles on french fries at the Soho Grand Hotel, several teenagers and a German tourist ask her to pose for selfies. Ever helpful and gracious, Kloss snaps each herself.

OCCUPY MARS | Perched next to the Dragon spacecraft, which delivers cargo to the International Space Station and eventually will carry people into space. Its first manned test flight is expected to launch in two to three years. Louis Vuitton jacket, price upon request, select Louis Vuitton stores; vintage swimsuit, and Nike shoes, undefined

OCCUPY MARS | Perched next to the Dragon spacecraft, which delivers cargo to the International Space Station and eventually will carry people into space. Its first manned test flight is expected to launch in two to three years. Louis Vuitton jacket, price upon request, select Louis Vuitton stores; vintage swimsuit, and Nike shoes, undefined

Though Kloss is still actively modeling—her ad contracts this season include Diane von Furstenberg , Kate Spade, Joe Fresh and Marc Fisher—she has other ambitions. This year she enrolled in Gallatin, New York University’s independent study program; signed with Scooter Braun (known for managing Justin Bieber’s career); and studied computer coding at Manhattan’s Flatiron School. The latter gave rise to Kode with Karlie, an initiative aimed at encouraging girls to study computer science. “I was craving a new challenge,” says Kloss, who has achieved fashion success on par with her mentor, supermodel Christy Turlington Burns . “Karlie is like a thoroughbred,” says Vogue fashion director Tonne Goodman. “She has the best kind of ambition, which propels her forward but in a generous way. She understands the power of success.”

“ This girl has got it. She had immediate presence. ” — Tonne Goodman

Clockwise from top left: Karlie with her sisters; in a Diane von Furstenberg show; an Instagram photo; in London with friends Joe Jonas, Gigi Hadid, Taylor Swift and Calvin Harris; with the late Oscar de la Renta; in July 2012 ‘Vogue,’ shot by Mario Testino. Photo: Courtesy of Karlie Kloss (3); mario testino/art partner licensing; Edward James/WireImage

“I’ve had a firsthand education from the greats, whether it be seeing [photographer] Steven Meisel set his lights or having Oscar de la Renta drape a gown on my body,” says Kloss, who was plucked from her freshman year of high school to walk exclusively for the Calvin Klein runway show in 2007. The current interest in coding was spurred by an epiphany about her friend, Instagram co-founder Kevin Systrom . “I thought he had the idea and then paid someone else to build the actual product,” she says. “I had no idea he knew how to code. It’s so important.” Right now, she says, “I’m just learning the ABCs.”

Clockwise from left: Outside NYU; a Karlie’s Kookie break; products with the Klossy logo; with Kode with Karlie students; with Swift on the March 2015 cover; in WSJ. with her parents, Kurt and Tracy Photo: Courtesy of Karlie Kloss (4); Mikael Jansson/Vogue; Dan martensen/Trunk Archive

In Kloss-speak, fashion has given her a “platform” that she wants to parlay into even greater influence, just as her baking hobby led to Karlie’s Kookies, which benefit the organization FEED and the Council of Fashion Designers of America. “The aspiration for the Kookies is to take it to the next level and make it like Newman’s Own,” she says, referring to the late actor Paul Newman’s line of food products, which benefit charity. But in the meantime, there are papers due for her NYU writing class and a philharmonic to attend with Annette de la Renta , Oscar’s widow and another Kloss mentor.

“I want to be doing my day job for a very long time,” says Kloss. “But I also want to grow businesses and make a meaningful impact.”