“I’m not dancing,” Karole Armitage says, talking about the upcoming set of performances that Dance Umbrella will be presenting in London this autumn. “It’s too hard!”

While this is perhaps unfortunate, it’s also understandable. At 57 Armitage has no desire to get up onstage and shake a leg or, more accurately given her erstwhile gifts as a dancer, rocket into and then throw off-kilter an incredible balance. Now she’d much rather leave it to others (“My remarkable dancers,” she calls them) to negotiate her often fabulous mix of classical and contemporary movement.

As a choreographer, and the artistic director of the New York-based company Armitage Gone! Dance, Armitage has cultivated a reputation for artistic innovation that ultimately helped transport her from her birthplace in Madison, Wisconsin to a decade and half of living and making work in Europe. “Though I have a very independent, American pioneer spirit,” she explains, “I am European in my expectation of how art can be produced and consumed. I’m still an outsider in the United States, and an explorer everywhere.”

Either side of the big slice of time she spent abroad, Armitage studied film-making, cooked up the dances for the terrific Broadway revival of Hair and worked with the likes of Mikhail Baryshnikov, Michael Clark (in his novice days), Madonna and Michael Jackson. In 2012 she’s been hired to choreograph a production for Cirque du Soleil.

Clearly what fuels her work is a healthy push-and-pull of eclectic creative forces. Just consider her career trajectory. Rigorously trained in ballet, she followed a few seasons of dancing for Ballet du Grand Théâtre de Genève (where the repertory was exclusively that of the Russian-born genius, George Balanchine) with five years as an outstanding member of the masterly Merce Cunningham’s Manhattan-based troupe. For a young dancer, who at the time knew next to nothing about modern dance, it could hardly get any better – or so it seemed. “The first couple of years with Merce were thrilling,” she says. “I was about 20 years old and he was creating me. I was learning a new way to think and move, and meeting Jasper Johns and Bob Rauschenberg, and touring with John Cage. I loved it.”

Armitage, however, had a mind of her own. Eventually, as she admits, “The thrill was gone and I wanted to explore new ideas.” And so she became her own muse, stimulated as well by the lovely abrasions that collaboration with cutting-edge composers (like Rhys Chatham) and trend-setting designers and visual artists (Charles Atlas, David Salle and, a little later, Jeff Koons) can bring.

A molten pixie with a voracious talent, Armitage became an overnight sensation in 1981 with Drastic-Classicism. An audacious mix of blistering, red-hot motion and blastingly high-decibel live sound, this controversial dance (at Queen Elizabeth Hall on 11 & 12 October) became her international calling card. It also reinforced her status as the reigning ‘punk ballerina’ of post-modern dance.

Those two words still cling to Armitage’s name, but she doesn’t mind. But how much of the punk label was real and how much, in the words of dance critic Arelene Croce, just ‘a sophisticated ploy’?

“In the mid-1970s I was thinking about how dance was all about no,” Armitage recalls. “No virtuosity, no emotion, no costume, no story, etc. This moralistic stance didn’t appeal to me; I felt it was leading to an audience of insiders. I wanted instead to connect to an audience with all the beautiful history of the art form, combining the refinement and poetry of ballet with the intimacy and intellectual tradition of modern dance - not to mention some rebellious rock (or punk) spirit thrown in. So yes, to a great extent it was a ploy, a device for forging a new dance vocabulary with a tongue-in-cheek relationship to punk. But the serious side of my interest in punk was that it wasn’t formulaic. Rock had become an industry (as hip hop has now) and lost its creativity. Punk was creative.”

As Croce wrote when Drastic premiered, “Classical values that were flayed alive, stayed alive.” Time may have inevitably undermined this era-defining work’s shocking freshness, but it remains mighty lively. Armitage revived Drastic in 2009, tightening it up and underlining the innate rhythmic drive of the movement. In doing so she couldn’t help but notice how society itself has changed. “This generation isn’t as free as we were [back then], and that of course is due to changes in a world with much more economic pressure on it and reduced resources. We were free spirits with little understanding of how hard it is to survive and no thoughts of making a career. The new generation of dancers and musicians is more sober. Everyone is pretty wild in Drastic, and they have a great time, but [the work] is not as ironic [as it once was].”

Armitage recently revived another of her classics. The Watteau Duets (14 October at the Victoria and Albert Museum) was devised in 1985. Armitage herself originally danced in it, utilising both pointe shoes and high heels to jab, swivel and stamp the piece across. Staged as a series of majestic confrontations between a heterosexual couple, she calls it “a really liberated look at a woman’s sexuality.” But, again, she notes how times have changed. “Today it’s hard to get a dancer to go far enough with it, and to dare to be raw enough.”

Still, Armitage is happy to have both of these ‘older’ dances out in front of the public once more. “Each of them works on many layers. They’re entertaining, aesthetically challenging and filled with exciting contradictions – hot emotion and cool technique, irony and sincerity, youthful rebellion and a love of tradition. They use dance to express contemporary culture, from sexual politics to the issue of how to mix high and low art forms - issues that artists are still dealing with today.”

In London, Drastic will be paired with two of the three sections that comprise one of Armitage’s newest dances. Two Theories (as it has been renamed) was inspired by The Elegant Universe, Brian Greene’s best-seller on the evolutionary conflicts of theoretical physics. Although Dance Umbrella won’t be importing Armitage’s kinetic take on Einstein’s theory of relativity, audiences will be able to dive into her interpretation of quantum mechanics and string theory. “I can’t explain these scientific theories,” she says, “nor do I try in the ballet, but I have an appreciation for their poetry. By looking at them through the body abstract ideas take on human content, linking human rhythms and perception to the hidden forces that make up the universe.”

Armitage’s shape-shifting ensemble have been said to handle her writhing, undulant and volatile choreography - deliberately blurry at some points, and then extremely articulate - with great aplomb. “They’re virtuosos who are very fluid and free-spirited,” she avows, “and each is a unique spice.” As for the audience, the feeling she hopes to induce in us is the sort of ‘awed wonder’ that science itself can impart.

A self-described classicist, Armitage once categorised herself as “a marginal, intellectual sort of rebel. I’m not a mainstream kind of person.” Rather than trash her artistic heritage, as she was once accused of doing, her underlying motive is “to warp and massage it and make it into something, image-wise, that’s very different than how people think it looks.” She remains committed to making work “that communicates what it feels like to be alive. Theatre is a good form for describing politics; dance is a good form for erotic, existential and spiritual content.” No surprise whatsoever then that it’s curiosity that keeps her going as an artist.