Making it up as you go along, for classical musicians, can be suicidal in that extremely uptight world. But Gabriela, a young Venezuelan-born American pianist manages to get away with it. As correspondent Morley Safer reports, her sheer talent has won over the critics. It's an amazing gift that came naturally and very, very early.
Asked if her family was musical when she grew up, Gabriela tells Safer, "No. Still they're not. No, no, no. I come from a completely normal family."
By the time she was eight years old, it was clear there was nothing normal about Gabriela Montero's talent: she was featured on Venezuelan television, playing Chopin. And even then, she couldn't wait to finish and start making up her own music.
"It was always the most pleasurable thing and the most fun. I just sat down and improvised," she says. "It's how I communicate the best. The way I see it is that music is not something that's scholarly, but a means to an end. You know, to tell the stories that I want to tell."
You would think, given her early start, that Gabriela Montero's career path would have been straight and uncomplicated.
But you'd be wrong. For in the starchy world of classical music, she is something of a misfit, right down to the tips of her remarkable fingers.
Asked if she has the hands of an artiste, Gabriela says laughing, "I hope so. Because you know, I don't find them particularly pretty."
"They're small. They look very big when I play, which is really funny. People think I have mammoth hands, but I don't," she says.
People can be forgiven for that. Gabriela Montero's hands make music that is dramatic, passionate and larger than life.
"Do you, in your most idle moments, are you hearing music?" Safer asks.
"All the time. It's a 24 hour radio," she says, laughing. "And I cannot shut it off, it is the worst part."
She is the hottest rising star in the classical music world, and the most controversial, as well.
That's because of her double life: in London one night, playing the classics at Queen Elizabeth Hall, in New York another night, improvising at Joe's Pub, playing Bach's Toccata.
Improvising, sitting down and playing whatever comes into your head, is what Jazz musicians do. "I can't tell you how much fun it is to improvise," Gabriela tells Safer. "I just love it."
In their days, Bach, Beethoven and Mozart did it too. But in the classical world, the practice died out a century ago. And today, improvisation is still largely frowned upon.
"It's spontaneous creation. It's spontaneous music making. And is it perfect? I don't know. It's not, I mean it's something that is just born and dies," Gabriela says.