In my opinion, one of the finest if not the finest pianists alive today is Keith Jarrett. You will not find Jarrett playing much classical music though he certainly plays it well when he does. He is instead known for improvisation. In fact, he regularly composes and improvises entire concerts on the spot. And the music he improvises (a fusion of classical, jazz, and other styles) is as complex and almost as well developed as any classical music you will ever find.
It is unfortunate that Jarrett is apparently not a very nice person. He definitely has some issues, but then, so did the classical greats of the past. It takes nothing away from his genius as a musician.
Here are some thoughts from Jarrett on why classically-trained musicians can’t improvise:
As Jarrett sees it, moving from the interpretation based world of classical music to the improvisational one of jazz requires a radical shift that shakes the foundations of self. When he performed a lot of Mozart in the 80’s, he says “I wasn’t playing anything other than Mozart. I had to become another person.” And, he adds, “to teach a classical musician to improvise is almost more impossible than to teach an accountant or plumber to improvise.”
“I once had a conversation with Vladimir Ashkenazy. We were on a cruise with the English Chamber Orchestra and I gave him a tape with some recent improvisations. When he had listened to it he said, ‘How do you play all the right notes?’ I said, “No, you see they just become the right notes by virtue of their environment.’ Then he said ‘I’d love to be able to improvise but I know I’d need so much time to get into the right headspace to do that.’ Of course he didn’t use the word ‘headspace.’ But he knew he’d have to shut everything down. From where they are you can’t get to the improvisation and have it be you, because you’ve been trained outside of yourself.”
I can see why Jarrett says what he does. There is a radical difference between playing classical music and improvising your own music whether it is church music or jazz. But I think it is possible to make that shift. If you are older, you can still learn if you go about it diligently and systematically. And if you have young children that are learning music, expose them to improvisational techniques as soon as you can. They will thank you later.