I had to basically quit playing classical music (I was never that good anyway) before I could really get an ear for improvisation. I kept thinking that you had to hit the notes just as the composer intended and I think I sacrificed a lot of the soul of the music in search of perfection.
I think Gerswhin changed the way a lot of people thought about what is or is not classical music. Porgy and Bess was a paradigm shift for opera.
I think Mozart would have been a great jazz pianist. I'm just suprised he didn't invent it.
Improvisation on established themes was the central musical experience for Bach, Mozart, Schubert, you name it. Gershwin and pre-ideological jazz are thus much closer to that tradition than cerebrally through-composed stuff.