The entire music education (jazz and classical) will soon return to its roots and be based on composition and improvisation.
When J.S.Bach taught his sons music, the center of his teaching was improvisation.
C.P.E. Bach's the True Art of Playing Keyboard Instruments describes the skills of a modern jazz pianist: variation, improvisation, figured bass.
For example, figured bass playing - is similar to the ability to interpret jazz chord symbols.
Composition and improvisation were the core skills for all musicians up to the 20th century.
To be continued...
In this article the pianist Gabriela Montero demonstrates spontaneous composition on the theme from "Harry Potter" by John Williams.
Please watch the last video - it is a fugue improvised on Rachmaninov's 3 concerto's opening theme. Masterpiece!!!