Rachmaninoff for composition. No one else in the 20th century came close to him in composition, in my opinion.
There were many great performers. Vladimir Horowitz is known is one of the greatest pianists of all time. I also think Glenn Gould plays Bach better than anyone besides Bach himself. Sviatoslov Richter, Artur Rubinstein and Georges Cziffra are worth mentioning as well.
There were also many genius conductors as well: Bernstein, Herbert von Karajan, Vladimir Ashkenazy and Wilhelm Furtwangler.
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