To give you an idea of Tatum's greatness, there is a quote from his contemporary, Fats Waller. When Tatum walked into a club where Waller was playing, Waller stated "I'm just the piano player, but tonight, God is in the house"
"Every Monday piano players would start gathering about nine or ten o'clock. Tatum wouldn't show up until maybe one or two in the morning and by the time he got there all the heavies would be shootin' their best shots. So after a while, after everybody had played, Tatum would get up and give everyone a master class on how it should be done." Billy Taylor, quoted in W. Royal Stokes, The Jazz Scene (New York:O.U.P. 1991)