Actor and jazz pianist Dudley Moore, with Peter Cook in a TV comedy sketch.
Scott Joplin comes first, of course. He comes over as a cut above many pianists of his time, with his highly sophisticated rags which he insisted should not be played too fast. As well as his vast output of rags, he had pretensions to being a serious composer. His most spectacular rag is probably Euphonic Sounds, which obviously interested James P. Johnson since Johnson recorded it in 1939.
Most of the other ragtime pianists just had one hit. For example, James Scott with Grace and Beauty, George Botsford with Black and White Rag, Charles L. Johnson with Dill Pickles.
The first jazz pianist was Jelly Roll Morton; in fact he claimed to have invented jazz himself, though many would dispute this claim now. We have recorded evidence of his playing on piano rolls and records. His style is a mix of 8 to the bar and 12 to the bar. A striking example is Big Foot Ham where he plays 8 to the bar until the trio where he changes to 12 to the bar.
Then we have the New York school, the undisputed leader of which was James P. Johnson. He made piano rolls and records. His early material is 8 to the bar, for example Harlem Strut. But the vast majority of his recordings are 12 to the bar. Nevertheless he maintained the ragtime left hand throughout his career. He was never in any sense a modern jazz pianist, even though one of his most famous compositions was You've Got to be Modernistic. James P. Johnson was more famous for his pupils than in his own right. His pupils included Fats Waller, Duke Ellington and Count Basie.
Art Tatum (pictured below) was in a class of his own. He was the first virtuoso pianist, and was a major influence on all who came after, including Nat King Cole and Oscar Peterson. Art Tatum used a ragtime left hand, but his amazing right hand technique was straight out of the concert hall. Yet he never wrote a standard.
From the modern era we have Bud Powell and Thelonious Monk: also Britain's very own Dudley Moore, better known to some as actor and comedian. The ragtime left hand has gone; all the work goes into the right hand improvisation. The format is to play the tune once, and then improvise as many choruses as you can on the chord sequence. Erroll Garner is famous for his tune Misty which jazz pianists of all styles include in their repertoire.