"The Duke" is Dave Brubeck's greatest composition, and a great tune. Inspired by Ellington and Darius Milhaud, with whom Dave studied briefly, the best version is, as many songs are, by Gil Evans with Miles Davis on, I think, Miles Ahead. (I won't check my vinyl in the garage.)
1. Chord progressions that, on a cheat sheet look arbitrary, sound to the ear organic.
2. Not so much the birth of the cool as the puberty of the cool, "the cool" being more or less the west coast response to bebop.
3. Really fun to play if you can wrap your head and hands around the constantly morphing chord changes.
4. Played in the exact right tempo, it swings hard whether solo piano or quartet or big band.
Though more often than not, Dave's experimentation with polyrhythms and progressive harmonies feuded with both Paul Desmond and what ended up being the legacy of novelty in jazz, and most hardcore (and arrogant!) jazzers would find Dave's music ultimately gimmicky. Understandable, but not necessarily fair.
Album to own: Time out.
Definitely a worthy ambassador of jazz and a tremendous human being. Which is more important we'll still never know.