Here is an avid jazz listener's proof of Thelonious Sphere Monk's (1917-1982) genius as a composer. First, nobody questions a collection of Monk interpretations, and how many other composers in the idiom receive as much attention for single-album concepts? Second, the inclusion of a Monk tune on a mixed program is usually a solid choice because his tunes attract listener interest naturally. Third, any single Monk tune usually survives a wide variety of interpretations and treatments.
I'm not a player nor do I have more than a dangerous knowledge of jazz theory, but it seems to me Monk's maxim, that the inside of tune makes the outside sound good, speaks to why his melodies are so attractive to players and listeners alike. "Monk's Mood" is a personal favorite, of which there are more than 50 versions currently available on iTunes, and Terry Adams has recently released a version on Talk Thelonious.