For a lot of people, jazz is just a stereotype -- a nebulous free-form art that comedians (or any of us, really) will parody without ever knowing what it's really about. Just hit some keys and scat a few syllables: jazz! And there are certainly performers who embrace the improvisational liberties offered by jazz so enthusiastically that they endanger their accessibility to mainstream audiences. However, Dave Brubeck was not only accessible but popular. His defining quartet, which toured and recorded together for 10 years (1958-1967), created the first million-selling jazz album, Time Out, in 1959 -- the same year that Miles Davis released Kind of Blue and Charles Mingus put out Mingus Ah Um (all on the same label, by the way).
Brubeck's accessibility was not the result of catering to the marketplace, but grew out of a confluence of public interest in "difficult" music and artists (Brubeck, Davis, and Mingus among them) who had been working in jazz for decades and had simultaneously matured as recording artists.