If we think of traditional jazz only as a pleasant noise that makes us tap our feet and want to dance, we are missing the enormous amount of learning that lies behind it. And the greatest musicians make it look so easy that we may not recognise how 'erudite' it is.
The musicians have had to:
master the techniques of playing their instrument(s) [many hundreds of hours of practice];
study the history of traditional jazz and learn from the work and recordings of past masters;
learn to play in various keys and become fluent in the appropriate chords and arpeggios - major, minor, diminished and so on - and be able to improvise freely around them;
study and learn to use syncopation, riffs, jazzy devices and a variety of tempos and rhythms;
understand the structures of the tunes;
learn and hold in their heads the melodies and harmonic progressions of many tunes [often hundreds];
study the role of their own instrument and use this knowledge effectively in contributing to the playing as a team-member;
master the conventions and the methods of communication within a performance.
Compared with most conventional kinds of musicians who play instruments directly from printed music and without any requirement to improvise or deviate from what is written, jazz musicians may be considered exceptionally erudite.
Imagine you would like to speak a foreign language but you are starting from scratch. Think how much study it will take for you to reach a point when you will be able to hold a fluent natural conversation with native speakers of that language.
Learning to play an instrument in a traditional jazz band is very similar to that.
Yes, well said that lady: traditional jazz is erudite all right.