Doug Ramsey is a well-respected writer on the subject of Jazz. In a recently re-posted article, he pointed out how many Jazz musicians have imbued their music with Classical riffs. He went on to say that,
"If one of the primary aims of jazz improvisation is the creation of melody, could there be a more inspirational concentration of examples than in Franz Schubert's Quintet in C?"
Ramsey went on to cite several towering figures in the world of Jazz whose music pays homage to Classical music, saying as Louis Armstrong grew up in New Orleans, opera was a huge part part of the city's musical atmosphere, that Charlie Parker quoted Classical melodies in his music, and that Paul Desmond found inspiration in Stravinsky's music. Armstrong was part of attempts to make classics such as A Midsummer Night's Dream swing. Swingin' the Dream had a fully integrated cast in a musical version of the Shakespeare classic, set in Louisiana. Louis Armstrong was cast as Bottom and Maxine Sullivan as Titania. Even the Dandridge sisters had a role. Agnes DeMille did the choreography and scenery was based on cartoons by Walt Disney. In an interview with NPR, saxophonist Ravi Coltrane speaks of the record collection built by his parents, John and Alice Coltrane. That collection, which Ravi still has, featured plenty of Classical music, such as Stravinsky's Firebird. Seems to me that, if Schubert were alive today, he would be invited to sit in. You can hear a movement from Schubert's Quintet above. Below, trumpeter Herb Smith, who not only plays with the Rochester Philharmonic, but is a Jazz bandleader and composer, speaks about the Jazz/Classical connection. https://www.youtube.com/watch?v=5o5tG5y0qK4