From child prodigy to mainstream jazz violinist, Buckley Mills is quickly raising the already high jazz standards set by such legends as Joe Venuti and Stephane Grappelli.

At the age of three, Buckley, yearning for his father’s attention, ran into his office, but his father, a professional musician, was tutoring a student. Young Buckley listened intently for a moment, then high-tailed it into the next room. He picked up a violin and quickly learned to pluck the notes he had jus...