It was his interest in contemporary music that led to a decisive meeting with John Cage in 1960. The two men became lifelong friends and professional colleagues. In 1964 Snyder moved to Madison, Wisconsin where he wrote the first doctoral dissertation ever written on John Cage, for the University of Wisconsin–Madison. Snyder included compositions by Cage in the standard repertoire of music that he performed both in the United States and internationally including the album of new music that he recorded for Advance Records in 1974 and a recital that he gave at Lincoln Center's Alice Tully Hall in 1977. He also published two interviews with John Cage, one in 1985 and the other in 1990. In 1990 John Cage composed a piece for piano for Snyder called "One5, for ellsworth," which Snyder premiered on an all-Cage program in Madison in 1991. Cage was in attendance for the performance, one year before his own death at age 80.