Blum was born Shirley Marie Neilsen in 1932 in
Petaluma,
California, to parents Dana (née Keyes) and Melvin Louis Neilsen. She received a M.A. degree in 1955 from
University of Chicago and a Ph.D. in Netherlandish art in 1964 from
University of California, Los Angeles (UCLA). Her thesis advisor was Karl M. Birkmeyer. In 1967, she married a co-worker at the Ferus Gallery and art dealer, Irving Blum, which ended in 1976. Shirley and Irving Blum had a son born in 1969, film producer
Jason Blum. Shirley and Walter ran Ferus gallery together for many years. Walter Hopps and Shirley bought out Andy Warhol's first exhibition at Ferus Gallery in 1962, a collection which ended up being worth $15 million by 1996. She taught art history at her alma mater University of Chicago, from 1961 until 1962. From 1970 until 1989, Blum served as a professor at
State University of New York at Purchase (SUNY Purchase). At SUNY Purchase, she founded the Art History Department. Neilsen was the
Charles A. Dana Department Chair at
Colgate University, from 1973 until 1974. == Selected publications ==