Born in New York City, Goldwater received his BA in 1929 from Columbia University, and his MA from Harvard in 1931.
Goldwater was one of the participants of the informal gatherings of art scholars organized by Meyer Schapiro (c.1935) that included Lewis Mumford, Alfred Barr and Erwin Panofsky.
Goldwater organized the first exhibition of African art by a New York museum, which opened in 1957 in a town house on West 54th Street.
A new wing was proposed, to be named in honor of Rockefeller's son Michael who disappeared in 1961 during an expedition in New Guinea with Dutch anthropologist René Wassing.
Goldwater served as Consultative Chairman of the Metropolitan Museum's Department of Primitive Art from 1971 until his death.