He grew up in Hastings-on-Hudson, New York, son of the geographer John Kirtland Wright and Katharine McGiffert Wright, and namesake of his uncle, Austin Tappan Wright, writer of the utopian novel, Islandia . He graduated from Harvard University in 1943. He served in the Army (1943—1946). He graduated from the University of Chicago, with a master's degree in 1948, and a Ph.D. in 1959.
He married Sara Hull Wright, in 1950. They had three children: Joanna Wright (died 2000), Katharine Wright of Berkeley, CA, and Margaret Wright, and two granddaughters, Madeline Giscombe and Elizabeth Perkins.