Having obtained his BS in mathematics from U Chicago in 1940, Stein joined the United States Army Air Force. After the Second World War he gained his PhD in mathematical statistics at Columbia U under the supervision of Wald. He joined the faculty at Stanford U in 1953. He was the IMS Wald Lecturer in 1961, its Rietz Lecturer in 1975, and its Neyman Lecturer in 1984. He was elected to the NAS in 1975.

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ss/1177013517 Fuller biography, interview, and photographs.