Walter Baum earned the Ph.D. at Eidgenössische Technische Hochschule Zürich in 1950 under Heinz Hopf, with a dissertation entitled Die Nullwegegruppe und ihre Verallgemeinerungen. Accoding to Hemmingsen's The Department of Mathematics up until about 1960 "Baum had a medical degree, but never practiced medicine in the U.S". Hemmingsen wrote me in a letter of 13 June 2002 "Baum's father was a physician somewhere in Germany. Baum and his mother escaped the Nazis, but just barely (I heard a comment once that Baum and his mother got out the back door just as the Gestapo came in the front door, but that may have been only figuratively true). They somehow got across the border to Switzerland where old Mrs. Baum got some kind of job and supported Baum in his studies at ETH. Helen Berlin, who was a secretary in mathematics years ago, said that because Walter's father had wanted him to become a physician, he went to medical school during the day; but he preferred mathematics, so he studied mathematics in the evening. Helen remembers not feeling well at one day, and (while standing in the middle of the quad) listening to Walter for an hour try to diagnose her and put his description into English. Otway Pardee said that Walter's wife Lily also had a medical degree from Europe.
Hemmingsen told me that Baum came to the US in 1951, was at Tennessee for one year, and then joined the Syracuse faculty. In his document Hemmingssen noted "[I]n his first year at Syracuse he called Kibbey's attention to Albert Edrei who was looking for a job. Edrei and Baum had both attended ETH in Zürich and Baum knew Edrei well." Baum and Hemmingsen started a topology seminar also attended by Exner. At SU he had 6 Ph.D. students: Charles Olgilvy (1954), Louis Robinson (1954), Edwin Gillette (1955), May Kinsolving (1957), Kaphyung Yoon (1958) and Thomas Frank (1962). Tom said that Walter had received a grant from the National Institute of Health in 1962. Hemmingsen wrote that "[f]or two years he was later a visiting professor in the Zoology Department, where he worked on a biological question involving the growth of bone tissue."
According to Hemmingsen "He had had Parkinson's disease for many years and had gotten so bad that even a strong public address system installed in his classroom could not help his weakened voice." He retired on disability as an associate professor in May 1975. (I understand from his daughter with whom Lily lives that Walter died, but I was refused the year of death.)
Sources: Mathematics Genealogy web site; the recollections of those listed.
Phil Church 5/31/02 & 6/18/02.