Gottschalk was born in
Lynchburg, Virginia, on November 3, 1918, and moved to
Salem, Virginia as a child. His father, Carl Gottschalk, was a German immigrant who worked as a machinist and later owned several small businesses in Salem; his younger brother,
Carl W. Gottschalk, became a notable medical researcher. Gottschalk did both his undergraduate studies and graduate studies at the
University of Virginia, finishing with a Ph.D. in 1944 under the supervision of
Gustav A. Hedlund. After graduating, he joined the faculty of the
University of Pennsylvania, and was chair of the Pennsylvania mathematics department from 1954 to 1958. In the academic year 1947/1948 he was a visiting scholar at the
Institute for Advanced Study. At Pennsylvania, his doctoral students included
Philip Rabinowitz, who became known for his work in
numerical analysis, and
Robert Ellis, who became known for his work on topological dynamics. Gottschalk moved to
Wesleyan University in 1963; at Wesleyan, he also served two terms as chair before retiring in 1982. He died on February 15, 2004, in
Providence, Rhode Island, where he had lived since his retirement. ==Contributions==