He completed post-doctoral research at the
Institute for Advanced Study in 1953 and at the Institute for Hydrodynamics of the
University of Maryland from 1953 to 1954. In 1954, he became an assistant professor at the
University of Southern California and in 1956 an associate professor at
California Institute of Technology. Beginning in 1959, he was a professor at
Stanford University. At the beginning of his career, Finn did research on
minimal surfaces and
quasiconformal mappings and later in his career on mathematical problems of hydrodynamics, such as mathematically rigorous treatments of capillary action. He was a visiting professor at the
University of Bonn and several other universities. He was an exchange scientist in 1978 at the
Soviet Academy of Sciences and in 1987 at the
German Academy of Sciences at Berlin. In 1994 he received an honorary doctorate from the
Leipzig University. For the academic years 1958–1959 and 1965–1966, he held
Guggenheim Fellowships. From 1979, he was an editor of the
Pacific Journal of Mathematics. == Personal life ==