Schaeffer was the son of Albert John and Mary Plane Schaeffer (née Herrick). He studiedcivil engineering at theUniversity of Wisconsin, Madison (bachelor's degree 1930) and was, from 1930 to 1933, employed as a highway engineer. In 1936, he received a PhD in mathematics underEberhard Hopf atMIT. From 1936 to 1939, he was an instructor atPurdue University. In 1939, he became an instructor atStanford University where he became, in 1941, assistant professor, in 1943 associate professor and in 1946 professor. From 1947 to 1950, he was a professor at Purdue University. From 1950 to 1957, he was a professor at the University of Wisconsin, Madison, and in the academic year 1956/57, the chair of the mathematics department.[1]
Schaeffer worked withDonald Spencer at Stanford University on variational problems ofconformal mapping, for example, coefficient ranges forschlicht functions (functions analytic and one-to-one). Specifically, they worked on special cases of theBieberbach conjecture, for which they gave a proof that the third coefficient satisfied the conjectured estimate (a result already proved byCharles Loewner). Their goal was to give a proof for the fourth coefficient, but their approach would have required the numerical integration of about one milliondifferential equations. A little later,Paul Garabedian and Max Schiffer, then at Stanford, improved the Schaeffer–Spencer method and greatly reduced the number of necessary integrations. With this improvement, Garabedian and Schiffer were able in 1955 to prove the conjectured estimate for the fourth coefficient. In 1948, Schaeffer shared theBôcher Memorial Prize with Spencer for their joint work on schlicht functions.[2]
^Halsey Royden:History of Mathematics at Stanford -Who Was Who in America. Vol. 3:1951–1960. Marquis Who's Who, Chicago 1963, p. 759
^Schaeffer, Spencer: "Coefficients of schlicht functions", parts I, II, III, IV, in:Duke Mathematical Journal, vol. 10, 1943, pp. 611–635; vol. 12, 1945, pp. 107–125 andProceedings of the National Academy of Sciences, vol. 32, 1946, pp. 111–116; vol. 35, 1949, pp. 143–150
