Albert Charles Schaeffer (13 August 1907,

Belvidere, Illinois Belvidere is a city in Boone County, settled on the Kishwaukee River in far northern Illinois, United States. Known as the 'City of Murals', Belvidere is home to several public art installations throughout the North and South State Street histo ...

– 2 February 1957) was an American mathematician who worked on

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

Biography

Schaeffer was the son of Albert John and Mary Plane Schaeffer (née Herrick). He studied

civil engineering Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage ...

at the

University of Wisconsin, Madison A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...

(bachelor's degree 1930) and was from 1930 to 1933 employed as a highway engineer. In 1936 he received a PhD in mathematics under

Eberhard Hopf Eberhard Frederich Ferdinand Hopf (April 4, 1902 in Salzburg, Austria-Hungary – July 24, 1983 in Bloomington, Indiana, USA) was a mathematician and astronomer, one of the founding fathers of ergodic theory and a pioneer of bifurcation theory who ...

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...

. From 1936 to 1939 he was an instructor at

Purdue University Purdue University is a public land-grant research university in West Lafayette, Indiana, and the flagship campus of the Purdue University system. The university was founded in 1869 after Lafayette businessman John Purdue donated land and money ...

. In 1939 he became an instructor at

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

, where he became in 1941 assistant professor, in 1943 associate professor, and in 1946 professor. From 1947 to 1950 Schaeffer was a professor at

. 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. Schaeffer worked with Donald Spencer at Stanford University on variational problems of

conformal mapping In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U and V be open subsets of \mathbb^n. A function f:U\to V is called conformal (or angle-preserving) at a point u_0\in ...

, ''e.g.'' coefficient ranges for schlicht functions (functions analytic and one-to-one). Specifically they worked on special cases of the

Bieberbach conjecture In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It ...

, for which they gave a proof that the third coefficient satisfied the conjectured estimate (a result already proved by

Charles Loewner Charles Loewner (29 May 1893 – 8 January 1968) was an American mathematician. His name was Karel Löwner in Czech and Karl Löwner in German. Karl Loewner was born into a Jewish family in Lany, about 30 km from Prague, where his father Sig ...

). Their goal was to give a proof for the fourth coefficient, but their approach would have required the numerical integration of about one million differential equations. A little later

Paul Garabedian Paul Roesel Garabedian (August 2, 1927May 13, 2010) was a mathematician and numerical analysis, numerical analyst. Garabedian was the Director-Division of Computational Fluid Dynamics at the Courant Institute of Mathematical Sciences, New York Univ ...

and Max Schiffer, then at Stanford, improved the Schaeffer-Spencer method and greatly reduced the number of necessary integrations; thus Garabedian and Schiffer were able in 1955 to prove the conjectured estimate for the fourth coefficient. In 1948 Schaeffer shared the

Bôcher memorial prize The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five year ...

with Donald Spencer for their joint work on

schlicht function In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It ...

s. In 1931 he married Caroline Juliette Marsh; they had two sons and a daughter.

Selected publications

* * *with G. Szegő: *with G. E. Forsythe: *with

R. J. Duffin R. or r. may refer to: * ''Reign'', the period of time during which an Emperor, king, queen, etc., is ruler. * '' Rex'', abbreviated as R., the Latin word meaning King * ''Regina'', abbreviated as R., the Latin word meaning Queen * or , abbreviat ...

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References

External links

* {{DEFAULTSORT:Schaeffer, Albert Charles 1907 births 1957 deaths 20th-century American mathematicians Mathematical analysts People from Belvidere, Illinois Mathematicians from Illinois

Biography

Selected publications

See also

References

External links