Joseph Leo Doob

Joseph L. "Joe" Doob
Tokyo, 1969 (courtesy MFO)
Born	(1910-02-27)February 27, 1910 Cincinnati, Ohio, U.S.
Died	June 7, 2004(2004-06-07) (aged 94) Urbana, Illinois, U.S.
Residence	U.S.
Nationality	American
Fields	Mathematician
Institutions	University of Illinois at Urbana-Champaign
Alma mater	Harvard University
Doctoral advisor	Joseph L. Walsh
Doctoral students	Warren Ambrose David Blackwell Yuan-Shih Chow Paul Halmos J. Laurie Snell
Known for	Doob martingale

Joseph Leo "Joe" Doob (February 27, 1910 – June 7, 2004) was an American mathematician, specializing in analysis and probability theory.

The theory of martingales was developed by Doob.

Doob was born in Cincinnati, Ohio, February 27, 1910, the son of Leo Doob and Mollie Doerfler Doob. The family moved to New York City before he was three years old. The parents felt that he was underachieving in grade school and placed him in the Ethical Culture School, from which he graduated in 1926. He then went on to Harvard where he received a BA in 1930, an MA in 1931, and a PhD (Boundary Values of Analytic Functions, advisor Joseph L. Walsh) in 1932. After postdoctoral research at Columbia and Princeton, he joined the Department of Mathematics of the University of Illinois in 1935 and served until his retirement in 1978. He was a member of the Urbana campus's Center for Advanced Study from its beginning in 1959. During the Second World War, he worked in Washington, D. C. and Guam as a civilian consultant to the Navy from 1942 to 1945; he was at the Institute for Advanced Study for the academic year 1941–1942 when Oswald Veblen approached him to work on mine warfare for the Navy.

Doob's thesis was on boundary values of analytic functions. He published two papers based on this thesis, which appeared in 1932 and 1933 in the Transactions of the AMS. Doob returned to this subject many years later when he proved a probabilistic version of Fatou's boundary limit theorem for harmonic functions.