Early life and education
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 "under-achieving" 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 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.
He was the foremost probabilist outside of Russia. In the middle of the 20th century, probability was not generally viewed as a fruitful area of research in mathematics except in Russia, where Kolmogorov and others were influential. Feller contributed to the study of the relationship between Markov chains and differential equations. He wrote a two-volume treatise on probability that has since been universally regarded as one of the most important treatments of that subject.
Numerous topics relating to probability are named after him as Feller process, Feller explosion test, Feller-Brown movement, Feller property, Lindberg-Feller theorem. Books written by him and published as the textbooks are being considered invaluable in popularisation of the theory of probability and the best written during the 20th century.
Despite the fact that he spent the better part of his life out of Croatia where he was born and grew up, and where he started his education, he was in touch with relatives and the colleagues at University of Zagreb whom he often visited, and where he frequently lectured. He received numerous awards and was an honoured member of numerous educational institution (Boston, Zagreb, London, Copenhagen).
Feller initiated the publication of the now well-known review journal Mathematical Reviews.