**Joseph Doob** was an American mathematician who worked in probability and measure theory.

- Joseph's interest in science started when he was at grammar school.
- When he entered Harvard in September 1926 he registered for courses in physics but, by the end of his first year of study, Doob had decided that he did not want to proceed to a physics degree.
- In his second year of study Doob registered for courses in mathematics.
- Doob was awarded a AB by Harvard in 1930 and asked his advisor Marshall Stone if he would supervise his doctorate.
- After completing his doctorate, Doob was supported by Birkhoff in an application for a two year National Research Council Fellowship.
- Since in 1932 Elsie, Doob's wife, was a medical student in New York, he had applied to work at Columbia University with J F Ritt.
- However, these were difficult times and Doob could not look forward to the future with any confidence.
- The Great Depression had begun in 1929 and by 1932, the year Doob went to New York, one quarter of the workers in the United States were unemployed.
- Hotelling managed to obtain a Carnegie fellowship to enable Doob to remain at Columbia University and work with him on probability during the year 1934-35.
- At the same time Doob was supervising Warren Ambrose whose thesis Some properties of measurable stochastic processes was submitted a year later.
- Doob's next outstanding doctoral student was David Blackwell who entered the University of Illinois in the year Doob was appointed there and completed his doctorate on Properties of Markov chains in 1941.
- Doob became a full professor at the University of Illinois in 1945.
- Doob's work was in probability and measure theory, in particular he studied the relations between probability and potential theory.
- Doob built on work by Paul Lévy and, during the 1940's and 1950's, he developed basic martingale theory and many of its applications.
- Doob's work has become one of the most powerful tools available to study stochastic processes.
- Another classic text by Doob is Classical potential theory and its probabilistic counterpart first published in 1984 and reprinted in 2001.
- He asked Doob to cooperate with him in writing the sections on probability theory but in the end Doob wrote the whole book.
- Doob is also the author of a well known book on measure theory published in 1994 when he was 84 years old.
- As we indicated above, Doob was a member of the faculty of the University of Illinois from the time of his appointment in 1935.
- The tradition of the Saturday Hike started in 1909 and Doob joined the hikers in 1939 and went regularly every Saturday.
- Doob was elected a member of the National Academy of Sciences and was also elected to French Academy of Sciences.

Born 27 February 1910, Cincinnati, Ohio, USA. Died 7 June 2004, Clark-Lindsey Village, Urbana, Illinois, USA.

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Origin Usa

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive