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

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.

Doob returned to this subject many years later when he proved a probabilistic version of Fatou's boundary limit theorem for harmonic functions.

Thus a subject that had originated from intuitive ideas suggested by real life experiences and studied informally, suddenly became mathematics.

In writing this book, Doob shows that his two favorite subjects, martingales and potential theory, can be studied by the same mathematical tools.