The prize (originally called the Book Prize) was endowed in 2005 by Paul and Virginia Halmos and renamed in honor of AMS President Joseph L. DoobPaul Halmos (1916-2006) was Doob's first Ph.D. student.  Doob received his Ph.D. from Harvard in 1932 and three years later joined the faculty at the University of Illinois, where he remained until his retirement in 1978.  He worked in probability theory and measure theory, served as AMS President in 1963-1964, and received the AMS Steele Prize in 1984 "for his fundamental work in establishing probability as a branch of mathematics.  Doob passed away on June 7, 2004 at the age of 94.