Editing Paul Halmos (section)

==Early life and education==
Born in the [[Kingdom of Hungary]] into a [[History of the Jews in Hungary|Jewish]] family, Halmos immigrated to the United States at age 13. He obtained his B.A. from the [[University of Illinois at Urbana-Champaign|University of Illinois]], majoring in mathematics while also fulfilling the requirements for a degree in philosophy. He obtained the degree after only three years, and was 19 years old when he graduated. He then began a Ph.D. in philosophy, still at the [[Champaign–Urbana]] campus. However, after failing his masters' oral exams,<ref>The Legend of John Von Neumann. P. R. Halmos. The American Mathematical Monthly, Vol. 80, No. 4. (Apr., 1973), pp.&nbsp;382–394.</ref> he shifted to mathematics and graduated in 1938. [[Joseph L. Doob]] supervised his dissertation, titled ''Invariants of Certain Stochastic Transformations: The Mathematical Theory of Gambling Systems''.<ref>Halmos, Paul R. [http://projecteuclid.org/euclid.dmj/1077491241 "Invariants of certain stochastic transformations: The mathematical theory of gambling systems."] Duke Mathematical Journal 5, no. 2 (1939): 461–478.</ref>