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Paul Halmos
Paul Richard Halmos ((ハンガリー語:Halmos Pál); March 3, 1916 – October 2, 2006) was a Hungarian-Jewish-born American mathematician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.
==Early life and education==
Halmos arrived in the U.S. at 13 years of age, but never lost his Hungarian accent. Halmos obtained his B.A. from the University of Illinois, majoring in mathematics, but fulfilling the requirements for both a math and philosophy degree. He took only three years to obtain the degree, and was only 19 when he graduated. He then began a Ph.D. in philosophy; but, after failing his masters' oral exams,〔The Legend of John Von Neumann. P. R. Halmos. The American Mathematical Monthly, Vol. 80, No. 4. (Apr., 1973), pp. 382–394.〕 he shifted to mathematics, graduating in 1938. Joseph L. Doob supervised his dissertation, titled ''Invariants of Certain Stochastic Transformations: The Mathematical Theory of Gambling Systems''.
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