Paul Halmos

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Paul Richard Halmos (born March 3 1916) is a Hungarian-born American mathematician who has done research in the fields of logarithm theory, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). In a series of papers published in 1962 as Algebraic Logic, Halmos devised polyadic algebras, a purely algebraic version of first order logic differing from the better known cylindric algebras of Alfred Tarski and his students.

In addition to his original contributions to mathematics, Halmos acquired a reputation as an unusually clear and engaging expositor of university mathematics. His monographs include Naive Set Theory, Introduction to Hilbert Space and the Theory of Spectral Multiplicity, Measure Theory, Lectures on Boolean Algebras, and Finite-Dimensional Vector Spaces. His 1985 "automathography" I Want to be a Mathematician (Springer-Verlag, New York, 1985) is an outstanding account of what it was like to be an academic mathematician in the 20th century USA. (Halmos chooses to call it an "automathography" rather than "autobiography" because the focus is almost entirely on his life as a mathematician, not his personal life.)

In an article in the American Scientist 56(4): 375-389, Halmos makes the case for mathematics as a creative art and for mathematicians as artists, not number crunchers. He discusses the division of the field into mathology and mathophysics and the degrees to which a mathematician and a painter live within very similar environments.

The use of "iff" to abbreviate "if and only if" is sometimes mistakenly credited to Halmos; however, he has said that he borrowed this notation. The use of the "tombstone" notation to signify the end of a proof is also credited to him; the tombstone symbol ∎ (Unicode U+220E) is sometimes called a halmos.

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