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Paul Halmos information


Paul Halmos
Born
Paul Richard Halmos

(1916-03-03)March 3, 1916
Budapest, Austria-Hungary
DiedOctober 2, 2006(2006-10-02) (aged 90)
Los Gatos, California, U.S.
NationalityHungarian
American
Alma materUniversity of Illinois
AwardsChauvenet Prize (1947)
Lester R. Ford Award (1971,1977)
Leroy P. Steele Prize (1983)
Scientific career
FieldsMathematics
InstitutionsSyracuse University
University of Chicago
University of Michigan
Indiana University
Santa Clara University
Doctoral advisorJoseph L. Doob
Doctoral studentsErrett Bishop
Bernard Galler
Donald Sarason
V. S. Sunder
Peter Rosenthal

Paul Richard Halmos (Hungarian: Halmos Pál; 3 March 3 1916 – 2 October 2006) was a Hungarian-born American mathematician and statistician 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. He has been described as one of The Martians.[1]

  1. ^ A marslakók legendája - György Marx

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Paul Halmos

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Paul Richard Halmos (Hungarian: Halmos Pál; 3 March 3 1916 – 2 October 2006) was a Hungarian-born American mathematician and statistician who made fundamental...

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Criticism of nonstandard analysis

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Paul Halmos, and Alain Connes. These criticisms are analyzed below. The evaluation of nonstandard analysis in the literature has varied greatly. Paul...

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Polyadic algebra

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Polyadic algebras (more recently called Halmos algebras) are algebraic structures introduced by Paul Halmos. They are related to first-order logic analogous...

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John von Neumann

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Glimm, Impagliazzo & Singer (1990), p. 39. Halmos 1958, p. 86. Halmos 1958, p. 87. Pietsch 2007, p. 168. Halmos 1958, p. 88. Dieudonné 2008. Ionescu-Tulcea...

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Experimental mathematics

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careful analysis of the data acquired in this pursuit." As expressed by Paul Halmos: "Mathematics is not a deductive science—that's a cliché. When you try...

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Errett Bishop

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the National Bureau of Standards. He completed his Ph.D. in 1954 under Paul Halmos; his thesis was titled Spectral Theory for Operations on Banach Spaces...

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Table of mathematical symbols by introduction date

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Apprenticeship of a Mathematician, Springer, p. 114, ISBN 9783764326500. Halmos, Paul (1950). Measure Theory. New York: Van Nostrand. pp. vi. The symbol ∎...

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Borel set

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existence (via the axiom of choice), not an explicit example. According to Paul Halmos, a subset of a locally compact Hausdorff topological space is called...

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Squaring the circle

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grand problem no longer unsolved: the circle squared beyond refutation." Paul Halmos referred to the book as a "classic crank book." The problem of squaring...

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Nonstandard analysis

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Journal of Mathematics. Some of the ideas used in Halmos' proof reappeared many years later in Halmos' own work on quasi-triangular operators. Other results...

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If and only if

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Kelley's 1955 book General Topology. Its invention is often credited to Paul Halmos, who wrote "I invented 'iff,' for 'if and only if'—but I could never...

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Naive set theory

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Cardinals (1974). ISBN 0 444 10535 2. Halmos 1974, p. 9. Halmos 1974, p. 10. Jech 2002, p. 4. Halmos 1974, Chapter 2. Halmos 1974, See discussion around Russell's...

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Cardinality of the continuum

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Surprised?, Fernando Q. Gouvêa, American Mathematical Monthly, March 2011. Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted...

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Spectral theorem

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vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158 Paul Halmos, "What Does the Spectral Theorem Say?", American Mathematical Monthly...

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Natural number

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mathematicians such as George A. Wentworth, Bertrand Russell, Nicolas Bourbaki, Paul Halmos, Stephen Cole Kleene, and John Horton Conway have preferred to include...

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Logarithm

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mathematicians disapprove of this notation. In his 1985 autobiography, Paul Halmos criticized what he considered the "childish ln notation", which he said...

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List of autobiographies

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Russell Autobiography 1967 Freeman Dyson Disturbing the Universe 1979 Paul Halmos I Want to be a Mathematician: An Automathography 1985 Stanislaw Ulam...

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Axiom of empty set

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OCLC 50422939. Burgess, John, 2005. Fixing Frege. Princeton Univ. Press. Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted...

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Monadic Boolean algebra

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logic. Paul Halmos discovered monadic Boolean algebras while working on polyadic algebras; Halmos (1962) reprints the relevant papers. Halmos and Givant...

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October 2

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1945) 2006 – Helen Chenoweth-Hage, American politician (b. 1938) 2006 – Paul Halmos, Hungarian-American mathematician (b. 1916) 2007 – Tex Coulter, American...

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Mathematical proof

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a rectangle, such as □ or ∎, known as a "tombstone" or "halmos" after its eponym Paul Halmos. Often, "which was to be shown" is verbally stated when writing...

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Birthday problem

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outputs are many more. The argument below is adapted from an argument of Paul Halmos. As stated above, the probability that no two birthdays coincide is 1...

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Conditional expectation

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in 1933, formalized it using the Radon–Nikodym theorem. In works of Paul Halmos and Joseph L. Doob from 1953, conditional expectation was generalized...

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