"Halmos" redirects here. For the mathematical symbol, see Tombstone (typography). For the church music composer, see László Halmos.
The native form of this personal name is Halmos Pál. This article uses Western name order when mentioning individuals.
Paul Halmos
Born
Paul Richard Halmos
(1916-03-03)March 3, 1916
Budapest, Austria-Hungary
Died
October 2, 2006(2006-10-02) (aged 90)
Los Gatos, California, U.S.
Nationality
Hungarian American
Alma mater
University of Illinois
Awards
Chauvenet Prize (1947) Lester R. Ford Award (1971,1977) Leroy P. Steele Prize (1983)
Scientific career
Fields
Mathematics
Institutions
Syracuse University University of Chicago University of Michigan Indiana University Santa Clara University
Doctoral advisor
Joseph L. Doob
Doctoral students
Errett 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]
Paul Richard Halmos (Hungarian: Halmos Pál; 3 March 3 1916 – 2 October 2006) was a Hungarian-born American mathematician and statistician who made fundamental...
PaulHalmos, and Alain Connes. These criticisms are analyzed below. The evaluation of nonstandard analysis in the literature has varied greatly. Paul...
Polyadic algebras (more recently called Halmos algebras) are algebraic structures introduced by PaulHalmos. They are related to first-order logic analogous...
careful analysis of the data acquired in this pursuit." As expressed by PaulHalmos: "Mathematics is not a deductive science—that's a cliché. When you try...
the National Bureau of Standards. He completed his Ph.D. in 1954 under PaulHalmos; his thesis was titled Spectral Theory for Operations on Banach Spaces...
Apprenticeship of a Mathematician, Springer, p. 114, ISBN 9783764326500. Halmos, Paul (1950). Measure Theory. New York: Van Nostrand. pp. vi. The symbol ∎...
existence (via the axiom of choice), not an explicit example. According to PaulHalmos, a subset of a locally compact Hausdorff topological space is called...
grand problem no longer unsolved: the circle squared beyond refutation." PaulHalmos referred to the book as a "classic crank book." The problem of squaring...
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...
Kelley's 1955 book General Topology. Its invention is often credited to PaulHalmos, who wrote "I invented 'iff,' for 'if and only if'—but I could never...
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...
Surprised?, Fernando Q. Gouvêa, American Mathematical Monthly, March 2011. PaulHalmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted...
vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158 PaulHalmos, "What Does the Spectral Theorem Say?", American Mathematical Monthly...
mathematicians such as George A. Wentworth, Bertrand Russell, Nicolas Bourbaki, PaulHalmos, Stephen Cole Kleene, and John Horton Conway have preferred to include...
mathematicians disapprove of this notation. In his 1985 autobiography, PaulHalmos criticized what he considered the "childish ln notation", which he said...
Russell Autobiography 1967 Freeman Dyson Disturbing the Universe 1979 PaulHalmos I Want to be a Mathematician: An Automathography 1985 Stanislaw Ulam...
logic. PaulHalmos discovered monadic Boolean algebras while working on polyadic algebras; Halmos (1962) reprints the relevant papers. Halmos and Givant...
a rectangle, such as □ or ∎, known as a "tombstone" or "halmos" after its eponym PaulHalmos. Often, "which was to be shown" is verbally stated when writing...
outputs are many more. The argument below is adapted from an argument of PaulHalmos. As stated above, the probability that no two birthdays coincide is 1...
in 1933, formalized it using the Radon–Nikodym theorem. In works of PaulHalmos and Joseph L. Doob from 1953, conditional expectation was generalized...