Paul Halmos

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Paul Halmos

Paul Richard Halmos (born March 3, 1916 in Budapest , † October 2, 2006 in Los Gatos , California , USA ) was an American mathematician of Hungarian origin who worked in the fields of probability theory , statistics , ergodic theory , functional analysis (especially Hilbert spaces ) and researched mathematical logic . He has also authored several textbooks.

Paul Halmos studied chemistry , philosophy and mathematics in Chicago .

In his evidence, he first used the symbol "■" called gravestone , box or halmos as an abbreviation for the q. e. d. at the end of a proof, which is sometimes presented openly ("□").


Halmos received his BA from the University of Illinois with a major in Philosophy and a minor in Mathematics . He then started a Ph.D. - Studied philosophy, but after some difficulties, changed his subject to mathematics, in which he received his doctorate in 1938. Joseph L. Doob supervised his dissertation called Invariants of Certain Stochastic Transformation: The Mathematical Theory of Gambling Systems . Soon after, Halmos went to the Institute for Advanced Study . Six months later he worked under John von Neumann , which was to be a formative experience. While at the institute, Halmos wrote his first book, Finite Dimensional Vector Spaces , which immediately earned him a reputation for being a good textbook author.

Halmos has taught at the University of Syracuse , the University of Chicago , the University of California at Santa Barbara , the University of Hawaii, and Indiana University . In 1983 he was awarded the Leroy P. Steele Prize of the American Mathematical Society .

From his retirement in 1985 until his death, he was associated with the mathematics faculty at Santa Clara University .

He and his wife Virginia donated a conference center to the Mathematical Association of America in Washington DC and to the MAA's Euler Book Prize .

His PhD students include Errett Bishop , Donald Sarason .


  • Finite-Dimensional Vector Spaces (= Annals of Mathematics Studies. Vol. 7, ISSN  0066-2313 ). Princeton University Press et al., Princeton NJ et al. 1942.
  • Measure Theory. Van Nostrand, New York NY et al. 1950
  • Introduction to Hilbert Space and the Theory of Spectral Multiplicity. Chelsea Publishing Co., New York NY et al. 1951.
  • Lectures on Ergodic Theory. Chelsea Publishing Co., New York NY et al. 1956.
  • Naive set theory. Van Nostrand, New York NY et al. 1960, (In German: Naive set theory (= modern mathematics in elementary representation. Vol. 4, ISSN  0544-7089 ). Vandenhoeck & Ruprecht, Göttingen 1968).
  • Lectures on Boolean Algebras (= Van Nostrand Mathematical Studies. Vol. 1, ZDB -ID 793375-7 ). Van Nostrand, Princeton NJ et al. 1963.
  • with Viakalathur S. Sunder: Bounded Integral Operators on L 2 Spaces (= results of mathematics and its border areas. NF Vol. 96). Springer, Berlin et al. 1978, ISBN 3-540-08894-6 .
  • Autobiography: I Want to Be a Mathematician. Of automathography. Springer, New York NY et al. 1985, ISBN 0-387-96078-3 .
  • I have a photographic memory. American Mathematical Society, Providence, RI 1987, ISBN 0-8218-0115-5 .


  • Donald J. Albers, Gerald L. Alexanderson (Eds.): Mathematical People. Profiles and interviews. Birkhäuser, Boston MA et al. 1985, ISBN 3-7643-3191-7 .

See also

Web links

Individual evidence

  1. Halmos Foundation, MAA
  2. ^ Mathematics Genealogy Project