Paul Halmos

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

Paul Halmos studied in Chicago chemistry, philosophy and mathematics.

In his evidence he used the first time the grave, crate or Halmos said design "■" as an abbreviation for the qed the conclusion of a proof, which is also sometimes referred to open ( "□" ).


Halmos received his B. A. with a major in philosophy and a minor in mathematics at the University of Illinois. He then began a Ph.D. degree in philosophy, but after some difficulty, he changed his subject in mathematics, where 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 should be a formative experience. While he was at the Institute, Halmos wrote his first book Finite Dimensional Vector Spaces, which earned him immediate reputation for being a good textbook author.

Halmos taught at the University of Syracuse, at the University of Chicago, at the University of California at Santa Barbara, the University of Hawaii and at 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 the mathematical faculty of Santa Clara University related parties.

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

His doctoral include Errett Bishop, Donald Sarason.


  • Finite -Dimensional Vector Spaces, Springer 1942
  • Measure Theory, Van Nostrand, 1950
  • Introduction to Hilbert Space and the Theory of Spectral Multiplicity, Chelsea 1951
  • Lectures on Ergodic Theory, Chelsea 1956
  • Naive Set Theory ( German: Naive Set Theory, ISBN 3-525-40527-8 )
  • Lectures on Boolean Algebras, Van Nostrand, 1963
  • Autobiography: I Want to Be a Mathematician (1987 )
  • I have a photographic memory, ISBN 0-8218-0115-5 (1988 )