**Paul Richard Halmos** (March 3, 1916 — October 2, 2006) was a Hungarian-born American mathematician who wrote on probability theory, statistics, operator theory, ergodic theory, functional analysis (in particular, Hilbert spaces), and mathematical logic. He was also a great mathematical expositor. Image File history File links Mathematician Paul Halmos. ...
Image File history File links Mathematician Paul Halmos. ...
March 3 is the 62nd day of the year in the Gregorian calendar (63rd in leap years). ...
1916 (MCMXVI) was a leap year starting on Saturday (link will display the full calendar). ...
October 2 is the 275th day (276th in leap years) of the year in the Gregorian calendar, with 90 days remaining. ...
For the Manfred Mann album, see 2006 (album). ...
Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ...
It has been suggested that this article or section be merged with Probability axioms. ...
A graph of a Normal bell curve showing statistics used in educational assessment and comparing various grading methods. ...
In mathematics, operator theory is the branch of functional analysis which deals with bounded linear operators and their properties. ...
In mathematics, a measure-preserving transformation T on a probability space is said to be ergodic if the only measurable sets invariant under T have measure 0 or 1. ...
Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions. ...
The mathematical concept of a Hilbert space (named after the German mathematician David Hilbert) generalizes the notion of Euclidean space in a way that extends methods of vector algebra from the plane and three-dimensional space to spaces of functions. ...
Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation. ...
## Career
Halmos obtained his B.A. from the University of Illinois, majoring in philosophy and minoring in mathematics. He took only three years to obtain the degree, and was only 19 when he graduated. He then began a Ph.D. in philosophy, but after some difficulties, shifted to mathematics, graduating in 1938. Joseph Doob supervised his dissertation, titled *Invariants of Certain Stochastic Transformation: The Mathematical Theory of Gambling Systems*. Shortly thereafter, Halmos left for the Institute for Advanced Study, lacking both job and grant money. Six months later, he was working under John von Neumann, which proved a decisive experience. While at the Institute, Halmos wrote his first book, *Finite Dimensional Vector Spaces*, which immediately established his reputation as a fine expositor of mathematics. The University of Illinois at Urbana-Champaign (UIUC), is the largest campus in the University of Illinois system. ...
Joseph Leo Doob (February 27, 1910-June 7, 2004) was an American mathematician, specializing in analysis and probability theory. ...
Fuld Hall The Institute for Advanced Study is a private institution in Princeton Township, New Jersey, U.S.A., designed to foster pure cutting-edge research by scientists and scholars in a variety of fields without the complications of teaching or funding, or the agendas of sponsorship. ...
John von Neumann (Hungarian Margittai Neumann JÃ¡nos Lajos) (born December 28, 1903 in Budapest, Austria-Hungary; died February 8, 1957 in Washington D.C., United States) was a Hungarian-born American mathematician and polymath who made contributions to quantum physics, functional analysis, set theory, topology, economics, computer science, numerical...
Halmos taught at the University of Syracuse, the University of Chicago (1946-60), the University of Michigan, the University of California at Santa Barbara (about 1977), the University of Hawaii, and Indiana University. From his 1985 retirement from Indiana until his death, he was affiliated with the Mathematics department at Santa Clara University. Syracuse University (SU) is a private American research university. ...
The University of Chicago is an elite private university located principally in the Hyde Park neighborhood of Chicago. ...
The University of Michigan, Ann Arbor (UM, U of M or U-M) is a coeducational public research university in the U.S. state of Michigan. ...
The University of California, Santa Barbara (UCSB) is a coeducational public university located in Santa Barbara County, California. ...
This article is about the University of Hawaii system. ...
Indiana University, founded in 1820, is a nine-campus university system in the state of Indiana. ...
The Santa Clara Mission is a notable on-campus landmark. ...
## Accomplishments In a series of papers reprinted in his 1962 *Algebraic Logic*, Halmos devised polyadic algebras, an algebraic version of first-order logic differing from the better known cylindric algebras of Alfred Tarski and his students. An elementary version of polyadic algebra is described in monadic Boolean algebra. First-order logic (FOL) is a universal language in symbolic science, and is in use everyday by mathematicians, philosophers, linguists, computer scientists and practitioners of artificial intelligence. ...
The notion of cylindric algebra, invented by Alfred Tarski, arises naturally in the algebraization of first-order logic. ...
// Alfred Tarski (January 14, 1902, Warsaw, Russian-ruled Poland â€“ October 26, 1983, Berkeley, California) was a logician and mathematician who spent four decades as a professor of mathematics at the University of California, Berkeley. ...
In abstract algebra, a monadic Boolean algebra is an algebraic structure of the signature <A, ·, +, , 0, 1, ∃> where <A, ·, +, , 0, 1> is a Boolean algebra and ∃ is a unary operator, called the existential quantifier, satisfying the identities: ∃0 = 0 ∃x ≥ x ∃(x + y) = ∃...
In addition to his original contributions to mathematics, Halmos was an unusually clear and engaging expositor of university mathematics. This was so even though Halmos arrived in the USA at 13 years of age and never lost his Hungarian accent. He chaired the American Mathematical Society committee that wrote the AMS style guide for academic mathematics, published in 1973. In 1983, he received the AMS's Steele Prize for exposition. Some of his classics were: The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ...
*"How to read mathematics"* *"How to write mathematics"* *"How to speak mathematics"* In the *American Scientist* 56(4): 375-389, Halmos argued that mathematics is a creative art, and that mathematicians should be seen as artists, not number crunchers. He discussed the division of the field into mathology and mathophysics, further arguing that mathematicians and painters think and work in related ways. Halmos's 1985 “automathography” *I Want to Be a Mathematician* is an outstanding account of what it was like to be an academic mathematician in 20th century America. He called the book “automathography” rather than “autobiography”, because its focus is almost entirely on his life as a mathematician, not his personal life. In these memoirs, Halmos claims to have been the first to use the “tombstone” notation to signify the end of a proof, and this is generally agreed to be the case. The tombstone symbol ∎ (Unicode U+220E) is sometimes called a *halmos*. The tombstone, or halmos, symbol â€” (Unicode U+220E) â€” is used in mathematics to denote the end of a proof. ...
Look up QED in Wiktionary, the free dictionary. ...
Unicode is an industry standard designed to allow text and symbols from all of the writing systems of the world to be consistently represented and manipulated by computers. ...
## Books by Halmos In mathematics, a vector space (or linear space) is a collection of objects (called vectors) that, informally speaking, may be scaled and added. ...
In mathematics, a measure is a function that assigns a number, e. ...
The mathematical concept of a Hilbert space (named after the German mathematician David Hilbert) generalizes the notion of Euclidean space in a way that extends methods of vector algebra from the plane and three-dimensional space to spaces of functions. ...
In mathematics, a measure-preserving transformation T on a probability space is said to be ergodic if the only measurable sets invariant under T have measure 0 or 1. ...
Naive Set Theory is a mathematics textbook by Paul Halmos originally published in 1960. ...
In abstract algebra, a Boolean algebra is an algebraic structure (a collection of elements and operations on them obeying defining axioms) that captures essential properties of both set operations and logic operations. ...
The mathematical concept of a Hilbert space (named after the German mathematician David Hilbert) generalizes the notion of Euclidean space in a way that extends methods of vector algebra from the plane and three-dimensional space to spaces of functions. ...
In mathematics, an integral transform is any transform T of the following form: The input of this transform is a function f, and the output is another function Tf. ...
The Mathematical Association of America (MAA) is a professional society that focuses on undergraduate mathematics education. ...
The Mathematical Association of America (MAA) is a professional society that focuses on undergraduate mathematics education. ...
The Mathematical Association of America (MAA) is a professional society that focuses on undergraduate mathematics education. ...
## Books about Halmos - Ewing, J. H., and Gehring, F. W., eds., 1991.
*Paul Halmos: Celebrating 50 Years of Mathematics*. Springer-Verlag. Includes a bibliography of Halmos's writings through 1991. ## External links |