Paul Halmos facts for kids
Quick facts for kids
Paul Halmos
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| Born |
Paul Richard Halmos
3 March 1916 |
| Died | 2 October 2006 (aged 90) Los Gatos, California, U.S.
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| 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; March 3, 1916 – October 2, 2006) was a famous mathematician. He was born in Hungary and later became an American citizen. He made important discoveries in many areas of mathematics. These included mathematical logic, probability theory, and functional analysis. People also knew him as a great teacher and explainer of math. He was even called one of "The Martians," a group of brilliant Hungarian scientists who moved to the U.S.
Contents
Early Life and Education
Paul Halmos was born in Hungary to a Jewish family. He came to the United States when he was 13 years old. He went to the University of Illinois. He studied mathematics and philosophy there. He finished his degree in just three years, at age 19!
He first started a Ph.D. in philosophy. But after some exams, he switched to mathematics. He earned his math Ph.D. in 1938. His main project was about the math behind gambling systems. His professor was Joseph L. Doob.
Career in Mathematics
Shortly after graduating, Halmos went to the Institute for Advanced Study. Six months later, he started working with the famous mathematician John von Neumann. This was a very important time for him. While working there, he wrote his first book. It was called Finite Dimensional Vector Spaces. This book quickly showed he was great at explaining math clearly.
Halmos taught at many universities. These included Syracuse University, the University of Chicago, and the University of Michigan. He also taught at Indiana University and Santa Clara University. He retired from Indiana University in 1985. He then worked at Santa Clara University until he passed away.
Major Accomplishments
Paul Halmos made many important contributions to mathematics. He also became known for his clear way of explaining complex ideas.
Explaining Math Clearly
Halmos was very good at making university-level math easy to understand. He won the Lester R. Ford Award twice for his writing. He also helped create the style guide for academic mathematics. In 1983, he received the Leroy P. Steele Prize for his excellent explanations.
Math as Art
In 1968, Halmos wrote that mathematics is a creative art. He believed mathematicians should be seen as artists. He said they are not just "number crunchers." He thought mathematicians and painters think and work in similar ways.
His "Automathography"
In 1985, Halmos wrote a book called I Want to Be a Mathematician. He called it an "automathography." This meant it focused on his life as a mathematician. It did not focus on his personal life. The book shares his thoughts on doing mathematics.
He famously wrote:
Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
This quote encourages students to actively engage with math.
New Math Symbols
Halmos is known for inventing two common math symbols. He created the word "iff" which means "if and only if." He also was the first to use the "tombstone" symbol (∎). This symbol shows the end of a proof. Sometimes, this symbol is even called a halmos.
Euler Book Prize
In 2005, Halmos and his wife, Virginia, started the Euler Book Prize. This award is given every year. It honors a book that helps the public understand mathematics better. The first prize was given in 2007. This was the 300th anniversary of Leonhard Euler's birth.
Documentary Film
In 2009, a documentary film was made about Paul Halmos. It was also called I Want to Be a Mathematician. The film was created by George Csicsery.
Books by Halmos
Paul Halmos wrote many important math books. Here are some of them:
- 1942. Finite-Dimensional Vector Spaces.
- 1950. Measure Theory.
- 1951. Introduction to Hilbert Space and the Theory of Spectral Multiplicity.
- 1956. Lectures on Ergodic Theory.
- 1960. Naive Set Theory.
- 1962. Algebraic Logic.
- 1963. Lectures on Boolean Algebras.
- 1967. A Hilbert Space Problem Book.
- 1973. (with Norman E. Steenrod, Menahem M. Schiffer, and Jean A. Dieudonne). How to Write Mathematics. ISBN: 978-0-8218-0055-3
- 1978. (with V. S. Sunder). Bounded Integral Operators on L² Spaces.
- 1985. I Want to Be a Mathematician.
- 1987. I Have a Photographic Memory.
- 1991. Problems for Mathematicians, Young and Old.
- 1996. Linear Algebra Problem Book.
- 1998. (with Steven Givant). Logic as Algebra.
- 2009. (posthumous, with Steven Givant), Introduction to Boolean Algebras.
See also
In Spanish: Paul Halmos para niños
- Crinkled arc
- Commutator subspace
- Invariant subspace problem
- Naive set theory
- Criticism of non-standard analysis
- The Martians (scientists)
