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The Paul R. Halmos Papers

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By Beth Nettels

*The following article, featured as part of the Archives of American Mathematics Spotlight, was published in the September 2010 issue of *MAA FOCUS*. The full issue is available here (pdf).*

Paul R. Halmos c. 1939. (Click to enlarge.)

*Source: The Paul R. Halmos Papers at the Archives of American Mathematics.*

The Archives of American Mathematics (AAM) has recently processed and made available the papers of prominent American mathematician Paul R. Halmos, known for his work in operator theory, ergodic theory, and functional analysis, as well as for mathematical exposition and teaching. The papers consist of Halmosâ??s notes, publications, manuscripts, lectures, correspondence, course materials, and personal records. They document his career as a mathematician, teacher, author, and editor. The portions of the collection concerning Halmosâ??s work as editor of the *American Mathematical Monthly* were donated by Halmos himself in 1989. Later gifts were made in 2007 and 2008 by his wife, Virginia.

Halmos was born in Budapest, Hungary, in 1916. In 1929 he immigrated to the United States and lived with his family in Chicago. As the result of confusion about the Hungarian school system, Halmos entered the American school system at a level somewhere between a junior and a senior in high school. In 1931, at the age of fifteen, he left Chicago to attend the University of Illinois, intending to study chemical engineering. He graduated three years later (1934) with a bachelorâ??s degree in mathematics and philosophy. Halmos then entered graduate school at the University of Illinois to pursue a Ph.D. in philosophy. After failing the oral comprehensive exam for the masterâ??s degree, he changed the focus of his graduate studies and registered as a student in the department of mathematics. Halmos earned his doctorate in mathematics under Joseph L. Doob in 1938.

Following the completion of his doctorate, Halmos served as John von Neumannâ??s assistant at the Institute of Advanced Study (1939â??1942), a post that led to the publication of his first book, *Finite Dimensional Vector Spaces*, in 1942. After leaving the IAS, Halmos taught soldiers in the Armyâ??s Specialized Training Program at Syracuse University before moving to the University of Chicago, where he stayed from 1946 to 1960, and the University of Michigan (1961 to 1967). After one year as the mathematics department chair at the University of Hawaii, he began a professorship at Indiana University, where he would stay until 1985, with the exception of two years spent at the University of California, Santa Barbara (1975â??77). In 1985, he moved to Santa Clara University where he taught until his retirement in 1996. In addition to these posts, Halmos held visiting appointments at the University of Montevideo, Uruguay (1951â??52), the University of Miami (1965â??66), and the University of Washington (1959), among others.

Halmos served as editor of several publications, including the Mathematical Association of Americaâ??s *American Mathematical Monthly *(1982â??86) and the *Proceedings of the American Mathematical Society *(1958â??63). For the Van Nostrand publishing company he edited the University Series in Undergraduate Mathematics ematics. Halmos also served as editor for the *Ergebnisse der Mathematik und ihrer Grenzgebiete *series and *Graduate Texts in Mathematics *series, both published by Springer-Verlag.

Halmos was and still is celebrated for his work in mathematical exposition. His love of and talent for language is evidenced in his expository works. Halmos himself claims in his autobiography *I Want to be a Mathematician *that he was, in â??decreasing order of quality, a writer, an editor, a teacher, and a research mathematician.â? He is credited with creating â??iff,â? for â??if and only if,â? and with introducing the use of the â??tombstoneâ? (also called a â??halmosâ?) symbol to signify the end of a proof. He received the Chauvenet Prize from the MAA in 1948 and the Steele Prize for Mathematical Exposition from the American Mathematical Society in 1983.

With cat Roger, 1970. (Click to enlarge.)

*Source:The Paul R. Halmos Papers at the Archives of American Mathematics.*

Other honors and awards bestowed upon Halmos include the Distinguished Teacher Award from the Mathematical Association of America in 1993. Halmos was a Fellow of the Royal Society of Edinburgh and a Guggenheim Fellow. In 2000, he was awarded the Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics by the Mathematical Association of America. In addition to his legacy of mathematical exposition, research, and teaching, Halmos and his wife donated $3 million for the renovation of the MAA Carriage House in Washington, D.C. Some of the highlights of the Halmos papers include his notes and mathematical diaries, manuscripts and drafts for his publications and lectures, and his correspondence, which illuminate Halmosâ??s long life as a member of the American and international mathematical community. The correspondence contains communications with publishers, former students, celebrated mathematicians, and even well-known poets.

The Archives of American Mathematics (AAM) is a unit of the Dolph Briscoe Center for American History at the University of Texas at Austin. Individuals interested in conducting research or donating materials or who have general questions about the AAM should contact Carol Mead, Archivist: carolmead@austin.utexas.edu, (512) 495-4539.

*Beth Nettels is an intern at the Archives for American Mathematics.*