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Well-known and warmly remembered mathematical researcher, educator, and expositor and “great friend of the MAA” Paul R. Halmos (1916-2006) enjoyed snapping photographs of mathematicians he met around the world and at his various home campuses in the U.S. In 2011, 343 of Halmos’ photos were digitized by the Archives of American Mathematics, Dolph Briscoe Center for American History, University of Texas, Austin, under the direction of Archivist Carol Mead with a grant from the History of Mathematics Special Interest Group of the Mathematical Association of America (HOM SIGMAA).

We present here a weekly-increasing subset of the 343 photos by inveterate photographer Halmos, and we invite you to share what you know about them with authors Janet Beery and/or Carol Mead. Please provide or correct names, dates, locations, and events (*e.g.* conference, invited speaker, social visit, etc.). Please also share any other pertinent information, warm memories, etc. connected to the photograph. And be sure to look for new photos at this site each week throughout the year!

The photograph of Halmos above is from the *Convergence* Portrait Gallery. Permission to reproduce the remaining photos must be obtained from the Dolph Briscoe Center for American History, University of Texas, Austin.

For more information about the life of Paul Halmos, please see the following biographies:

Mathematical Association of America (MAA) Biography of Paul Halmos

MacTutor History of Mathematics Archive Biography of Paul Halmos

The mathematical people in the photographs in the collection will be identified in captions appearing beneath the photos in order to give you a chance to try to identify them first.

We begin with a photograph of Gerald (Jerry) Alexanderson, Halmos' colleague at Santa Clara University in California. Halmos joined the mathematics faculty at Santa Clara in 1985, at the invitation of Alexanderson, who had taught there since 1958. Alexanderson was largely responsible for the donation of Halmos' papers and photographs to the Archives of American Mathematics and, in particular, for the monumental task of organizing Halmos' photograph collection for the Archives.

Alexanderson (left) is pictured with Vladimir Drobot at Santa Clara University, where both were faculty members, in March of 1984, the year before Halmos joined them as a faculty member there. At the time this photo was taken, Alexanderson was First Vice President of the MAA. He would become MAA President in 1997. Vlad Drobot taught at SCU for 17 years and then, in 1990, moved across town to San Jose State University, where he taught for 16 years.

J. Frank Adams (1930-1989), then of Trinity College, Cambridge, was photographed at the annual British Mathematical Colloquium at the University of Hull, England, in April, 1986. Sir Michael Atiyah (pictured on page 2 and page 10) describes Adams as "the leader in the field [of homotopy theory] in its maturity." Halmos was a plenary speaker at the 1986 Colloquium, presenting "Fifty Years of Linear Algebra: A Personal Reminiscence" (see British Mathematical Colloquium, MacTutor History of Mathematics Archive).

Frederick (Fred) Almgren (1933-1997), is pictured in December, 1983, possibly at Princeton University, where the geometric analyst spent most of his mathematical career, or possibly at Indiana University in Bloomington, where Halmos was a professor at the time, or possibly somewhere else ....

Warren Ambrose (1914-1995) was photographed by Halmos in 1958 (black and white photo printed July 15, 1958).

Warren Ambrose also appears in the group photo above (center front) taken in March, 1990. Ambrose, who spent most of his career at M.I.T., was a mathematical "brother" of Halmos, sharing Ph.D. advisor Joseph Doob (1910-2004) (at upper right in the group photo above) at the University of Illinois, Urbana-Champaign, during the late 1930s. Halmos completed his degree in 1938 and Ambrose in 1939. David Blackwell (1919-2010), at lower right in the group photo, also completed his Ph.D. with Doob at Illinois at about the same time, in 1941. The group gathered at the home of Joseph and Elsie Doob at 208 W. High Street in Urbana, Illinois, in March of 1990 in the photo above consisted of

- back row, left to right: Colin Blyth, Elsie Doob, Joseph Doob,
- front row, left to right: Donald Burkholder, and mathematical "brothers" Warren Ambrose, Paul Halmos, and David Blackwell.

David Blackwell became a statistician and spent most of his career at Howard University and the University of California, Berkeley. Joseph Doob was a probabilist and measure theorist who had a long career at the University of Illinois, where Halmos, Ambrose, and Blackwell were his first three Ph.D. students. Donald Burkholder (1927-2013) joined the University of Illinois Mathematics Department in 1955 and the UIUC Center for Advanced Study in 1978. He started out at Illinois as a statistician but soon became a probabilist under the influence of Doob. Statistician Colin Blyth, who had been professor of mathematics at the University of Illinois from 1950 to 1974, probably would have been visiting Urbana from Kingston, Ontario, Canada, where he had retired as a professor at Queen's University in 1987. We thank Frank Miles of California State University, Dominguez Hills, who grew up in Urbana and whose brother was in the same high school class as the Doobs' son Steve, for identifying the Doobs' home in the photo above. We are grateful to Joseph Rotman of UIUC as well for the information he provided about the "House of Probability."

Steve Armentrout attended a meeting of the American Mathematical Society's Executive Committee and Board of Trustees in Ann Arbor, Michigan, in May of 1982 (Archives of American Mathematics). Armentrout had been a Ph.D. student of R. L. Moore at the University of Texas and had several Ph.D. students of his own at the University of Iowa during the 1960s (Mathematics Genealogy Project).

**Sources:**

- Archives of American Mathematics, Dolph Briscoe Center for American History, University of Texas, Austin. Information for which a source is not cited or given in the list below either appeared on the reverse side of the photograph or was obtained by AAM archivist Carol Mead from various sources during 2011-12.
- Vladimir Drobot Home Page
- ElectricScotland.com (Colin R. Blyth autobiography)
- MacTutor History of Mathematics Archive, St. Andrews University, Scotland (Frank Adams, Frederick Almgren, David Blackwell, Joseph Doob, Paul Halmos, British Mathematical Colloquium)
- Massachusetts Institute of Technology: MIT News (Warren Ambrose); see also "A Tribute to Warren Ambrose," by I. M. Singer and H. Wu,
*AMS Notices*(April 1996); pp. 425-427 - Mathematical Association of America (Paul Halmos: A Life in Mathematics and MAA Presidents: Gerald Alexanderson)
- Mathematics Genealogy Project, North Dakota State University (all mathematicians)
- Queen's University (Kingston, Ontario) Department of Mathematics (Colin Blyth)
- San Jose State University (California) Department of Mathematics (Vladimir Drobot)
- Santa Clara University (California) Department of Mathematics (Gerald Alexanderson)
- University of Illinois, In Memoriam: Donald Burkholder
- University of Illinois, In Memoriam: Joseph Leo Doob

Janet Beery (University of Redlands) and Carol Mead (Archives of American Mathematics, University of Texas, Austin), "Who's That Mathematician? Images from the Paul R. Halmos Photograph Collection," *Convergence* (January 2012), DOI:10.4169/loci003801