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For more information about Paul R. Halmos (1916-2006) and about the Paul R. Halmos Photograph Collection, please see the introduction to this article on page 1. A new page featuring six photographs will be posted at the start of each week during 2012.

Paul Halmos photographed William Arveson (1934-2011) on January 6, 1970, possibly in Bloomington, Indiana, at the Indiana University Mathematics Department offices, where Halmos was a professor at the time. Arveson had been a faculty member at the University of California, Berkeley, since 1968. He would spend the rest of his long career at Berkeley, where he worked on functional analysis and operator algebras. He retired in 2003 but continued to publish research papers until his death in 2011.

Michael Aschbacher is shown at Indiana University in Bloomington in February of 1980, the year he won the American Mathematical Society’s Cole Prize in Algebra for his work in finite group theory. Aschbacher, who was and is professor of mathematics at the California Institute of Technology (Caltech), won both the AMS Steele Prize for Mathematical Exposition and the Wolf Prize in 2012.

Halmos and Richard (Dick) Askey "met in the middle" in Evanston, Illinois, at least twice during the early 1980s. Halmos was a faculty member at Indiana University, Bloomington, from 1969 to 1985 and Askey has been a faculty member at the University of Wisconsin, Madison, since 1963 (professor emeritus since 2003). The photo of Askey at left was taken in May of 1980 in Evanston, perhaps during an AMS Sectional Meeting at Northwestern University.

Halmos photographed Askey again in November of 1983 in Evanston. The occasion was almost certainly an AMS Sectional Meeting, as Halmos noted that he himself spoke during an AMS Special Session on Operator Theory in Classical Function Spaces. Askey has worked on orthogonal polynomials and special functions throughout his long career at the University of Wisconsin, Madison. He also has shown a strong interest in mathematics education. Askey reports that he first met Halmos "in the summer of 1961, when I went to the Univ. of Chicago for two years and Paul was still there for the summer but on his way to the Univ. of Michigan."

The photo at left shows Lloyd Lininger (left) and Sir Michael Atiyah (right) in Ann Arbor, Michigan on April 3, 1968. Halmos was a faculty member at the University of Michigan from 1961 through 1968. Atiyah had won the Fields Medal in 1966 and published his book *K-theory*, which included discussion of the Atiyah-Singer Index Theorem, in 1967 (MacTutor History of Mathematics Archive). He was knighted in 1983. According to the Mathematics Genealogy Project, Lininger had earned his Ph.D. in 1964 at the University of Iowa with the dissertation “Some Results on Crumpled Cubes” under Steve Armentrout, whose photograph appears on page 1 of this collection. Ken Millett (University of California, Santa Barbara) suggests that the young man in the background facing the camera may be topologist William Thurston, who would have been in his first year of graduate school at the University of California, Berkeley. Bill Thurston would win the Fields Medal in 1982.

The photo above shows Atiyah (left) with Joseph Doob (right) in Honolulu, Hawaii on March 29, 1969. Halmos spent the 1968-1969 academic year at the University of Hawaii in Honolulu. In fact, he affixed an address label to the back of this photograph that gave his address as “3760 Diamond Head Circle, Honolulu, Hawaii” and this photo may well have been taken at his home. The woman at upper left in the photo is Joan Shields, wife of mathematician Allen Shields, who was a colleague of Halmos at the University of Michigan and whose visit to the University of Hawaii during the 1969 spring semester was described by Lawrence Wallen in "Walking and Talking with Halmos" (1991). Larry Wallen earned his Ph.D. from M.I.T. in 1967. He spent the 1967-68 academic year at the University of Michigan, where he worked with Halmos, and the remainder of his career at the University of Hawaii. Shields, who had earned his Ph.D. from M.I.T. in 1952 and joined the University of Michigan faculty in 1955, returned to Michigan after working with Halmos and Wallen in Hawaii in 1969. Halmos himself accepted a position at the University of Indiana in Bloomington, where he would remain until 1985. Probabilist Joseph Doob had been Halmos' Ph.D. advisor at University of Illinois, Urbana-Champaign. He also is pictured on page 1 and page 12 of this collection.

Page 1 also includes an introduction to this article and to the Paul R. Halmos Photograph Collection, as well as information about Paul R. Halmos. Watch for a new page featuring six new photographs each week during 2012.

**Sources:**

- American Mathematical Society (AMS) Prizes and Awards (Michael Aschbacher)
- 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 this list either appeared on the reverse side of the photograph or was obtained by AAM archivist Carol Mead from various sources during 2011-12.
- California Institute of Technology Department of Mathematics (Michael Aschbacher)
- Cornell University Department of Mathematics (William Thurston)
- MacTutor History of Mathematics Archive, St. Andrews University, Scotland (Richard Askey, Sir Michael Atiyah, William Thurston, Joseph Doob, Allen Shields, Wolf Prize)
- Mathematics Genealogy Project, North Dakota State University (all mathematicians)
- University of California, Berkeley, Department of Mathematics (William Arveson)
- University of Hawaii Department of Mathematics (Lawrence Wallen)
- University of Wisconsin, Madison, Department of Mathematics (Richard Askey)
- Wallen, Lawrence J., "Walking and Talking with Paul Halmos," in
*Paul Halmos: Celebrating 40 Years of Mathematics,*edited by John H. Ewing and F. W. Gehring, Springer-Verlag, New York, 1991, pp. 136-138. Accessed via Google Books Feb. 10, 2012.

Janet Beery (University of Redlands) and Carol Mead (Archives of American Mathematics, University of Texas, Austin), "Who's That Mathematician? Paul R. Halmos Collection - Page 2 ," *Loci* (January 2012), DOI:10.4169/loci003801