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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.

Halmos photographed Joseph Keller in December of 1978 at Indiana University in Bloomington, where Halmos was a professor at the time. Keller is an applied mathematician best known for developing the geometrical theory of diffraction to describe the propagation of waves. After teaching military engineering and working for the Division of War Research on submarine detection using sonar during World War II, he returned to his alma mater, New York University, in 1945 and earned his Ph.D. in 1948 with the dissertation “Reflection and Transmission of Electromagnetic Waves by Thin Curved Shells.” From 1948 to 1979, he was a mathematics professor at NYU’s Institute of Mathematical Sciences (which became the Courant Institute in 1964), serving as Director of the Division of Wave Propagation and Applied Mathematics there from 1967 to 1979. In 1978 he became Lewis M. Terman Professor of Mathematics and Mechanical Engineering at Stanford University, where he is now Professor Emeritus. (Sources: MacTutor Archive, Stanford Mathematics)

John L. Kelley (1916-1999) was photographed by Halmos in July of 1962. Kelley earned his Ph.D. in 1940 from the University of Virginia with the dissertation “A Study of Hyperspaces.” After holding positions at the University of Notre Dame (1940-42), the Aberdeen Proving Grounds (1942-45), the Institute for Advanced Study (1945-46), and the University of Chicago (1946-47), Kelley spent the rest of his career (from 1947 onward) at the University of California, Berkeley, becoming Professor Emeritus in 1985. He and Halmos may have first met at IAS during the nearly five months Halmos spent there during the spring and summer of 1946 or they may have met in the fall of 1946 at the University of Chicago, where both were new faculty members. Kelley was a topologist and functional analyst best known as the author of the classic text *General Topology* (Springer Graduate Texts in Mathematics, 1952, 1968, 1976), and also was a leader in mathematics education initiatives. (Sources: Mathematics Genealogy Project; UC Berkeley Public Information Office; IAS; Paul R. Halmos, *I Want to Be a Mathematician* (Springer, 1985), pp. 127-8, 131, 140)

Halmos photographed his Ph.D. student Robert L. Kelley (d. 2006) in July of 1969. Kelley earned his Ph.D. in 1966 from the University of Michigan with the dissertation “Weighted Shifts on Hilbert Spaces,” with Halmos as his first advisor and Allen Shields as his second advisor. He spent most of his career in the mathematics department at the University of Miami in Coral Gables, Florida, where he had earned a masters degree in 1960. (Halmos spent the academic year 1965-66 at the University of Miami and one wonders if Kelley traveled there with him.) Kelley was known as an excellent teacher with interests including botany (he led tours at the university’s arboretum), music, and Maya archaeology. (Sources: Mathematics Genealogy Project; “A Man without Equal,” *University of Miami College of Arts and Sciences Magazine*)

Applied probabilist and data analyst David Kendall (1918-2007) was photographed by Halmos in 1958 in Cambridge, England. Kendall studied at Oxford University at least until 1943, served in the Ministry of Supply during World War II (1940-45), and lectured at Oxford from 1946 to 1962. In 1962, he became Professor of Mathematical Statistics at Cambridge, where he spent the rest of his career. According to J. J. O’Connor and E. F. Robertson of the MacTutor Archive, he was “a leading world authority on applied probability and data analysis” and “[a]n exceptional lecturer.” Kendall was president of the London Mathematical Society from 1972 to 1974. (Sources: MacTutor Archive, Mathematics Genealogy Project)

Halmos photographed Paul Erdös (1913-1996), left, and David Kendall (the subject of the preceding photograph) in Cambridge, England on June 4, 1968. Erdös (also pictured on page 3 and page 14) was well known for traveling all over the world posing problems in number theory, combinatorics, and graph theory and solving them with many and varied collaborators. Those who published papers with him (509 people at last count) have Erdös number 1. (Sources: MacTutor Archive, Wolfram MathWorld)

Halmos photographed Jack Kiefer (1924-1981) on Feb. 7, 1978, in Santa Barbara, California. After studying engineering and economics at the Massachusetts Institute of Technology, Kiefer earned his Ph.D. in mathematical statistics in 1952 from Columbia University with the dissertation “Contributions to the Theory of Games and Statistical Decision Functions” and went on to specialize in optimal design of experiments. He was on the mathematics faculty at Cornell University from 1951 to 1979, holding the Horace White Professorship from 1973 onward, and on the faculty of the University of California, Berkeley, from 1979 until his death. (Source: MacTutor Archive)

For an introduction to this article and to the Paul R. Halmos Photograph Collection, please see page 1. Watch for a new page featuring six new photographs each week during 2012.

**Regarding sources for this page:** Information for which a source is not given either appeared on the reverse side of the photograph or was obtained from various sources during 2011-12 by archivist Carol Mead of the Archives of American Mathematics, Dolph Briscoe Center for American History, University of Texas, Austin.

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 27," *Loci* (January 2012), DOI:10.4169/loci003801