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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 and early 2013.

Halmos photographed Nora and Frank Smithies in May of 1973 in Cambridge, England. Another photograph of Nora Smithies appears on page 24 of this collection and another of Frank Smithies on page 48, where you can read more about him.

Russ and Linda Smucker were photographed by Halmos in April of 1980 during Honors Weeks at Kent State University in Kent, Ohio. Russ Smucker was a Ph.D. student of Halmos, earning his degree in 1973 from Indiana University with the dissertation “Quasidiagonal and Quasitriangular Operators.” He most likely was a faculty member at Kent State at the time of this photo; Halmos was on the faculty at Indiana University from 1969 to 1985. In his *I Want to Be a Mathematician,* Halmos described Smucker as a member of his “gang of five” Ph.D. students at Indiana who took his real variable and/or functional analysis courses during 1969-1971, worked in operator theory, participated in a “private seminar (which met sometimes in my living room with beer and pretzels),” spent a semester at the University of Edinburgh with Halmos, and were awarded their Ph.D.s from 1973 to 1975. Smucker moved to Muskingum College in New Concord, Ohio, in 1982, and was a faculty member there until his retirement in 2007. (Sources: Mathematics Genealogy Project; Paul R. Halmos, *I Want to Be a Mathematician: An Automathography,* Springer, 1985, pp. 366-367; Muskingum University Mathematics)

Halmos photographed Raymond Smullyan in 1968. From an early age, Smullyan excelled at music and mathematics, and, as a young man, he became expert as well at composing puzzles, especially chess puzzles, and performing a professional magic show. After studying mathematics and logic mainly on his own but also at the University of Wisconsin and the University of Chicago, Smullyan finally earned his Ph.D. in logic in 1959 from Princeton University with the dissertation “Theory of Formal Systems,” written under advisor Alonzo Church. He joined the faculty of Yeshiva University in New York City in 1961 and moved to City University of New York in 1968, becoming Professor Emeritus in 1982. In their MacTutor Archive article on Smullyan, O’Connor and Robertson praised his many and varied books, writing

Smullyan’s publications have been quite remarkable with the two outstanding books on retrograde analysis chess problems .., a whole series of marvelous popular puzzle books …, and some books on the foundations of mathematics and mathematical logic which are in many ways in a class of their own.

(Sources: MacTutor Archive, Mathematics Genealogy Project)

Ernst Snapper (1913-2011), left, and John B. Conway were photographed by Halmos in August of 1975 at the Joint Summer Mathematics Meetings in Kalamazoo, Michigan. At the time, Snapper was on the faculty at Dartmouth College in Hanover, New Hampshire, and Halmos and Conway were faculty members at Indiana University in Bloomington. Just over Snapper's left shoulder in the photo is Billy E. Rhoades, who was a colleague of Conway and Halmos at Indiana University at the time and now is Professor Emeritus of Mathematics there. Rhoades earned his Ph.D. in 1958 from Lehigh University with the dissertation “Hausdorff Summability Methods.” (Sources: Mathematics Genealogy Project, Indiana University Mathematics)

Born in Groningen, Holland, Ernst Snapper studied at the University of Amsterdam before earning his Ph.D. in 1941 from Princeton University with the dissertation “Structure of Linear Sets,” written under Joseph Wedderburn. He remained at Princeton until 1945, when he joined the mathematics faculty at the University of Southern California in Los Angeles. In 1955, he became Buckingham Professor of Mathematics at Miami University of Ohio and, in 1958, he moved to Indiana University. In 1963, he joined the mathematics faculty at Dartmouth College, becoming Cheney Professor of Mathematics in 1971 and Emeritus Professor in 1979. In his memorial to Snapper in the January 2013 issue of the *AMS Notices,* his former Ph.D. student Joseph Buckley (Indiana, 1964) noted the wide range of Snapper’s scholarly work:

Snapper’s research made significant contributions in commutative algebra, algebraic geometry, cohomology of groups, character theory, and combinatorics.

Buckley noted as well Snapper’s accomplishments as a mathematics educator, from the “lucid lectures” that made him “much in demand by the MAA, and … in numerous summer institutes for both high school and college mathematics teachers,” to his 1971 textbook *Metric Affine Geometry,* coauthored with his former Ph.D. student Robert Troyer (Indiana, 1960), that based instruction in geometry "on a foundation of linear algebra.” (Sources: Mathematics Genealogy Project; AMS Notices, Jan. 2013; Princeton University Memorial, Princeton in the 1930s interview, Open Museum: Faces of Norwich VT)

John B. Conway earned his Ph.D. in 1965 from Louisiana State University with the dissertation “The Strict Topology and Compactness in the Space of Measures.” An operator theorist like Halmos, he was a faculty member at Indiana University from 1965 to 1990, department chair at the University of Tennessee at Knoxville from 1990 to 2003, an NSF program officer from 2003 to 2006, and department chair at George Washington University in Washington, D.C., from 2006 to 2011. He has served the American Mathematical Society in a number of ways, including as editor of its *Proceedings* (1984-1988) and as a member of its Executive Committee (1997-2001) and its Board of Trustees (2001-2011). He is Professor Emeritus of Mathematics at both University of Tennessee and George Washington University. (Sources: Mathematics Genealogy Project, UT Knoxville Mathematics, GWU Mathematics)

Halmos photographed Ian Sneddon (1919-2000) on July 6, 1970, in Bloomington, Indiana. Halmos was a professor at Indiana University at the time and Sneddon most likely was a visiting lecturer there. Born in Glasgow, Scotland, Sneddon began his university studies at the University of Glasgow in 1936 at the age of 16. He continued his studies at Cambridge from 1940 to 1942, when he was assigned war work on elasticity at the Cavendish Laboratory, Ministry of Supply. After working briefly as a researcher in nuclear physics at Bristol University, he joined the physics faculty at the University of Glasgow in 1946 and was awarded the D.Sc. for his research there. After one more sojourn away from Glasgow – he served as chair of mathematics at the then-new University College of North Staffordshire (later Keele University) from about 1950 to 1956 – Sneddon returned to the University of Glasgow as Simson Chair of Mathematics in 1956. In their MacTutor Archive article on Sneddon, O’Connor and Robertson praised most highly Sneddon’s series of at least seven lucid and forward-looking texts on applied mathematics published from 1948 to 1969, two of which were reprinted by Dover Publications in 2006 and 2010. (Sources: MacTutor Archive, Dover Publications)

Halmos photographed Robert Solovay on October 9, 1964, at Princeton University. Solovay earned his Ph.D. in 1964 from the University of Chicago with the dissertation “A Functorial Form of the Differentiable Riemann-Roch Theorem,” written under advisor Saunders Mac Lane. He taught at Princeton from 1962 to 1964 and was a member of the Institute for Advanced Study in Princeton during 1964-65 (and again during 1971-72). In 1965, Solovay joined the faculty at the University of California, Berkeley, where he is now Professor Emeritus. As a set theorist, he has written most recently on computer verification of formal proofs, but, as he wrote recently, "I follow my curiosity wherever it leads me. Sometimes it leads me back to set theory; sometimes far afield." (Sources: UC Berkeley Mathematics, Mathematics Genealogy Project, IAS)

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 49," *Loci* (June 2013), DOI:10.4169/loci003801