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.
Index to the Collection
Halmos photographed Richard Varga and Leila Dragonette Bram on January 22, 1970, in San Antonio, Texas. Varga had joined the faculty at Kent State University as Professor of Mathematics in 1969; the Kent State shootings would occur in May of 1970. Halmos had joined the faculty at Indiana University in 1969 and Bram was Head of the Mathematics Program at the Office of Naval Research.
After earning his Ph.D. from Harvard University in 1954 with the dissertation “Properties of a special set of entire functions and their respective partial sums,” Richard Varga worked for six years for the Westinghouse Electric Corporation’s Bettis Atomic Power Laboratory in Pittsburgh, Pennsylvania, where his mathematical interests quickly shifted from complex analysis to numerical analysis. In 1960, he left Bettis to become Professor of Mathematics at his alma mater, Case Institute of Technology, in Cleveland, Ohio, which became part of Case Western Reserve University in 1967. Varga joined the faculty of Kent State University, also in Ohio, in 1969, becoming Director of the Institute for Numerical Mathematics in 1980, Research Director of this Institute in 1988, and Emeritus University Professor of Mathematical Sciences in 2006. He has advised 25 Ph.D. students during his career. In their MacTutor Archive biography of Varga, O’Connor and Robertson noted the high praise accorded each of Varga’s six books:
Matrix iterative analysis (1962, 2000)
Functional analysis and approximation theory in numerical analysis (1971)
Topics in polynomial and rational interpolation and approximation (1982)
Zeros of sections of power series (1983)
Scientific computation on mathematical problems and conjectures (1990)
Gerschgorin and his circles (2004)
Reviewers lauded these books not only for Varga’s new developments in numerical analysis and for his more rigorous treatment of numerical analysis topics, but also for the connections he made between numerical analysis and pure mathematics, with each helping to solve problems in the other. (Source: MacTutor Archive, Kent State University Mathematics)
Leila Dragonette (d. 1979) earned her Ph.D. from the University of Pennsylvania in 1951 with the dissertation, “Asymptotic formula for the mock theta series of Ramanujan,” written under advisor Hans Rademacher. From 1951 to her death in 1979 at age 52, she was Mathematician, then Head of the Mathematics Bureau, and then Head of the Mathematics Program at the Office of Naval Research in Washington, D.C. (Sources: Mathematics Genealogy Project; “News and Notices,” American Mathematical Monthly 86:10 (Dec. 1979), p. 880)
C. Terence Wall was photographed by Halmos in April of 1986 at the British Mathematical Colloquium in Hull, England. Terry Wall earned his Ph.D. from Cambridge University in 1960 with the dissertation “Algebraic Aspects of Cobordism,” written under advisors Chris Zeeman and Frank Adams. (A photograph of Adams appears on page 1 of this collection, where you can read more about him.) Wall was based at Cambridge until 1964 and then at Oxford during 1964-65. In 1965, he accepted the Chair of Pure Mathematics at the University of Liverpool, England, where he has spent the rest of his career, becoming Emeritus Professor and Senior Fellow in 1999. As described by O’Connor and Robertson of the MacTutor Archive, Wall’s research is primarily in
… geometric topology and related algebra. In particular he has made substantial contributions to the study of singularities, especially isolated singularities, of differentiable maps and algebraic varieties. He has written a number of highly influential books including Surgery on compact manifolds (1970), … , The geometry of topological stability [with A. A. du Plessis, 1995], … [and the graduate text] Singular points of plane curves in 2004.
He also wrote A geometric introduction to topology (1972), intended as an introduction to algebraic topology requiring no prior knowledge of general topology. (Source: MacTutor Archive)
Halmos photographed topologist Andrew H. Wallace (1926-2008) in February of 1962 in Bloomington, Indiana. Born and raised in Edinburgh, Scotland, Andrew Wallace earned his Ph.D. from St. Andrews University in 1949. At the time this photograph was taken, he was a mathematics professor at Indiana University (1959-1965); he joined the mathematics faculty at the University of Pennsylvania in 1965, becoming Professor Emeritus of Mathematics in 1986. Halmos would join the faculty at Indiana University in 1969; at the time of this photo, he was at the University of Michigan. (Sources: Mathematics Genealogy Project, University of Pennsylvania Mathematics)
Lawrence J. Wallen was photographed by Halmos on September 11, 1967, at the University of Michigan in Ann Arbor, where the two were colleagues. Halmos and Wallen spent the 1968-69 academic year at the University of Hawaii in Honolulu, where the two of them comprised the “Pacific Basin Two Man Seminar (or T.M.S.)” during the 1968 fall semester, Wallen wrote in “Walking and Talking with Halmos” (p. 137). During the 1969 spring semester, the Two Man Seminar expanded to three mathematicians, when Allen Shields (whose photograph appears on page 48 of this collection, where you can read more about him), another colleague from the University of Michigan, joined them.
Larry Wallen earned his Ph.D. from M.I.T. in 1967 under advisor Isadore Singer (whose photograph appears on page 48 of this collection, where you can read more about him) and Kenneth Hoffman. 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, where he is now Professor Emeritus. Shields returned to Michigan after working with Halmos and Wallen in Hawaii in 1969 and spent the rest of his career there. Halmos himself, after serving as chair of the mathematics department at Hawaii during 1968-69, accepted a position at the University of Indiana in Bloomington, where he would remain until 1985. (Sources: Mathematics Genealogy Project; UM Faculty History Project Memorial: Shields; 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)
Halmos photographed Raymond O. Wells in April of 1980 in Bloomington, Indiana. Wells earned his Ph.D. from New York University in 1965 with the dissertation “On the local holomorphic hull of a real submanifold in several complex variables,” written under advisor Lipman Bers (pictured on page 5 of this collection, where you can read more about him, and also on page 32). Wells joined the mathematics faculty at Rice University in Houston, Texas, in 1965 and spent most of his career there, becoming Professor Emeritus of Mathematics in 2000. During 1998-2001, Wells helped found International University Bremen, Germany, where he was both Vice President and Professor of Mathematics from 2001 to 2005 and Distinguished Professor of Mathematics from 2005 onward. International University Bremen became Jacobs University Bremen in 2007. He now spends most of the year in Boulder, Colorado, where he is Adjunct Professor of Mathematics at the University of Colorado, in addition to his positions at Rice and Jacobs. Besides his many publications in complex analysis, Wells may be best known for his and his Rice University colleague Howard L. Resnikoff’s book, Mathematics in Civilization (1973; 1985 edition available from Dover Publications). (Sources: Mathematics Genealogy Project, Rice University Mathematics, Jacobs University Mathematics)
Halmos photographed Fritz Joachim Weyl (1915-1977) in November of 1962. Weyl was born in Zürich, Switzerland, where his father, Hermann Weyl, held the chair of mathematics at Eidgenössische Technische Hochschule (ETH) from 1913 to 1930. Fritz Weyl earned his Ph.D. from Princeton University in 1939 with the dissertation “Analytic Curves” written under advisor Salomon Bochner. He wrote on analytic curves and meromorphic functions, often with his father, from 1938 to 1943, but eventually gravitated toward applied mathematics. He was on the mathematics faculties of the University of Illinois, University of Maryland, and Indiana University; served as a consultant to government agencies; and, at his death, was Dean of Science and Mathematics at Hunter College in New York City. The SIAM Review’s 1978 memorial of Fritz Wyel summed up his mathematical outlook in words reminiscent of his father’s famous quotation, “My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful”:
In memoriam: Fritz Joachim Weyl,
in warm recognition of his enduring vision for both the beauties and the practicalities of applied mathematics,
in everlasting gratitude for his untiring service to the Society for Industrial and Applied Mathematics and to the newly-formed SIAM Institute for Mathematics and Society,
and above all in deep appreciation for his personal enthusiasm, sympathy, kindness, understanding, and friendship,
the members and officers of SIAM and SIMS offer their heartfelt tribute.
(Sources: MacTutor Archive: Hermann Weyl; Mathematics Genealogy Project; MathSciNet; "F. Joachim Weyl," American Men and Women of Science (13th ed., vol. 6), 1976, p. 4806; Society of Industrial and Applied Mathematics: “In Memoriam–Fritz Joachim Weyl,” SIAM Review 20:1 (1978), p. vi)
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.
Index to the Collection