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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 Fritz Joachim Weyl (1915-1977), left, and Ronald Rivlin (1915-2005) in April of 1970 at Lehigh University in Bethlehem, Pennsylvania. Weyl appears also in a photograph on page 54 of this collection, where you can read more about him. Another photograph of Ronald Rivlin appears on page 43 of this collection, where you can read more about him.

Physicists John Wheeler (1911-2008), left, and Arthur Komar (1931-2011) were photographed by Halmos in May of 1979 at a conference on Gravity and Quantum Theory in New Orleans, Louisiana.

John Wheeler was one of the leading theoretical physicists of the 20^{th} century and coined many now familiar terms in physics, three of which he included in the title of his autobiography *Geons, Black Holes and Quantum Foam: A Life in Physics* (1998). He earned his Ph.D. at Johns Hopkins University in 1933 with the dissertation “Theory of the dispersion and absorption of helium” and, in 1938, joined the faculty at Princeton University. At Princeton, he was doctoral advisor to Richard Feynman (1918-1988), who earned his Ph.D. in 1942, and to several other well-known physicists. According to Princeton University’s obituary of Wheeler (2008):

[H]e was known for his drive to address big, overarching questions in physics, subjects which he liked to say merged with philosophical questions about the origin of matter, information and the universe. He was a young contemporary of Albert Einstein and Niels Bohr, was a driving force in the development of both the atomic and hydrogen bombs and, in later years, became the father of modern general relativity.

In fact, he and Bohr “co-wrote the original paper on the mechanism of nuclear fission that helped lead to the development of the atomic bomb.” Wheeler also was praised as an outstanding teacher and mentor; his Princeton Ph.D. student Kip Thorne reported that “he was the most influential mentor of young scientists whom I have known” (quoted in Princeton University obituary). After he retired from Princeton in 1976, Wheeler directed the Center for Theoretical Physics at the University of Texas at Austin until 1986 and remained active in physics at least until 2006, based primarily at Princeton. (Sources: Princeton University obituary, Mathematics Genealogy Project)

Arthur Komar was both an undergraduate and doctoral student of John Wheeler at Princeton University, earning his Ph.D. in 1956 with the dissertation, “Some Consequences of Mach’s Principle for General Relativity.” After a year as a fellow at the Niels Bohr Institute in Copenhagen, Denmark, he joined the faculty at Syracuse University in 1957 and then moved to Yeshiva University in New York City in 1963, retiring in 1997. He also taught at New York University from 1984 to 1997. His main research interest throughout his career was gravitational physics and, in particular, developing a quantum theory for gravity. He also was known for his work on conserved quantities, time and space, and thermodynamics, and for his namesake covariant Komar energy-momentum tensor. (Sources: Physics Today obituary, Princeton Alumni obituary)

Halmos photographed W. Forrest “Woody” Stinespring (d. 2012), left, and J. H. C. (Henry) Whitehead (1904-1960), in 1960.

W. Forrest Stinespring earned his Ph.D. in 1957 from the University of Chicago with the dissertation “Integration theory for gages and duality theorems,” written under advisor Irving Segal. (For a photograph of Segal, see page 48 of this collection, where you can read more about him.) After visiting the Institute for Advanced Study in Princeton during 1957-1959 and teaching at the University of Illinois at Urbana-Champaign, Massachusetts Institute of Technology, and University of Chicago, he joined the faculty at the University of Illinois at Chicago in 1966, becoming Professor Emeritus in 1999. An operator theorist, Stinespring was best known for his Dilation Theorem or Factorization Theorem. In both 1947 and 1949, he was an individual Putnam Fellow and a member of the winning Harvard team. (Sources: Mathematics Genealogy Project, University of Illinois at Chicago obituary, IAS, MAA Putnam Competition)

Born in India and raised in England, Henry Whitehead earned his Ph.D. in 1932 from Princeton University with the dissertation “The representation of projective spaces,” written under advisor Oswald Veblen. In the same year, Whitehead and Veblen published *The Foundations of Differential Geometry,* the book containing "the first proper definition of a differential manifold" (O'Connor and Robertson, MacTutor Archive). Whitehead continued to work on differential geometry and on topology, especially homotopy equivalence, throughout his career at Oxford University, where he established a school of topology and was appointed Waynflete Chair of Pure Mathematics in 1947. He was finishing up a 1959-1960 visit to the Institute for Advanced Study in Princeton, when he died of a heart attack in May of 1960. (Sources: MacTutor Archive, IAS)

George W. Whitehead, Jr. (1918-2004), was photographed by Halmos in August of 1963 in Ann Arbor, Michigan. George Whitehead earned his Ph.D. in 1941 from the University of Chicago with the dissertation “Homotopy properties of the real orthogonal groups,” written under advisor Norman Steenrod. (For a photograph of and information about Steenrod, see page 50 of this collection.) He remained a homotopy theorist throughout his career and helped create modern algebraic topology, especially with his paper, “Generalized Homology Theories” (1962), which “established the language and basic structure underlying a great part of contemporary algebraic topology” (MIT obituary). After earning his Ph.D. in 1941, Whitehead taught at Purdue, Princeton, and Brown universities from 1941 to 1949. He joined the faculty of the Massachusetts Institute of Technology (MIT) in 1949, becoming Professor Emeritus in 1985. (Sources: Mathematics Genealogy Project, MIT obituary)

Halmos photographed Samuel Eilenberg (1913-1998), left, and Gordon T. Whyburn (1904-1969) in 1958 at the International Congress of Mathematicians in Edinburgh, Scotland. Eilenberg is pictured on page 13 of this collection, where you can read more about him.

Whyburn earned his Ph.D. in general topology in 1927 from the University of Texas at Austin with the dissertation, “Concerning continua in the plane,” written under R. L. Moore (pictured on page 35 of this collection, where you can read more about him). He taught at UT Austin during 1927-29, spent 1929-30 in Vienna (studying with Hans Hahn) and Warsaw (meeting Kazimierz Kuratowski and Waclaw Sierpinski) on a Guggenheim Fellowship, and taught at Johns Hopkins University in Baltimore, Maryland, during 1930-33. He moved to the University of Virginia in Charlottesville, Virginia, in 1934 to become chair of the mathematics department there and remained for the rest of his career, retiring in 1966. Whyburn advised at least 31 Ph.D. students during his career. He was president of the American Mathematical Society during 1953-54. (Sources: MacTutor Archive, Mathematics Genealogy Project, AMS Presidents)

Halmos photographed Harold Widom on Oct. 28, 1969, at Indiana University in Bloomington. Widom earned his Ph.D. in 1955 from the University of Chicago under advisor Irving Kaplansky (pictured on page 26 of this collection). His early research was on integral equations and operator theory, but he is best known today for his research on random matrix theory. He and his collaborator Craig Tracy of the University of California, Davis, won both the 2002 George Pólya Prize and the 2007 Norbert Wiener Prize for their work on random matrices and, more specifically, for their discovery of the Tracy-Widom distribution, a new class of distribution functions useful to physicists. Widom taught at Cornell University in Ithaca, New York, before moving to the University of California, Santa Cruz, in 1968, becoming Professor Emeritus in 1994. (Source: Mathematics Genealogy Project, UC Santa Cruz Mathematics)

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 and early 2013.

**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 55," *Convergence* (June 2013), DOI:10.4169/loci003801