Photos by Paul Halmos

Functional analyst Billy James Pettis (1913-1979) was photographed by Halmos in August of 1975 at the Joint Summer Mathematics Meetings in Kalamazoo, Michigan. Pettis earned his Ph.D. in 1937 from the University of Virginia with the dissertation “Integration in Vector Spaces,” written under advisor Edward J. McShane. In fact, Pettis was McShane’s first Ph.D. student. (McShane is pictured on page 34 of this collection.) Pettis was a faculty member at Tulane University in New Orleans, Louisiana, and, from 1957 onward, at the University of North Carolina, Chapel Hill. (Sources: Mathematics Genealogy Project; A Guide to the B. J. Pettis Papers, 1938-1980, Archives of American Mathematics)

Who’s That Mathematician? Images from the Paul R. Halmos Photograph Collection

Richard Rado (1906-1989), Robert Rankin (1915-2001), and Hans Reimann, left to right, were photographed by Halmos in April of 1965 at the British Mathematical Colloquium in Dundee, Scotland. Halmos was one of three main speakers at this conference (I Want to Be a Mathematician, Springer, 1985, pp. 290-292). Another photograph of Rankin appears on page 7 of this collection, where you can read more about him. 

Born in Berlin, Germany, Richard Rado earned doctoral degrees from the University of Berlin in 1933 and from Cambridge University in 1935. At the University of Berlin, he wrote the dissertation, “Studies on combinatorics,” under advisor Issai Schur and at Cambridge, he wrote the dissertation, “Linear Transformations on Bounded Sequences,” under advisor G. H. Hardy. Although he would write papers in both fields, his research throughout his career was primarily in combinatorics. In 1934, Rado met Paul Erdős, who had earned his Ph.D. in Budapest that year and accepted a fellowship at the University of Manchester in England, and the two began to collaborate. Erdős described the strengths each brought to their collaboration as follows:

I was good at discovering perhaps difficult and interesting special cases and Richard was good at generalising them and putting them in their proper perspective (quoted by O’Connor and Robertson in their MacTutor Archive biography of Rado).

After spending 1935-36 at Cambridge University, Rado was on the mathematics faculty at the University of Sheffield, England, from 1936 to 1947, then at King’s College, London, from 1947 to 1954, and finally at the University of Reading in England from 1954 onward. Much like another couple featured in this collection, Leonard and Reba Gillman (see page 17), Richard Rado and his wife, Luise Zadek Rado (d. 1990), were highly accomplished musicians, he as a pianist and she as a singer, and gave both public and private concerts. (Sources: MacTutor Archive, Mathematics Genealogy Project) 

Hans-Martin Reimann earned his Ph.D. in 1969 at the Eidgenössische Technische Hochschule (ETH) in Zürich, Switzerland. If our identification is correct (based on the notation “Reimann (Swiss)” by Halmos), Reimann would have been a beginning graduate student at the time this photograph was taken. He has spent most of his career at the University of Bern, Switzerland, becoming Professor Emeritus in 2006, and lists his research interests as complex analysis, quasiconformal mappings, Lie groups, symplectic geometry, and wavelets. (Sources: Mathematics Genealogy Project, Universität Bern Mathematics)

Who’s That Mathematician? Images from the Paul R. Halmos Photograph Collection

Science Friday mentions Who’s That Mathematician? Images from the Paul R. Halmos Photograph Collection. 

In late August, SciFri writer Annette Heist sent out a call for photographs of women in mathematics. The article, titled “Picture Another Mathematician”, featured two photos from the Halmos Collection of Olga Taussky-Todd (pictured) and Mary Ellen Rudin.

Heist wrote:

Laura McHugh of the Mathematical Association of America wrote to tell me about mathematician and photographer Paul Halmos. Throughout his career, Halmos snapped thousands of photos of his fellow mathematicians. After his death, Halmos’s wife donated the photos to the University of Texas’s Archives of American Mathematics. The photos are in the process of being digitized and made available online according to archivist Carol Mead, who sent the photos below.

The photo 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.

Who’s That Mathematician? Images from the Paul R. Halmos Photograph Collection

Halmos photographed Phillip Jones, Bartel van der Waerden, and Theophil Hildebrandt on April 2, 1968, in Ann Arbor, Michigan. That spring, Halmos was still a faculty member at the University of Michigan in Ann Arbor, but he would move to the University of Hawaii in Honolulu for the 1968-69 academic year and then to Indiana University in Bloomington in the fall of 1969.

Phillip S. Jones (1912-2002) earned his Ph.D. in 1948 from the University of Michigan, where he had earned bachelors and masters degrees in mathematics ten years earlier, with a dissertation on the history of geometry and linear perspective written under the mathematics historian Louis Karpinski. He became a faculty member at Michigan in 1947 and remained there for the rest of his career, specializing in mathematics history and education. He was a national leader in both of his specialties and was perhaps best-known for combining the two: using mathematics history as a mathematics teaching tool and writing the history of mathematics education in the U.S. (Source:Phillip S. Jones (1912-2002) (pdf file), History and Pedagogy Newsletter 64, March 2007, 1-4)

Bartel van der Waerden (1903-1996) earned his Ph.D. in 1926 from the University of Amsterdam with the dissertation, “The algebraic foundations of the geometry of numbers,” after studying also at the University of Göttingen, Germany, with Emmy Noether (algebra) and Hellmuth Kneser(topology). After studying for a semester with Emil Artin at the University of Hamburg, van der Waerden began writing his most famous book, Moderne Algebra, basing Volume I (1930) on work of Noether and Artin and Volume II (1931) on his own work in algebra. He was professor of mathematics at the University of Leipzig from 1931 through the end of World War II in 1945 and at the University of Zürich, Switzerland, from 1951 onward. Although he was interested in mathematics history throughout his career, he published most of his work in this field later in his career. (Source: MacTutor Archive)

Theophil H. Hildebrandt (1888-1980) earned his Ph.D. in 1910 from the University of Chicago under advisor E. H. Moore. He joined the mathematics faculty at the University of Michigan in 1909 and spent his career there, specializing in functional analysis and integration theory. Hildebrandt is best known for giving the first general proof of the principle of uniform boundedness for Banach spaces and for serving as president of the American Mathematical Society during 1945-1946. (Source: Mathematics Genealogy Project, MacTutor Archive: Moore, AMS Presidents)

Who’s That Mathematician? Images from the Paul R. Halmos Photograph Collection

This is a photograph of Gerald (Jerry) Alexanderson, Halmos’ colleague at Santa Clara University in California. Halmos joined the mathematics faculty at Santa Clara in 1985, at the invitation of Alexanderson, who had taught there since 1958. Alexanderson was largely responsible for the donation of Halmos’ papers and photographs to the Archives of American Mathematics and, in particular, for the monumental task of organizing Halmos’ photograph collection for the Archives.

Alexanderson (left) is pictured with Vladimir Drobot at Santa Clara University, where both were faculty members, in March of 1984, the year before Halmos joined them as a faculty member there.  At the time this photo was taken, Alexanderson was First Vice President of the MAA.  He would become MAA President in 1997.  Vlad Drobot taught at SCU for 17 years and then, in 1990, moved across town to San Jose State University, where he taught for 16 years.

Who’s That Mathematician? Images from the Paul R. Halmos Photograph Collection 

Photo Caption: Lancaster 1984 - Sheldon Axler and Halmos

“[This photo*] was taken at a conference in Lancaster (England) in 1984, and it represents four mathematical generations. I am at right, next to me is Don (D.E. Sarason), my student, next to him is Sheldon, his Ph.D. student, and next to Sheldon is Pam (Axler), who is, of course, Sheldon’s Ph.D. student.” –Paul R. Halmos, I Have a Photographic Memory

 *This photo is a slightly different angle than the photo featured in I Have a Photographic Memory
 

Photo Caption: Sheldon Axler August 75

Sheldon Axler is Dean of the College of Science & Engineering at San Francisco State University.  In 1996, he received the Lester R. Ford Award for expository writing from the Mathematical Association of America for his article “Down with Determinants!” He also served as an Associate Editor of The American Mathematical Monthly.

Sheldon Axler Homepage

Sheldon Axler Biography by MSRI  

Photo Caption: M Atiyah 29 Mar 69 

“The Atiyah-Singer index theorem was the toughest hurdle for me, but, somehow, we conquered it too. (To be sure, after it appeared in print, Singer told me that it didn’t come out quite right—the relation with the Riemann-Roch theorem was unclear or perhaps even misstated—but there it was, and I feel sure that my fellow ignoramuses and I learned something worth knowing that we hadn’t known before.)”–Paul R. Halmos, I Want to Be a Mathematician

Michael Francis Atiyah contributed to a wide range of topics in mathematics centering on the interaction between geometry and analysis. His work showed how the study of vector bundles on spaces could be regarded as the study of cohomology theory, called K-theory. He was awarded the Fields Medal in 1966.

The ideas which led to Atiyah being awarded a Fields Medal were later seen to be relevant to gauge theories of elementary particles.

The theories of superspace and supergravity and the string theory of fundamental particles, which involves the theory of Riemann surfaces in novel and unexpected ways, were all areas of theoretical physics which developed using the ideas which Atiyah was introducing. 

In addition to the Fields Medal, Atiyah received many honors during his career including the Feltrinelli Prize from the Accademia Nazionale dei Lincei in 1981, the King Faisal International Prize for Science in 1987, the Benjamin Franklin Medal, and the Nehru Medal. In 2004, he and Isadore Singer were awarded the Neils Abel prize of £480 000 for their work on the Atiyah-Singer Index Theorem.

Michael Francis Atiyah Biography

Photo Caption: Amir Moez, 1967

“Ali has been a linear algebra enthusiast for much of his professional life.” — Paul R. Halmos, I Have a Photographic Memory

Ali Reza Amir-Moez earned his BA at the University of Teheran in 1942, and served as a Math Instructor at Teheran Technical College from 1942 - 46.

He immigrated to the United States in 1947. His first love was drama and the performing arts, however, he was forced to study math to receive an extension on his visa, and thus he continued his education earning his MA in 1951, and PhD in 1955, both from UCLA. He served as a Professor of Math at the University of Idaho; Queens College, New York City; Purdue University; University of Florida, Gainesville; Clarkson College, Potsdam, New York; and Texas Tech University, Lubbock.

Amir-Moez was dedicated to mathematics research and established scholarships at both Texas Tech University and the University of California at Los Angeles. In 1975, he was awarded the medal of Pro Mundi Beneficio, Academia Brasileira De Ciencias Humanas.

He was the author of books including, Elements of Linear Space; Extreme Properties of Linear Transformations and Geometry in a Unitary Space; Classes Residues et Figure ance Ficelli; and plays including Kaleeleh and Demneh and Three Persian Tales. His writings included over 150 papers, articles, and books, and he was often featured in Highlights for Children. a

Ali Reza Amir-Moez Obituary (Texas Tech University, August 25, 2007)

Dr. Ali Reza Amir-Moez (Lubbock Online, August 27, 2007)

Photo Caption: Ed Begle

“Ed started out as a topologist, a student of Lefschetz’s at Princeton, but then became famous for two other reasons. He was, for one thing, Secretary of the AMS between 1951 and 1956, and, as one of the prime movers of the SMSG (School of Mathematics Study Group) he was also one of the prime movers of the “new math”. A lot of people liked the SMSG and worked hard for it, but, in the interests of historical honesty, I must report that some of the others referred to it as Some Mathematics, Some Garbage.” –Paul R. Halmos, I Have a Photographic Memory

Begle was awarded a thesis in 1940 for his thesis Locally Connected Spaces and Generalized Manifolds. In his thesis, Begle started with the concepts of a realization and a partial realization of finite complex on a space which had been by Lefschetz in a 1936 paper. He gave new definitions of these concepts which allowed him to use other techniques and simplify the study of generalized manifolds. He used Vietoris cycles throughout his thesis.

Edward Griffith Begle Biography