Photos by Paul Halmos

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: 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

Photo Caption: Budapest 1931

“My family lived in a third floor apartment, in Budapest, that faced out on a busy street (now called Lenin Boulevard). It was an exciting street—colorful, crowded, noisy. There were many shops—a glamorous hardware store displaying shiny knives behind its huge plate glass front, several bookstores with books of many colors piled and strewn around, coffee houses with grouchily servile waiters carrying white napkins on their black left sleeves, and stores full of toys and candy and crutches and clothes and shoes and watches. The sidewalk was broad, and milling, crowds of people separated the shop windows from teh curb-side trees and scales (your weight for a penny) and newspaper kiosks and taxi stands. The crowds seemed always to be there—they were there when went to school early in the morning and they were there on the rare occasions when I was brought home late at night from an excursion or from a movie. Later, when I grew up, went to Hungary as an American tourist, and was out real late at night, the crowds were still there. The lights were bright and gypsy music could be heard from the coffee houses.” —Paul R. Halmos, I Want to Be a Mathematician…

Photo Caption: RL Wilder Lansing Aug 1960 

“Ray Wilder has been president of both the major mathematical organizations in the U.S.; he was a member of the National Academy, and the author of several books and many articles. When he was 80, fifteen years after he retired from the University of Michigan, he told me that his days of study were definitely not over (and neither was the feeling of pressure that makes one study): he was still reading mathematics, going to colloquia, and trying to keep up with what was going on.” —Paul R. Halmos, I Want to Be a Mathematician…

Wilder moved to the University of Texas in 1921 where again he was appointed as an instructor while he worked for his doctorate. It was here that his interests moved towards pure mathematics under the influence of Robert Moore. When he asked permission from Moore to take his topology course, Moore replied”-

No, there is no way a person interested in actuarial mathematics could do, let alone be really interested in, topology.

After Wilder persuaded Moore to let him take the course, Moore proceeded to ignore him until he solved one of the hardest problems Moore posed to the class. Wilder gave up his plans to study actuarial mathematics and became Moore’s research student. He suggested Wilder write up the solution to the problem for his doctorate which indeed he did, becoming Moore’s first Texas doctorate in 1923 with his dissertation Concerning Continuous Curves.

R.L. Wilder Biography

Photo Caption: WVD Hodge and ML Cartwright (1950)

“Bill Hodge (later Sir William) did algebraic geometry; there is something called a Hodge variety. His book with Pedoe was a large and difficult step forward when it came out.” — Paul R. Halmos, I Have a Photographic Memory

William Vallance Douglas Hodge was a Scottish mathematician, specifically a geometer.

“Hodge returned to Cambridge in 1932. He was appointed as a university lecturer in the following year and, in 1935, was elected to a fellowship at Pembroke College, Cambridge. During this period he developed the relationship between geometry, analysis and topology and produced some of his best remembered work on the theory of harmonic integrals. For these contributions Hodge won the Adams Prize in 1937 and Weyl described this contribution as ‘… one of the great landmarks in the history of science in the present century.’

Hodge published a polished account of his important theory in 1941. This work marked an important change in direction for the Cambridge school of geometry which, under Baker’s leadership, had become somewhat isolated from other areas of mathematics.” Read More

William Vallance Douglas Hodge Biography

William Valance Douglas Hodge Obituary by M.F. Atiyah

Related entry: Dame Mary Cartwright

Photo Caption: Doob, Aug 1, 1974

“Ambrose and I were blasé graduate students; we knew everything about the department, we knew everyone, and we could be trusted to deal with anything that was likely to come up that was likely to come up one early September afternoon—the department secretary left us in charge to watch over the main office. This boy came in, looking like a new graduate student, crew cut, shirt sleeves, and all. He was 25 years old at the time, I later learned, but he looked 19 or 20. What do you want?, we asked. Is Coble here?, he wanted to know; my name is Doob, D,O,O,B. Ambrose and I had heard of the bright young hot shot who was coming to Illinois from a fellowship at Columbia; we yanked our feet off the desk and told him who we were.” —Paul R. Halmos, I Want to Be a Mathematician

Joseph Leo Doob’s work was in probability and measure theory, in particular he studied the relations between probability and potential theory. Building on the work by Paul Lévy, Doob developed basic martingale theory and many of its applications during the 1940s and 1950s. His work has become one of the most powerful tools available to study stochastic processes. In the introduction to his Stochastic Processes (1953),Doob states that:

“… [a stochastic process is] any process running along in time and controlled by probabilistic laws … [more precisely] any family of random variables {xt| t ∈ T [where] a random variable is … simply a measurable function.” 

Joseph Leo Doob

Photo Caption: Nash 

“John is a non-cooperative game theorist (non-associative phrase) who has also written about cooperative games, and is famous for his imbedding theorem for Riemannian manifolds.” —Paul R. Halmos,I Have a Photographic Memory 

In 1949, while studying for his doctorate, John Nash wrote a paper which 45 years later was to win a Nobel Prize for economics. During this period Nash established the mathematical principles of game theory. P Ordeshook wrote: 

The concept of a Nash equilibrium n-tuple is perhaps the most important idea in noncooperative game theory. … Whether we are analysing candidates’ election strategies, the causes of war, agenda manipulation in legislatures, or the actions of interest groups, predictions about events reduce to a search for and description of equilibria. Put simply, equilibrium strategies are the things that we predict about people.

John Nash

Photo Caption: Mary Cartwright 3 June 68 Cambridge

“She became Mistress of Girton College (Cambridge), and, later, Dame Mary; she is just an outstanding complex analyst.” —Paul R. Halmos, I Have a Photographic Memory

Dame Mary Cartwright (1900-1998)
Mary Lucy Cartwright was the first woman mathematician elected to the Royal Society of London. While at Cambridge University, under the supervision of G.H. Hardy and E.C. Titschmarsh, her thesis on zeros of integral functions generated a series of papers and eventually led to her book on integral functions. Although she did important work with Dirichlet series, Abel summation, analytic functions regular on the unit circle, integral functions, and cluster sets, she is best known for her work with Littlewood on van der Pol’s equation and nonlinear oscillators. Cartwright served as Mistress of Girton College and as president of the British Mathematical Association and the London Mathematical Society. She was a recipient of the Sylvester Medal from the Royal Society and the De Morgan Medal from the London Mathematical Society. She authored nearly 100 articles and books. She was a very effective administrator at Cambridge University and ambassador for several mathematical and scientific organizations. In 1969, Queen Elizabeth II elevated her to Dame Mary Cartwright, the female equivalent of a knighthood.

Mary Cartwright