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.

Index to the Collection

Paul Halmos photographed Felice and Paul Bateman on July 12, 1974, in Urbana, Illinois. Both Felice and Paul Bateman were mathematics faculty members at the University of Illinois, Urbana-Champaign, where they are now emeriti. In 1974, Halmos was a faculty member at Indiana University, but he had earned his Ph.D. at University of Illinois in 1938 and his many friends there included his thesis advisor Joseph Doob (1910-2004). Number theorist Paul Bateman earned his Ph.D. from the University of Pennsylvania in 1946 with the thesis "On the representation of a number as a sum of three squares," written under Hans Rademacher, and went on to advise 20 Ph.D. students of his own at the University of Illinois (Mathematics Genealogy Project). Felice Davidson Bateman graduated from Smith College in 1943 and earned her Ph.D. in algebra from the University of Michigan in 1950 (Smith College, Mathematics Genealogy Project). She and Paul Bateman were at the Institute for Advanced Study during 1949-1950 (IAS).

Edward Begle (1914-1978) was photographed on August 27, 1964, in Amherst, Massachusetts perhaps during a Joint Summer Meeting there. Begle earned his Ph.D. in topology from Princeton in 1940 under Solomon Lefschetz (Mathematics Genealogy Project). He then spent nearly 20 years at Yale University (1942-1961), where his focus gradually shifted from topology to mathematics education. From 1961, he was both Professor of Mathematics and Professor of Education at Stanford University and a leader in the mathematics education community (MacTutor History of Mathematics Archive). It is possible that he and Paul Halmos first met while Begle was a Ph.D. candidate or an instructor (1940-41) at Princeton and Halmos was first at the Institute for Advanced Study (1939-1941, IAS).

William Johnson, Alexandra Bellow, and Haskell Rosenthal enjoy a meal at the AMS Sectional Meeting at Northwestern University in Evanston, Illinois, in November of 1983. (For a photograph of Richard Askey at the same conference, see page 2.) Johnson gave two talks at this conference, one in a session on operator theory in classical function spaces in which Paul Halmos also spoke. He earned his Ph.D. from Iowa State University in 1969, and has spent most of his career at Ohio State University and Texas A&M University, where he is Distinguished Professor and Owen Chair of Mathematics. Bellow earned her Ph.D. at Yale University in 1959 with a dissertation on “Ergodic theory of random series,” written under Shizuo Kakutani. She spent most of her career at Northwestern University (Mathematics Genealogy Project), where she is now emeritus. She also appears in a photograph on page 9 of this collection. Rosenthal earned his Ph.D. at Stanford in 1965, and taught at the University of California, Berkeley, during the 1970s and at the University of Texas, Austin, from the 1980s onward. He recently retired from UT Austin as the John T. Stuart III Centennial Professor.

Georgia Benkart during a visit to Indiana University, where Halmos was then a faculty member, on February 22, 1979. Benkart earned her Ph.D. in algebra from Yale University in 1974 under advisor Nathan Jacobson. She spent most of her career at the University of Wisconsin, Madison, where she advised 21 Ph.D. theses (Mathematics Genealogy Project) and retired as E. B. Van Vleck Professor of Mathematics in 2006. She served as president of the Association for Women in Mathematics (AWM) from 2009 to 2011, helping direct AWM's 40th anniversary celebrations in 2011. Benkart currently serves as AMS Associate Secretary for the Central Section.

Halmos photographed Lipman Bers (1919-2004), second from right, and his family in 1958 in Edinburgh, Scotland, where Halmos and Bers were attending the St. Andrews Colloquium. Although Halmos made no such notation, we assume the three people with whom Bers is walking are his son Victor, wife Mary, and daughter Ruth (AMS *Notices:* "Remembering Lipman Bers").

Halmos snapped "Lipa" Bers again on May 13, 1974, at the AMS Hilbert Problems Conference, held in DeKalb, Illinois. Bers served as president of the AMS in 1975-1976 (AMS Presidents). According to the Mathematics Genealogy Project, he advised 53 Ph.D. students from 1945 to 1988, most of them at New York University's Courant Institute or at Columbia University, the two institutions at which he spent most of his career. He and Halmos may have first met in 1945 at Syracuse University, where Halmos was a faculty member from 1942 to 1946 and Bers a faculty member from 1945 to 1949. In these early years, Bers worked mainly in fluid dynamics, but in about 1950 switched to quasiconformal mappings (MacTutor History of Mathematics Archive).

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.

**Sources:**

- American Mathematical Society (AMS) Notices, January 1995, "Remembering Lipman Bers," by William Abikoff, Carol Corillon, Jane Gilman, Irwin Kra, and Tilla Weinstein
- AMS Presidents (Lipman Bers)
- Archives of American Mathematics, Dolph Briscoe Center for American History, University of Texas, Austin. Information for which a source is neither cited nor given in this list either appeared on the reverse side of the photograph or was obtained by AAM archivist Carol Mead from various sources during 2011-12.
- Association for Women in Mathematics (Alexandra Bellow, Georgia Benkart)
- Institute for Advanced Study Past Members (Felice Bateman, Paul Bateman, Georgia Benkart, Lipman Bers, Paul Halmos)
- MacTutor History of Mathematics Archive, St. Andrews University, Scotland (Edward Begle, Lipman Bers, Joseph Doob, Paul Halmos, Nathan Jacobson, Shizuo Kakutani, Solomon Lefschetz, Hans Rademacher)
- Mathematics Genealogy Project, North Dakota State University (all mathematicians)
- Northwestern University Department of Mathematics (Alexandra Bellow)
- Smith College Mathematicians (Felice Bateman)
- Texas A&M University Department of Mathematics (William Johnson)
- University of Illinois Department of Mathematics (Felice Bateman, Paul Bateman)
- University of Texas, Austin, Department of Mathematics (Haskell Rosenthal)
- University of Wisconsin Department of Mathematics (Georgia Benkart)

Index to the Collection