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 Reba Gillman and Leonard Gillman (1917-2009) at the AMS-MAA Joint Mathematics Meetings in Phoenix, Arizona, in January of 1989. Leonard Gillman earned his Ph.D. from Columbia University in 1953 with the dissertation, "On Intervals of Ordered Sets," written under Edgar Lorch and Alfred Tarski. He taught at Purdue University (1952-60) and the University of Rochester (1960-69) before joining the faculty of the University of Texas at Austin in 1969. Although his research was in set theory and topology, his best known articles may be "Teaching Programs That Work" (*MAA FOCUS,* 1990) and "An Axiomatic Approach to the Integral" (*American Mathematical Monthly,* 1993). Gillman served as MAA president in 1987-88. (Sources: Mathematics Genealogy Project, MAA Presidents)

Reba and Leonard Gillman perform for friends, including Paul Halmos, in December of 1971. Leonard was an accomplished pianist and Reba a professional soprano who remains involved with musical groups in Austin, Texas.

R. H. Bing (1914-1986), left, and Andrew Gleason (1921-2008) were photographed at the Joint Summer Mathematics Meetings in Boulder, Colorado, in August of 1963.

R. H. Bing was a Texas high school teacher turned R. L. Moore-trained topologist who spent most of his career at the universities of Wisconsin and Texas. He and Paul Halmos may have first met at the Institute for Advanced Study in Princeton, where both were members during 1957-58. In 1973, after 26 years (1947-73) at the University of Wisconsin, Bing returned to the University of Texas at Austin, where he had earned his Ph.D. in 1945. He served as MAA president in 1963-64 and AMS president during 1977-78. For two more photographs of Bing, see page 6 of this collection. (Sources: MacTutor Archive, Mathematics Genealogy Project, AMS Presidents, MAA Presidents)

After serving as a codebreaker during World War II, Andrew Gleason became a Junior Fellow at Harvard in 1946. As a Junior Fellow, Gleason neither wrote a traditional dissertation nor earned a traditional Ph.D., but, since he did the sort of work Ph.D. candidates do from 1946 to 1950, his date of doctoral completion is sometimes listed as 1950. By 1952, he had helped solve Hilbert's 5th Problem on the relationship between connected locally compact groups and Lie groups. During his career at Harvard, Gleason researched Banach spaces and classical geometry and advised at least 28 Ph.D. students. In 1959, he served as chair of the advisory committee to the inventors of the infamous "New Math" and, during the 1990s, he was a member of the Calculus Consortium based at Harvard (CCH), which produced the most commercially successful of the "calculus reform" textbooks of that decade. Gleason served as president of the AMS during 1981-82. (Sources: MacTutor Archive, Mathematics Genealogy Project, AMS Presidents)

Halmos photographed Andrew Gleason again in Bloomington, Indiana, on December 5, 1969. Halmos had joined the faculty at Indiana University in Bloomington earlier that year.

Next, we have operator theorists Israel Gohberg (1928-2009), left, and Marinus Kaashoek at a conference in Tihany, Hungary, in September of 1970.

Born in Tarutino, Ukraine, Israel Gohberg earned his Ph.D. at the University of Leningrad (now St. Petersburg State University) in 1954. He spent most of his career at Kishinev (or Kishinyov or, more recently, Chisinau) State University in Moldova and the Institute of Mathematics of the Academy of Sciences of Moldova, where he advised at least 22 Ph.D. students. In 1974, he moved to Tel Aviv University in Israel and, in 1983, he became a professor at the Free University (Vrije Universiteit) of Amsterdam. He has advised at least 42 Ph.D. students in all and published at least 460 papers. (Sources: Mathematics Genealogy Project, MacTutor Archive, IEEE Xplore: Israel Gohberg)

Marinus "Rien" Kaashoek earned his Ph.D. in 1964 from the University of Leiden under advisor Adriaan Zaanen, whose photograph appears on page 9 of this collection. Kaashoek has spent his career at the Free University (Vrije Universiteit) of Amsterdam, where he has advised at least 18 Ph.D. students and written at least nine books, and is now Professor Emeritus. (Sources: Mathematics Genealogy Project, Free University of Amsterdam)

Halmos photographed Israel Gohberg again in Lancaster, England, in July of 1984.

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