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

José Barría works at the chalkboard under the inquisitive eye of Paul Halmos in May of 1973. Barria was a doctoral student of Halmos, earning his Ph.D. from Indiana University in 1974 (Mathematics Genealogy Project).

Halmos photographed José Barría again nearly ten years later, in January of 1983. Barría became a mathematics professor at Santa Clara University, where Halmos himself joined the faculty in 1985 and where Barría continues to publish research papers on operator theory. Barría and Halmos published their third joint paper in 1990 while they were colleagues at SCU (MathSciNet).

Below, Robert Bartle asks Marshall Stone to sign his picture in the book of photographs of mathematicians that quickly became known as the "Halmos Picture Book." Its title was *I Have a Photographic Memory* and it was published by the American Mathematical Society (AMS) in 1987. This photograph was taken in June of 1988 at Hofstra University in Hempstead, New York.

Robert (Bob) Bartle (1927-2003) earned his Ph.D. at the University of Chicago in 1951, where he would have met both Halmos, who was a faculty member there from 1946 to 1961, and Stone, who was mathematics department chair from 1946 to 1968. Bartle was a faculty member at the University of Illinois, Urbana-Champaign, from 1955 to 1990, where he wrote well-known textbooks, including *The Elements of Real Analysis* (1964) and, with colleague Donald Sherbert, *Introduction to Real Analysis* (1982). He also served for six years, 1976-78 and 1986-90, as executive editor of *Mathematical Reviews *(*MR*) in Ann Arbor, Michigan. According to *MR* colleague Jane Kister, who herself served as *MR* executive editor from 1998 to 2004, Bartle was a universally loved editor who oversaw *MR*'s first steps toward computerization, tremendous growth in the database, and revision of the Mathematics Subject Classification (MSC). (Source: *AMS Notices,* Feb. 2004, "Inside the MAA: Robert G. Bartle (1927-2003)," by Jane E. Kister and Donald R. Sherbert.)

Marshall Stone (1903-1989) is best known for the Stone-Weierstrass Theorem and for his leadership of the University of Chicago Mathematics Department from 1946 to 1968. Halmos was a faculty member at Chicago from 1946 to 1961, so he and Stone would have known each other well. Stone chaired the Chicago Mathematics Department only from 1946 to 1952, at which point Saunders Mac Lane took over as chair. However, he assembled such an impressive faculty and attracted and developed such excellent students during that short time that his tenure as chair became known reverently as the "Stone Age." He retired from the University of Chicago in 1968 and accepted a position at the University of Massachusetts, which he held until 1980. Stone had earned his Ph.D. in differential equations from Harvard University in 1926 under advisor George D. Birkhoff, and, after spending 1925-27 at Columbia University, he joined the mathematics faculty at Harvard, where he would remain (except for 1931-33 at Yale University and war work from 1942 to 1945) until 1946 when the University of Chicago lured him away (MacTutor History of Mathematics Archive). He was AMS president in 1943-1944 (AMS Presidents).

Halmos first photographed Hyman Bass in autumn of 1958, probably at the University of Chicago, where Halmos was a faculty member from 1946 to 1961 and where Bass would complete his Ph.D. in commutative algebra under Irving Kaplansky in 1959. Halmos had written a paper introducing monadic algebras in 1956, and Bass's first paper in 1958 would be on this topic (MacTutor History of Mathematics).

Halmos photographed Hyman (Hy) Bass again in August of 1968 at a Joint Summer Meeting of the AMS and MAA in Madison, Wisconsin. Bass was a faculty member at Columbia University from 1959 to 1999, where he advised at least 24 Ph.D. theses (Mathematics Genealogy Project). During the 1990s, he turned his attention to mathematics education, eventually joining the University of Michigan faculty as Roger Lyndon Collegiate Professor of Mathematics and Mathematics Education in 1999. He is now Samuel Eilenberg Distinguished University Professor of Mathematics and Professor in the School of Education as well. He was AMS president in 2001-2002 (AMS Presidents).

Joseph Bastian, a Ph.D. student of Halmos at Indiana University, is pictured in May of 1972 in Bloomington, Indiana. Bastian earned the Ph.D. in 1973 with the dissertation, "Decompositions of Weighted Translation Operators" (Mathematics Genealogy Project). After five years in academia, Bastian did a summer consulting project for the U.S. Air Force that introduced him to digital signal processing. He reports that he never returned to academia, instead pursuing a career in modeling, simulation, and digital signal processing for electro-optical sensors with a private aerospace firm with headquarters in Boulder, Colorado, where he retired in June of 2011.

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) MathSciNet (all mathematicians)
- AMS Notices, February 2004, "Inside the MAA: Robert G. Bartle (1927-2003)," by Jane E. Kister and Donald R. Sherbert (Robert Bartle)
- AMS Presidents (Hyman Bass, Marshall Stone)
- 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.
- MacTutor History of Mathematics Archive, St. Andrews University, Scotland (Hyman Bass, Samuel Eilenberg, Marshall Stone)
- Mathematics Genealogy Project, North Dakota State University (all mathematicians)
- University of Illinois Department of Mathematics (Donald Sherbert)
- University of Michigan Department of Mathematics (Hyman Bass)
- University of Michigan School of Education (Hyman Bass)

Index to the Collection