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

Maurice Auslander (1926-1994) at Indiana University, Bloomington, where Paul Halmos was a faculty member from 1969 to 1985, on Feb. 18, 1974. By this time, Auslander was working on representation theory of Artin algebras and we imagine that he may have given a talk on this topic at Indiana University. Auslander spent his career at Brandeis University in Waltham, Massachusetts, but frequently held visiting positions elsewhere (MacTutor History of Mathematics Archive).

Reinhold Baer (1902-1979) and his wife, Marianne Baer, at a conference at the Oberwolfach Institute in Germany on July 22, 1968. Baer was a group theorist who advised at least 59 Ph.D. students at the University of Illinois, Urbana-Champaign, from 1938 to 1956 and at Goethe Universität Frankfurt am Main from 1956 onward (MacTutor History of Mathematics Archive, Mathematics Genealogy Project). He and Halmos would have met in 1938, the year Halmos earned his Ph.D. at the University of Illinois and the year Baer joined the faculty there. They would have overlapped because Halmos remained at Illinois as an instructor during 1938-1939 (MacTutor History of Mathematics).

Reinhold Baer (1902-1979) seems to have been interrupted by the photographer while reading at the same conference at the Oberwolfach Institute in Germany on July 22, 1968.

Thomas Banchoff lectures at Indiana University in Bloomington, Indiana, on Oct. 27, 1975. Banchoff has been a faculty member at Brown University in Providence, Rhode Island, since 1967, where he has specialized in geometry and in computer graphics to help visualize geometry (MAA Presidents). Indeed, he may be best known for his work on visualizing the fourth dimension. Banchoff served as president of the Mathematical Association of America (MAA) during 1999-2000 (MAA Presidents).

From left to right, Charles Moore, Fannie Barnett, Isaac Barnett, and Paul Erdös chat in August or September of 1958 at ... the International Congress of Mathematicians in Edinburgh, Scotland? Charles N. Moore (1882-1967) earned his Ph.D. in analysis under Maxime Bôcher at Harvard in 1908 and had at least 17 Ph.D. students of his own during a career at the University of Cincinnati (Ohio Masters of Mathematics, Mathematics Genealogy Project). Isaac A. Barnett (1894-1974), earned his Ph.D. in differential equations under Gilbert Bliss at the University of Chicago in 1918, and, like Moore, was a faculty member at the University of Cincinnati. The University of Cincinnati later established a lecture series in number theory in honor of Isaac and Fannie Barnett (Ohio Masters of Mathematics). Paul Erdös (1913-1996), the famous itinerant polymath, already was well known for traveling all over the world posing problems and solving them with many and varied collaborators. His 509 co-authors have "Erdös number" 1 (Wolfram MathWorld). In 1958, Halmos was a faculty member at the University of Chicago. However, Erdös had left the U.S. in 1954 or shortly thereafter and did not return until 1963 (MacTutor History of Mathematics); it seems likely that both Halmos and Erdös would have attended the 1958 ICM. There are two more photos of Erdös on page 14 of this collection.

Lida Barrett was photographed by Halmos during the winter of 1981. Barrett moved from her position as mathematics department chair at the University of Tennessee, where she had worked in topology and applied mathematics, to an administrative position at Northern Illinois University in 1980, and this photo may have been taken in Illinois or Indiana, where Halmos was based. Barrett would continue her administrative career at Mississippi State University and the National Science Foundation and her teaching career at the United States Military Academy, West Point, New York. She has served the MAA throughout her career, including leading the MAA as president in 1989-1990 (MAA Presidents).

Barrett believes she and her husband, mathematician John H. Barrett, may have first met Halmos during 1959-60 while they were "on visiting appointments at the University of Wisconsin and Halmos was at the University of Chicago."

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:**

- 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 (Maurice Auslander, Reinhold Baer, Gilbert Bliss, Maxime Bôcher, Paul Erdös)
- Mathematical Association of America Presidents (Thomas Banchoff, Lida Barrett)
- Mathematics Genealogy Project, North Dakota State University (all mathematicians)
- Ohio Masters of Mathematics, MAA Ohio Section (originally, Bowling Green State University) (Charles Moore, Fannie Barnett, Isaac Barnett)
- Wolfram MathWorld (Erdös numbers)

Index to the Collection