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

Halmos photographed algebraic topologist Douglas Ravenel on March 24, 1974, at Indiana University in Bloomington. Ravenel recently recalled that he was at IU in 1974

for a weekend topology conference, the second of three held there in consecutive years. They were known as "opera conferences" because there was always an excursion to an opera put on by the IU music school. The best seats in the house were only $5. The three operas were "The Marriage of Figaro," "Rigoletto" (in 1974), and "Parsifal." The other person visible in the picture (over my right shoulder) is Larry Smith, who was briefly an IU faculty member. In 1973 and 1974 I got a ride to the conference with Haynes Miller, who was then a Princeton graduate student. He was driving, Jack Morava was in the front seat navigating, and I was asleep in the back seat. Both times we got lost in the same part of Philadelphia, and both times Jack had a topological explanation. The first time it had to do with the local topology not being simply connected, something to do with a bridge. The second time Jack said the problem was that the topology was not locally Hausdorff. In 1975 we all flew there instead of driving.

Ravenel earned his Ph.D. in 1972 from Brandeis University in Waltham, Massachusetts. He was then on the faculties of Columbia University and the University of Washington before moving to the University of Rochester in 1988, where he is now Daniel Burton Fayerweather Professor of Mathematics. During the 1990s, he and Rochester colleagues launched the popular WeBWorK mathematics homework system. In 2009, Ravenel and two collaborators solved all but one case of the Arf-Kervaire invariant problem in homotopy theory. Be sure to see Ravenel’s short synopsis of this result, which includes photos of players from both the 20^{th} and 21^{st} century history of the problem. (Sources: Mathematics Genealogy Project, University of Rochester Mathematics, Doug Ravenel (Nov. 2012))

Sisters Julia Robinson (1919-1985), left, and Constance Reid (1918-2010) were photographed by Halmos in July of 1984 in Eugene, Oregon. Constance Reid was the well-known author of popular books about mathematics, most notably *From Zero to Infinity: What Makes Numbers Interesting* (MAA, 1961), and of biographies of mathematicians, including E. T. Bell (or John Taine), Richard Courant (photographed on page 10 of this collection), David Hilbert, Jerzy Neyman (photographed on page 38 of this collection), and Julia Robinson. Another photograph of Julia Robinson appears on page 30 of the collection, where you can read more about her. (Sources: MacTutor Archive, MAA obituary: Constance Reid)

Halmos photographed Constance Reid (1918-2010) in July of 1984 in Eugene, Oregon. See the photo caption above for more information about Reid.

Mathematicians Irma Reiner (1922-2014) and Irving Reiner (1924-1986) were photographed by Halmos on October 11, 1974, in Bloomington, Indiana, in the home of Paul and Virginia Halmos. (We believe the painting just behind Irma Reiner in the photograph to be of Virginia Halmos.)

Irma Moses Reiner earned her Ph.D. in 1946 from Cornell University under advisor Burton W. Jones (see page 6 of this collection for a photo of Jones). Irving Reiner earned his Ph.D. in 1947, also from Cornell University under advisor Burton W. Jones. In fact, the Reiners were Jones’ first two Ph.D. students. Both Reiners spent their mathematical careers at the University of Illinois at Urbana-Champaign, where Irma Reiner was emeritus at the time this article was published. Irving Reiner is best known as co-author with Charles Curtis of the classic *Representation Theory of Finite Groups and Associative Algebras,* originally published in 1962 and revised and republished in two volumes in 1981 and 1987. (Sources: MacTutor Archive, Mathematics Genealogy Project, Irma Reiner (Nov. 2012), *Chicago Tribune* obituary of Irma Reiner)

Halmos photographed Reinhold Remmert in August of 1983 in Oberwolfach, Germany. Halmos and Remmert were attending the last in a series of seven conferences at the Oberwolfach Conference Center organized by Paul Butzer (page 9) from 1963 to 1983 on approximation theory and related topics in functional analysis. Another photo of Remmert appears on page 18 of this collection, where you can read more about him. Be sure to see also the Oberwolfach Photograph Collection.

Halmos photographed Natalie Davis and Alfréd Rényi (1921-1970) in September of 1961.

Natalie Zemon Davis, wife of mathematician Chandler Davis, is a noted social and cultural historian, primarily of early modern France. Her best known book is *The Return of Martin Guerre* (1983), also the title of a popular film released at the same time. Natalie and Chandler Davis were victims of the “Red scare” in the United States during the 1950s, with Chandler Davis losing his job at the University of Michigan in 1954 and even being imprisoned for six months. They moved to Toronto, Canada, during the summer of 1962, and Chandler Davis is now Professor Emeritus of Mathematics at the University of Toronto. (Sources: Wikipedia, University of Michigan History, University of Toronto Mathematics, Chandler Davis (Nov. 2012))

Natalie and Chandler Davis recalled more vividly a later visit to North America by Alfréd Rényi and his daughter Zsuzsi (see page 43 of this collection for a photo of Alfréd and Zsuzsanna Rényi, probably on that very visit). Natalie Davis later found "duplicate" evidence of Alfréd Rényi's earlier visit:

Going through all our old photographs yesterday for another reason, I came upon the original of the Halmos photograph of me and Rényi. It had the date September 1961 on the back and Paul [Halmos] had written "Belle of the Ball"....

Born in Budapest, Hungary, Alfréd Rényi earned his doctoral degree in 1945 from the University of Szeged, Hungary, under advisor Frigyes (Frédéric) Riesz. According to O’Connor and Robertson of the MacTutor Archive, this was after graduating from the University of Budapest, where he studied from 1940 to 1944 under Lipót Fejér and Paul Turán, escaping from a forced-labor camp, hiding out to avoid capture, and rescuing his parents from the Budapest ghetto by impersonating a soldier. After a postdoctoral year in Russia (1946-47) during which he obtained important results on the Goldbach Conjecture, Rényi continued to obtain results in number theory, probability, and analysis as a professor at the University of Budapest and a member of the Hungarian Academy of Sciences and director of its Institute for Applied Mathematics before dying suddenly at age 48. Rényi’s wife was the mathematician Katalin (Kató) Rényi, and possibly she and/or Chandler Davis were among the assembled party as well. We will search for photographic evidence! (Source: MacTutor 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.

**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