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 David Blackwell (1919-2010) in August of 1976 in Toronto, Ontario, Canada. Blackwell earned his Ph.D. in 1941 at the University of Illinois, Urbana-Champaign, under probabilist Joseph Doob, with a dissertation on Markov chains. He was awarded a fellowship at the Institute for Advanced Study (IAS) in Princeton for 1941-42. After two one-year appointments at colleges in Louisiana and Georgia, Blackwell became professor and, very quickly, chair at Howard University in Washington, D.C. At Howard, Blackwell’s research focus changed to theoretical statistics and, in 1955, he accepted a position at the University of California, Berkeley, in the Department of Mathematics and Statistics, where he spent the rest of his career and advised at least 65 Ph.D. students.

As an African-American mathematician and statistician, Blackwell faced many challenges and attained many firsts, including becoming the first African-American to be awarded an IAS fellowship, the first to be elected to the National Academy of Sciences, and the first to earn tenure at UC Berkeley. The annual National Association of Mathematicians (NAM)-MAA David Blackwell Lecture was instituted in 1994, and remains one of the featured invited addresses of the annual MAA MathFest. Howard University will host the David Blackwell Memorial Conference, to be held April 19-20, 2012, on the Howard University campus in Washington, D.C. The conference will celebrate Blackwell's legacy, including his contributions to probability theory, theoretical statistics, operations research, and game theory.

David Blackwell and Paul Halmos were photographed on June 30, 1998. “Two geezers” is the caption supplied by Halmos on the back of the photo.

Halmos and Blackwell attended the University of Illinois, Urbana-Champaign, at about the same time, with Halmos entering as a 15-year-old in 1931 and Blackwell as a 16-year-old in 1935. Both earned Ph.D.s at the age of 22 with probabilist Joseph Doob, Halmos in 1938 with a dissertation on measure-theoretic probability and Blackwell in 1941 with a dissertation on properties of Markov chains. Halmos spent 1938-39 as an instructor at Illinois, and then moved to the Institute for Advanced Study (IAS) in Princeton for three years, 1939-42. Blackwell was awarded an IAS fellowship for 1941-42. In 1942, Halmos joined the faculty at Syracuse University, where he would remain for four years, and Blackwell, after two one-year appointments at colleges in Louisiana and Georgia, became a professor at Howard University in Washington, D.C. Halmos and Blackwell remained lifelong friends, and both stayed close to Doob as well. Another friend was Warren Ambrose, who completed his Ph.D. with Doob at Illinois in 1939 and was at IAS from 1939 to 1941. Blackwell, Halmos, Ambrose, and Doob also are pictured on page 1 of this collection.

Halmos photographed Ralph P. Boas, Jr. (1912-1992) in 1980. Boas earned his Ph.D. at Harvard University in 1937. In 1943-45, he taught at Harvard, where he advised the Ph.D.s of R. Creighton Buck and Philip J. Davis, but he spent most of his career at Northwestern University in Evanston, Illinois. In addition to his research in real and complex analysis, Boas did extensive editorial work and was active in both the AMS and MAA, serving as MAA president in 1973-74. His son, Harold Boas, who earned his Ph.D. in complex analysis from M.I.T. in 1980 and is professor of mathematics at Texas A&M University, wrote in March of 2012 that “my father's unique bowties -- he always wore one -- were hand-made by my mother.” Mary L. Boas (1917-2010), who earned her Ph.D. in physics from M.I.T. in 1948, was professor of physics at DePaul University in Chicago for 30 years.

Graph theorist Béla Bollobás in May of 1973 at Cambridge University, England. Born in Budapest, Hungary, Bollobás caught the attention of mathematician Paul Erdös (pictured on page 3) while still a young teenager. Erdös became a mentor to Bollobás and interested him in graph theory. Bollobás earned Ph.D.s at Budapest University and, after he finally was allowed to leave Hungary, at Cambridge University. He became a fellow of Trinity College, Cambridge, in 1970, and, since 1996, has held positions both at Cambridge and at the University of Memphis, Tennessee.

Next, we have the two 1974 Fields medalists Enrico Bombieri and David Mumford on August 21, 1974, at the International Congress of Mathematicians (ICM) in Vancouver, B.C., Canada, where they were awarded their medals. Bombieri believes this photograph may have been taken the day after the awards ceremony, which would have been the second day of the conference. He reported in March of 2012 that he and his friend Mumford had worked together in 1973, producing "two joint papers on classification of algebraic surfaces in positive characteristic. Our Fields Medals were a totally unexpected surprise for both of us."

Enrico Bombieri (left) earned his Fields Medal primarily for advances in number theory, but also for results in analysis and in the partial differential equations of minimal surfaces. He studied in his native Milan, Italy, and also in Cambridge, England, and then taught in Pisa, Italy, for a number of years. In 1977, he became a faculty member of the School of Mathematics of the Institute for Advanced Study (IAS) in Princeton, New Jersey, and in 1988 became IBM von Neumann Professor at IAS.

David Mumford (right) earned his Fields Medal for advances in algebraic geometry. He spent most of his career at Harvard, moving at the turn of the millennium to the Division of Applied Mathematics at Brown University, where he has led the pattern theory group and has been affiliated with the brain science program, focusing on visual perception. He has supervised at least 47 Ph.D. students and was awarded the National Medal of Science in 2010.

Halmos photographed functional analyst Frank Bonsall (1920-2011) and number theorist Robert Rankin (1915-2001) on July 1, 1980 in St. Andrews, Scotland.

Bonsall studied at Oxford, then spent over a decade at Newcastle University, before becoming the first occupant of the Maclaurin Chair at the University of Edinburgh, a position he held for 20 years. Rankin earned his degree at Cambridge and spent most of his career at the University of Glasgow, Scotland. While at Cambridge, he had worked with G. H. Hardy on the mathematics of Srinivasa Ramanujan, and he continued to publish both mathematical and historical work on Ramanujan throughout his career.

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.

**Biographies of David Blackwell** (1919-2010)**:**

**Other Sources for this page:**

- 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.
- Harold Boas, email dated 2 March 2012 (Ralph P. Boas, Jr.)
- Enrico Bombieri, emails dated 5 March 2012 and 6 March 2012 (Bombieri, David Mumford)
- Brown University Division of Applied Mathematics (Philip J. Davis, David Mumford)
- DePaul University Physics Department (Mary L. Boas)
- Institute for Advanced Study (IAS) Faculty (Enrico Bombieri)
- Institute for Advanced Study (IAS) Past Members (Ambrose, Blackwell, Halmos, and others)
- International Mathematical Union (IMU) Fields Medal and Medalists (Bombieri, Mumford)
- MacTutor History of Mathematics Archive, St. Andrews University, Scotland (all mathematicians except Ambrose, Boas, Buck, and Davis)
- Massachusetts Institute of Technology (MIT) News Office (Warren Ambrose)
- MAA Presidents (Ralph P. Boas, Jr.)
- Mathematics Genealogy Project, North Dakota State University (all mathematicians)
- Texas A&M University Mathematics Department (Harold Boas)
- University of Wisconsin Department of Mathematics (R. Creighton Buck)

Index to the Collection