IN MEMORIAM

David Harold Blackwell

Professor of Mathematics and Statistics, Emeritus

UC Berkeley

1919-2010

David Harold Blackwell, professor emeritus of mathematics and statistics at the University of California, Berkeley, passed away peacefully in Berkeley on July 8, 2010. He was 91 years old. He had retired as emeritus professor in 1989 but continued to come into the department almost every weekday until just before he died.

David was a towering figure in probability, statistics, and the mathematical sciences. He was much involved with the advancement of these fields, particularly because of his interests in theory and teaching, and his concern for minorities. He lived through the periods of World War II and the time when the United States was rejecting and dealing with segregation in legal and social ways. He experienced racism but fought it with composure.

David was born at home in Centralia, Illinois, on April 24, 1919. Centralia was then a junction point of the Illinois Central Railroad. His father, Grover Blackwell, worked for the railroad as a hostler, that is, someone who serviced train engines at the end of their runs. David once remarked, "I still get a special feeling every time I see a picture of a steam locomotive."

David attended Centralia public schools, having learned to read on his own before entering. He completed elementary school in six years instead of the usual eight. He described his high school education as "fabulous." While in high school he had his first publication, a solution of a problem that appeared in a mathematics magazine.

David's higher education was all at the University of Illinois-Champaign. He entered that university in 1935, aged 16. He obtained an A.M. there in 1938 and a Ph.D in 1941. His doctoral supervisor was J. L. Doob and his thesis was titled "Properties of Markov Chains." Markov chains proved to be a continuing topic throughout his career.

In 1941 David was awarded a Rosenwald Fellowship at the Institute for Advanced Study in Princeton. In the year there he became acquainted with J. von Neumann, among other mathematicians. One of them, Hans Samuelson, later wrote that during that year there were two people who were not allowed into Fine Hall because of military work going on there: himself as an enemy alien and David Blackwell as a black American. Fine Hall was then the Princeton mathematics building. David next spent the summer of 1942 as assistant statistician at the Office of Price Administration in Washington, D.C.

During the 1941-1942 period David wrote some 105 letters of application, all to black colleges. He visited 30 of them to see what the country and black colleges were like. Eventually he received three job offers. He accepted the position of instructor at Southern University in Baton Rouge in 1942. The following year he moved on to an instructorship at Clark College, Atlanta. Finally in 1944 David obtained a regular appointment. It was in the Department of Mathematics at Howard University, in the District of Columbia. He remained there until 1954, at which time he had become a professor and department chair. Next, at Jerzy Neyman's invitation, Blackwell was a visiting professor at the University of California.

In 1955 David was appointed a professor of statistics at Berkeley. At the time of that appointment he had published some 20 papers appearing in the major mathematics and statistics journals. He had also collaborated with Meyer A. Girshick on a book

, Theory of Games and Statistical Decisions. Later he described Girshick as a person who had a major influence on his career.

David's Berkeley years were full. He became department chair in 1957. According to Erich Lehman in his book

Reminiscences of a Statistician: the Company I Kept,David did a remarkable job during a very trying time. In the department David created the concept of a Neyman Visiting Assistant Professorship, a position implemented to reduce the pain often associated for some with not being promoted to tenure. His campus committee service included: Committee on Committees, Advisory Committee on Discrimination, Athletics, and Faculty Research. He was a member of many professional committees, in particular those of the American Association for the Advancement of Science, American Mathematical Society, American Statistical Association, International Congress of Mathematicians, Institute of Mathematical Statistics, Mathematical Association of America, and National Research Council. During the Free Speech Movement period David joined Professors J. Feldman, H. Helson, M. Hirsch. L. LeCam, S. Smale, A. Thomasian, and G. Turin in a public statement announcing their shock at the massing of police on campus.

Blackwell’s broad interests, including pure as well as applied mathematics, led to his additional appointment at Berkeley in 1973 as professor of mathematics.

Concerning David's research the mathematician Paul Halmos has written, "David is both a pure mathematician, who knows about some of the fanciest parts of what is known as descriptive set theory, and as a statistician, who can use fancy set theory to get results that other statisticians regard as important."

When reading through Blackwell's bibliography one notes the many papers he wrote that continue to affect today's research. Their topics include: Bayesian statistics, decision theory, duels, dynamic programming, experimental design, game theory, information theory, logic, Markov chains, merging of opinions, probability theory, set theory, sequential analysis, and statistical inference.

In the summers of 1946 and 1950 David was at the Rand Corporation in Santa Monica. He became a key developer of Richard Bellman's dynamic programming ideas, particularly for the uncountable state space case. In papers published between 1961 and 1966 David developed methods for showing the existence of optimal strategies, and handling the case of varying discount rates. Blackwell's work on dynamic programming proved particularly important to researchers in economics and operations research.

His knowledge of and work in game theory was particularly notable, with important contributions by himself and his dissertation supervisees to the theory of the determinateness of definable infinite two-person games. He was among the first to appreciate fully the connection of alternating sequences of the logical quantifiers “for any” and “there exists” with determinateness and rightfully regarded himself as a logician. Indeed he was one of the first two members added to the faculty of Berkeley’s path-breaking interdisciplinary Group in Logic and the Methodology of Science (after its founding in 1958 by Alfred Tarski and others) and he played an active role in its affairs.

Blackwell’s love of elegance and simplicity led him to reconsider Nikolai Luzin’s famous 1927 theorem on the Borel separability of analytic sets. He felt that at heart games were involved and found an elegant new proof of Luzin’s theorem which led to the settlement of a long-standing puzzle of descriptive set theory and the dramatic, surprising, and philosophically provocative result on the alternation of the separation principle from side to side in the two-sided projective hierarchy if sufficient definable determinateness was assumed.

The impact of Blackwell's research contributions is made clear by the number of lectures and concepts named after him. These include the Mathematical Association of America-National Association of Mathematicians (MAA-NAM) David Blackwell Lecture, Blackwell-Tapia Award, Blackwell determinacy, Blackwell games, Blackwell's renewal theorem, Blackwell spaces, the Rao-Blackwell theorem, Blackwell optimal policies, Blackwell's theorem for G-sub delta winning sets, Blackwell's approachability theorem, Blackwell's theory of combination of experiments, and the Blackwell channel.

His probability and statistics work includes algorithms, approximations, Bayesian statistics, bounds, distributions, improved estimates, limit theorems, predictors, proofs, representations, and invariably at least one very clever step. Perhaps his name is most broadly known for the use of Rao-Blackwellization to improve estimates.

He wrote some 84 research papers. Some 42 appeared in the journals

Annals of Mathematical Statistics, Annals of Probability,andAnnals of Statistics.He further supervised 64 doctoral dissertations. The theses’ range of topics is exceedingly broad.

Blackwell was the first African American inducted into the National Academy of Sciences. He received 13 honorary doctorates, once remarking that the two most important to him were from Howard University and the University of Illinois, as they knew him best. International ones are from the Universities of Lesotho and Warwick. He was elected to the American Academy of Arts and Sciences; he received the R. A. Fisher Award, and also the von Neumann Theory Prize of the Operations Research Society of America. He received the Berkeley Citation and gave the Wald and Reitz Lectures of the Institute of Mathematical Statistics.

Throughout his life David had amusements. In his youth there were checkers, chess, marbles, baseball and softball. He was long a track devotee and attended the U.S. National Championships. In his youth he organized track meets. Later on in the department he would be seen acting as a

kriegspieljudge. The family had property in Mendocino County. He paid someone to bring a bulldozer to carve out a swimming area at the creek. David hoped to spend time up there under the redwoods sipping martinis, but he found chores to do. (His martinis were renowned for their strength: DRB never dared try one.)

Blackwell’s wonderful personality, his modesty and enthusiasm, his infectious smile and laugh, made him extremely popular both as a colleague and as a teacher. His graduate and undergraduate teaching (about which we can speak from experience) was outstanding. His ability to take complex notions and present them in a fresh and understandable way was exceptional.

Blackwell is survived by four of his eight children: Hugo of Berkeley; Ann Blackwell and Vera Gleason of Oakland; and Sarah Hunt of Houston, Texas. He was preceded in death by his wife, Ann Madison Blackwell, who died in 2006 after 62 years of marriage; and children Julia Madison Blackwell, David Harold Blackwell Jr., Grover Johnson Blackwell, and Ruth Blackwell Herch.

David R. Brillinger

J. W. Addison