David Blackwell

American mathematician

• Born: April 24, 1919; Centralia, Illinois
• Died: July 8, 2010; Berkeley, California

Twentieth-century African American mathematician David Blackwell’s research encompassed several areas, including probability theory, statistical theory, and game theory. He published more than ninety papers and several textbooks in various areas of mathematics and received international recognition for his work. Blackwell was the first African American mathematician elected to the National Academy of Science.

Primary field: Mathematics

Specialties: Decision theory; information theory

Early Life

David Harold Blackwell was born on April 24, 1919, in Centralia, Illinois. He was the eldest of Grover and Mabel Johnson Blackwell’s four children. Blackwell’s father worked as a hostler for the Illinois Central Railroad, and his mother was a housewife. Although neither parent had completed high school, Blackwell’s paternal grandfather had been a teacher and owned an extensive library, which included the first algebra book Blackwell ever encountered. As a child, Blackwell also spent time in his uncle’s grocery store, where he learned to read by studying the words on seed packages.

Although many U.S. public schools were racially segregated during the 1920s and 1930s, Blackwell attended integrated schools near his Centralia home and was drawn to mathematics through high school math club activities, games, and special problem-solving challenges. In 1935, at the age of sixteen, Blackwell entered the University of Illinois at Urbana-Champaign. Although his career goal at the time was to become an elementary school teacher, he postponed taking the required education courses. Eventually studying analysis, Blackwell began to envision himself teaching high school mathematics.

After his freshman year, Blackwell supported himself by working as a dishwasher, waiter, and a college laboratory cleaner. He excelled academically and also served as president of the mathematics club and became a member of the Alpha Phi Alpha fraternity, Tau chapter. Blackwell was awarded university fellowships and earned his undergraduate degree in mathematics in 1938, his graduate degree in 1939, and his doctorate in 1941. Blackwell’s doctoral thesis, sponsored by Joseph Doob, was on Markov chains.

In 1941, Blackwell was awarded a Rosenwald Postdoctoral Fellowship, a prestigious one-year appointment to the Institute for Advanced Study (IAS) in Princeton, New Jersey. Although his career goal by this time was to be a college professor of mathematics, the fellowship was actually the beginning of his career as a prominent statistician.

In 1944, Blackwell married former student Ann Madison. During their sixty-two-year marriage, they raised three sons and five daughters.

Life’s Work

Blackwell’s IAS fellowship offered an honorary faculty position at Princeton University, but there was initial controversy over the appointment because of his race. Blackwell was not made completely aware of the dispute between the university president and the IAS director, and he was therefore able to concentrate on his steady career progress instead.

At the IAS, he met mathematician and computer scientist John von Neumann and attended lectures by the mathematical statistician Samuel Wilks. Among Blackwell’s colleagues were Theodore W. Anderson, George W. Brown, Alexander Mood, Jimmie Savage, and Henry Scheffé.

While at the Institute, Blackwell began to search for a college-level teaching position, and he assumed he would have more employment opportunities at black universities. He sent applications to all 105 African American colleges and universities operating at that time and was offered a post at the Southern University at Baton Rouge in Louisiana, where he taught from 1942 to 1943. Blackwell taught the following year at Clark College in Atlanta, and, except for a sabbatical to California’s Stanford University as a visiting professor from 1950 to 1951, Blackwell taught at Atlanta’s Howard University from 1944 to 1954 and was head of the mathematics department for seven of those years.

Between 1942 and 1945, Blackwell published three papers expanding his research on Markov chains: “Idempotent Markoff Chains,” “The Existence of Anormal Chains,” and “Finite Non-Homogeneous Chains.” His later work encompassed a variety of areas, including statistics, probability theory, game theory, set theory, dynamic programming, and information theory.

At a 1945 conference of the Washington, DC, chapter of the American Statistical Association, Blackwell attended a presentation by statistician Meyer Abraham Girshick (1908–55) on Abraham Wald’s equation, used in probability theory. Blackwell later produced a counterexample to Wald’s equation and sent it to Girshick. Although the counterexample was incorrect, Girshick contacted Blackwell to meet to discuss the information. The meeting was the start of a lifelong friendship between the men and sparked Blackwell’s interest in statistics. In 1946, Blackwell introduced a new original proof of the equation in his first statistical paper, “On an Equation of Wald.”

Blackwell worked with Girshick and Jimmie Savage at the RAND Corporation as a summer consultant from 1948 to 1950 and was among the early developers of game theory, focusing on two-person, zero-sum games. Blackwell and Girshick collaborated on the graduate-level textbook Theory of Games and Statistical Decisions, published in 1954, where they introduced the study of duels in game theory. Blackwell later published additional research on sequential games. Meanwhile, Savage introduced Blackwell to the statistical work of Thomas Bayes, which impressed Blackwell who then incorporated the Bayesian approach into his research.

From 1954 to 1955, Blackwell was a visiting professor at the University of California, Berkeley, where the mathematics department had just been divided to create a Department of Statistics. Blackwell then joined the new department and worked as a statistics professor from 1955 until his retirement as a Distinguished Professor of Mathematics and Statistics in 1989. Blackwell also chaired the Department of Statistics from 1957 to 1961, and he served as assistant dean of the College of Letters and Science from 1964 to 1968.

From 1959 to 1960, the Mathematical Association of America selected Blackwell as a visiting lecturer in a program to enhance undergraduate mathematical education. He also traveled to Uganda in 1962 and Kenya in 1965 to participate in United Nations–supported conferences promoting the study and teaching of mathematics. In 1965, Blackwell became the first African American mathematician elected to the National Academy of Sciences.

Blackwell wrote a notable paper, “Infinite Games and Analytic Sets,” in 1967 in which he gave a game theoretic proof of the Kuratowski reduction theorem. Because Blackwell used an application of game theory to prove a theorem in topology, he established a connection between previously unrelated mathematical areas. In 1968, Blackwell was elected to the American Academy of Arts and Sciences. The first Bayesian-oriented statistics textbook, Blackwell’s Basic Statistics, was published the following year.

During a two-year hiatus from UC Berkeley that began in 1973, Blackwell served as director of the University of California Study Center for the United Kingdom and Ireland and became a W. W. Rouse Ball lecturer at Cambridge University.

Blackwell was an active member of several professional organizations and received many awards and honors. Among his awards were the 1979 John von Neumann Theory Prize and the 1986 R. A. Fisher Award from the Committee of Presidents of Statistical Societies.

David Blackwell died in 2010 at the age of ninety-one.

Impact

David Blackwell’s mathematical expertise covers statistical decision theory, Bayesian statistics, probability and dynamic programming, and information theory. His primary research in probability includes a theorem that bears his name: Blackwell’s renewal theorem. He founded the theory of the comparison of experiments, a key concept of mathematical statistics.

Blackwell’s scholarly research and professional activities brought him widespread recognition. He was awarded twelve honorary doctoral degrees, and he served as president of the Institute of Mathematical Statistics, the International Association for Statistics in the Physical Sciences, and the Bernoulli Society for Mathematical Statistics and Probability. He served as vice president of the American Mathematical Society, the International Statistical Institute, and the American Statistical Association.

In 2000, New York’s Cornell University established a lecture series and conference to honor Blackwell and Richard Tapia, a Rice University professor of computational and applied mathematics. Formally named the David Blackwell and Richard Tapia Distinguished Lecture Series in the Mathematical and Statistical Sciences, it continues to provide a forum for the research of African American, Latino, and American Indian scientists working in the fields of mathematics and statistics.

The Blackwell-Tapia Prize was established in 2002 by the Mathematical Sciences Research Institute in Berkeley and by Cornell University. The prize is presented to a mathematical scientist who not only has contributed significantly to his or her field of research, but who has also significantly addressed the problem of the underrepresentation of minorities in mathematics.

Bibliography

DeGroot, Morris H. “A Conversation with David Blackwell.” Statistical Science 1.1 (1986): 40–53. Print. Interview covering Blackwell’s accomplishments, favorite papers, influences, and views on the field of statistics.

Ferguson, Thomas, Lloyd Shapley, and James MacQueen, eds. Statistics, Probability, and Game Theory: Papers in Honor of David Blackwell. Hayward, CA: Inst. of Mathematical Statistics, 1996. Print. Research papers extend Blackwell’s work in various areas of mathematics. Biography, bibliography.

von Neumann, John, and Oskar Morgenstern. Theory of Games and Economic Behavior, Sixtieth Anniversary Edition. 1944. Introd. Harold Kuhn. Princeton, NJ: Princeton UP, 2007. Print. Features then ground-breaking mathematical theory of economic and social organization upon which modern game theory is based.