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Vidmantas Kastytis Bentkus, 1949 – 2010
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David Blackwell, statistician, probabilist, game theorist, mathematician, Professor Emeritus at the University of California at Berkeley and much more died July 8, 2010. He was born April 24, 1919, in Centralia, Illinois. His father, Grover Blackwell, worked as a hostler (moving steam locomotives in and out of the roundhouse) for the Illinois Central Railway, a job David describes as "the best job that a black man could get on the Illinois Central Railway." His mother, Mabel, raised David and his three siblings, ran the house and two rental properties and encouraged David toward studying business.
David finished high school at age 16, having been accelerated in elementary school, and then in 6 years completed three degrees (A.B., A.M. and Ph.D.) at the University of Illinois. After finishing his Ph.D. on Markov chains under Joe Doob, David accompanied Doob to the Institute of Advanced Studies at Princeton in 1941, supported by a Rosenwald Fellowship. That year, he applied for jobs to 105 African-American colleges; he took an automobile tour to 30 of them, arriving unannounced and ‘naively’, as he described it, simply asking to see the Mathematics department chair to ask for a job. He got 3 offers and took the first, going to Southern University in Baton Rouge, Louisiana. He spent one year there, one year at Clark in Atlanta and then moved to Howard University for 10 years from 1944 to 1954. At Howard, he became chair of the department in 1947, at the age of 28! In 1954, David was recruited to the Mathematics department at Berkeley by Jerzy Neyman, who had tried to get David for Berkeley in 1942 but was thwarted at that time by resistance to appointing a African-American man to faculty. David remained at Berkeley for the rest of his career, chairing the Statistics department from 1957 to 1961; he took over as chair from Neyman only a year after the creation of the department and only three years after coming to Berkeley. It is clear that David's ability to get along with everyone was a key factor in his selection as chair.
David once said “Basically, I'm not interested in doing research and I never have been. I'm interested in understanding, which is quite a different thing. And often to understand something you have to work it out yourself because no one else has done it.” David worked out many things, solved many problems, shone a bright light through hard ideas and illuminated the intellectual landscape for many. David's search for clarity produced a great body of influential papers. They were very sharply focused; for instance, David particularly liked his two-page paper “Infinite games and analytic sets” in the Proceedings of the National Academy of Science which linked game theory and Kuratowski's reduction theorem in topology. With Ken Arrow and Abe Girshick, David wrote an influential paper on sequential analysis. His 1954 book, Theory of Games and Statistical Decisions, written with Girshick had enormous impact. The Rao-Blackwell theorem was extremely influential. David acknowledged Rao’s priority though it appears that David’s publication drew real attention to this very important idea. His renewal theorem (which is essentially a local limit theorem – much more subtle than the global result usually called the elementary renewal theorem) is very widely cited and generally is known as Blackwell's renewal theorem. A simple web search shows there are many papers following up on this work and the topic remains active today. His clever use of the law of large numbers and its converse to prove Wald’s identity is much admired. David worked on Markov chains, on measure theory, on Shannon information theory, on Bayesian methods, on dynamic programming and on many other problems – wherever he found beautiful mathematics.
David’s work was recognized very widely. He had 12 honorary degrees from institutions including Howard, Harvard and Yale. The Institute for Operations Research and Management Sciences made him the fifth winner of the John von Neumann Theory Prize for his work in dynamic programming. He was Rouse Ball lecturer at Cambridge (where he was pleased to say he had heard of W. W. Rouse Ball through Rouse Ball's book of mathematical recreations before he ever heard of Cambridge). He was Wald Lecturer for the IMS, winner of the Fisher Award from COPSS and elected an Honorary Fellow of the Royal Statistical Society. He was elected to the American Academy of Arts and Sciences and he was the first African-American member, and for many years the only African-American member, of the National Academy of Sciences in the United States.
David served the statistical community on many occasions. He was the second President of the Bernoulli Society from 1975 to 1978, taking over from David Kendall. He served as President of the IMS, as Vice-President of the American Statistical Association, as Vice-President of the International Statistical Institute, and for three years as Vice-President of the American Mathematical Society.
It is hard to document with precision one of the most central facets of David's career: his teaching. I was David's Ph.D. student – number 62 of 65 listed on the Mathematical Genealogy web site. I remember well the chair outside his office and waiting for our weekly meetings. David was invariably friendly and approachable but it took me years to appreciate properly the role he took in supervising. I now know that David helped me find ideas and approaches without forcing them on me. It took ages for me to see how to prove two sigma fields were different and even longer to recognize the conversation where David planted the key idea in my head.
It was hearing David’s lecture which drew me to ask to be his Ph.D. student. I suppose those lectures drew many others. The 65 students I mentioned graduated between 1955 and 1981, all from Berkeley, so David graduated well over two a year; those lectures must have drawn many students to him. Everyone who was privileged to hear him speak knows that his clarity in thought and in writing was brilliantly matched to razor sharp clarity in presentation. The most difficult ideas were made strikingly clear, and even seemed easy, during his talks. Trying to say it yourself, to someone else, made it obvious that you had to get the ideas in the perfect order to make them that easy.
As an African-American man, race necessarily played a big role in David's life, though he was not always aware how big a role at the times things happened. While David went to an integrated school in Centralia and the University of Illinois was integrated, David's fraternity at Illinois was certainly not. When David went to the Institute of Advanced Studies, he received an honorary appointment as assistant professor at Princeton. That appointment was resisted by the president of the then all white (and all male) institution and there was a behind the scenes struggle to get the appointment; David learned of this struggle only later. In any case, the New York Times reports that David “was denied the right to attend lectures or do research at Princeton University”. The role of race is clear, of course, in the fact that David applied only to African-American colleges. David was told by Neyman that the position at Berkeley in 1942 had gone to a woman because of the draft; he only learned later of the internal struggles over his potential appointment. In spite of all this, it is clear from various interviews with David that race was not a great motivating issue in his life.
There is a wealth of information about David available on the web. You will be particularly rewarded by a visit to www.visionaryproject.org/blackwelldavid/ where the National Visionary Leadership Project has ten clips from a video interview which is now lodged in the Library of Congress. Also, very rewarding are interviews with Morris de Groot in Statistical Science and with Nadine Willmot at www.archive.org/details/blackwelldavidor00oralrich.
David is survived by his son, Hugo Blackwell, his daughters, Ann Blackwell, Vera Gleason and Sarah Hunt Dahlquist, his sister Elizabeth Cowan and 14 grandchildren. He leaves a great legacy to many communities: I and many others deeply regret the passing of this great mind and human being.
David Lockhart, Burnaby
Vidmantas Kastytis Bentkus, the head of the Mathematical Statistics Department in the Institute of Mathematics and Informatics, Vilnius, died on June 3, 2010, from a heart attack.
Vidmantas Kastytis Bentkus was born in Šilute (Lithuania) in 1949. In 1967 – 1970, he was a student of the Mathematical Department at the Vilnius University; in 1976 a student of the Mathematical- Mechanical Department at Moscow State Lomonosov University. In 1977, he received a doctor's degree from Moscow University. In 1986, he received the Habilitated Doctor of Sciences degree from Vilnius University. He was working at the Mathematical Statistics Department of the Institute of Mathematics and Informatics as a principal research associate.
Vidmantas’ research interests and achievements were impressive. He started his scientific carrier in the area of functional analysis and infinite dimensional partial differential equations and later moved to the area of limit theorems of mathematical statistics and probability theory. During the last 10 – 15 years, he was working on finding an optimal and most precise form of inequalities for sums of independent random variables. He is an author or a coauthor of more than 90 scientific papers published in the most prestigious science journals worldwide.
In 1987 and 1999, he was awarded the Lithuanian National Prize of Science. In 1990 – 1991, he was a fellow of the Alexander von Humboldt Stiftung in Germany.
