# Obituary: Eugene Dynkin 1924–2014

Eugene Dynkin, the A.R. Bullis Professor of Mathematics Emeritus at Cornell University, died November 14, 2014, in Ithaca, NY. He was 90. He is survived by his wife, Irene; a daughter, Olga Barel; three grandchildren; and seven great-grandchildren.

Evgenii Borisovich Dynkin was born in Leningrad (now St. Petersburg) in 1924. When he was 11 his family was exiled to Kazakhstan and, two years later, his father disappeared in the gulag. On accepting the AMS Leroy P. Steele Prize, Dynkin said it was almost a miracle he was accepted at Moscow University at the age of 16 to study mathematics. There, he attended the seminars of I. Gel’fand and A. Kolmogorov.

Early in his career, Dynkin made outstanding contributions to Lie theory and introduced the diagrams now known as Dynkin or Coxeter–Dynkin diagrams. This work found applications in the study of elementary particle physics. He also discovered the explicit formula for the universal coefficients of the Baker–Campbell–Hausdorff series describing the logarithm of the product of two exponentials. He kept a keen interest in Lie theory throughout his career, which he described as “Seventy Years in Mathematics”. Several of his Moscow former students became worldwide leaders in Lie theory and Algebra.

Dynkin made even more outstanding contributions to Probability Theory where he played a major role in the development of the theory of Markov Processes. His books, *Foundations of the theory of Markov processes* (1959) and *Markov processes* (1963), became highly influential. Among several important conceptual breakthroughs, Dynkin can be credited with the idea of looking at a Markov process as a single stochastic process under a collection of probability measures corresponding to the possible initial values, the introduction of the shift operators, and the rigorous formulation and proof of the strong Markov property.

At the 1962 International Congress of Mathematicians in Stockholm, Dynkin’s plenary lecture “Markov Processes and Problems in Analysis” was read by Kolmogorov. On each of the three occasions Dynkin was invited to speak at the International Congress of Mathematicians (Stockholm, Nice and Vancouver), his lecture was delivered by a colleague as he was not authorized to leave the Soviet Union.

In 1968, Dynkin’s work at the University of Moscow was interrupted and he became a senior scientist at the Central Economics and Mathematics Institute of the USSR Academy of Sciences. There, he attracted young researchers and developed results in mathematical economics regarding economic growth and economic equilibrium under uncertainty. It was for this work that he was invited to speak at the 1974 International Congress of Mathematicians in Vancouver.

At the end of 1976, Dynkin left the Soviet Union and immigrated to the United States. He found a new home in Ithaca, attracted by Cornell established tradition of excellence in Probability Theory and Mathematical Statistics. He was proud to have become part of this long tradition. At Cornell, he pursued his famous work on the relation between occupation times of a Markov process and Gaussian random fields, with striking applications to multiple points of Brownian motion, before turning to the development of the theory of superprocesses, a class of measure-valued Markov processes which gives probabilistic solutions to certain nonlinear PDE’s. He remained active in mathematical research until his death.

Dynkin was a courageous, organized and determined human being who dedicated most of his life to the study of mathematics and to the mathematical community. Many of his ideas and contributions were foundational in nature and have gained a permanent place in mathematics, influencing the work of many others. The Dynkin Collection of mathematics interviews (available at http://dynkincollection.library.cornell.edu/) contains interviews which were recorded over the span of more than fifty years, starting with H. Cramér in 1955. It illustrates Dynkin’s interest and faith in the mathematical community at large. He worked tirelessly to make sure this remarkable collection becomes available to all via the World Wide Web. Most important to him was his role as a mentor and supporter of young talents. Indeed, Dynkin has over 500 mathematical descendants. Through his unique work with talented high school students in Moscow mathematical circles, his Moscow seminar, and his outstanding lecturing and teaching, he touched and transformed the life of many an apprentice mathematician.

Dynkin’s contributions were recognized by numerous distinctions. He received the Prize of the Moscow Mathematical Society in 1951 and the Leroy P. Steele Prize for life time achievement from the American Mathematical Society in 1993. He was a fellow of the Institute of Mathematical Statistics, of the American Mathematical Society and of the American Academy of Arts and Sciences. He was a member of the National Academy of Sciences of the United States.

*Written by Laurent Saloff-Coste
Cornell University*

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