Eugene Borisovich Dynkin (; 11 May 1924 – 14 November 2014) was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

and American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He made contributions to the fields of

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

and

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

, especially

semisimple In mathematics, semi-simplicity is a widespread concept in disciplines such as linear algebra, abstract algebra, representation theory, category theory, and algebraic geometry. A semi-simple object is one that can be decomposed into a sum of ''sim ...

Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Eucli ...

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi ident ...

s, and

Markov process In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, ...

es. The

Dynkin diagram In the Mathematics, mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of Graph (discrete mathematics), graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise in the ...

, the Dynkin system, and Dynkin's lemma are named after him.

Biography

Dynkin was born into a

Jew Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, religion, and community are highly inte ...

ish family, living in

Leningrad Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

until 1935, when his family was exiled to

Kazakhstan Kazakhstan, officially the Republic of Kazakhstan, is a landlocked country primarily in Central Asia, with a European Kazakhstan, small portion in Eastern Europe. It borders Russia to the Kazakhstan–Russia border, north and west, China to th ...

. Two years later, when Dynkin was 13, his father disappeared in the

Gulag The Gulag was a system of Labor camp, forced labor camps in the Soviet Union. The word ''Gulag'' originally referred only to the division of the Chronology of Soviet secret police agencies, Soviet secret police that was in charge of runnin ...

Moscow University

At the age of 16, in 1940, Dynkin was admitted to

Moscow University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches. Al ...

. He avoided military service in

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

because of his poor eyesight, and received his MS in 1945 and his

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

in 1948. He became an assistant professor at Moscow, but was not awarded a "chair" until 1954 because of his political undesirability. His academic progress was made difficult due to his father's fate, as well as Dynkin's Jewish origin; the special efforts of

Andrey Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet ...

, his PhD supervisor, made it possible for Dynkin to progress through graduate school into a teaching position.

USSR Academy of Sciences

In 1968, Dynkin was forced to transfer from the Moscow University to the Central Economic Mathematical Institute of the

USSR Academy of Sciences The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991. It united the country's leading scientists and was subordinated directly to the Council of Ministers of the Soviet Union (u ...

. He worked there on the theory of

economic growth In economics, economic growth is an increase in the quantity and quality of the economic goods and Service (economics), services that a society Production (economics), produces. It can be measured as the increase in the inflation-adjusted Outp ...

and

economic equilibrium In economics, economic equilibrium is a situation in which the economic forces of supply and demand are balanced, meaning that economic variables will no longer change. Market equilibrium in this case is a condition where a market price is es ...

Cornell

He remained at the Institute until 1976, when he emigrated to the

United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...

. In 1977, he became a professor at

Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

Death

Dynkin died at the Cayuga Medical Center in Ithaca,

New York New York most commonly refers to: * New York (state), a state in the northeastern United States * New York City, the most populous city in the United States, located in the state of New York New York may also refer to: Places United Kingdom * ...

, aged 90. Dynkin was an atheist.

Mathematical work

Dynkin is considered to be a rare example of a mathematician who made fundamental contributions to two very distinct areas of mathematics:

and

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

. The algebraic period of Dynkin's mathematical work was between 1944 and 1954, though even during this time a probabilistic theme was noticeable. Indeed, Dynkin's first publication was in 1945, jointly with N. A. Dmitriev, solved a problem on the

eigenvalue In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...

s of stochastic matrices. This problem was raised at Kolmogorov's seminar on

Markov chain In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally ...

s, while both Dynkin and Dmitriev were undergraduates.

Lie Theory

While Dynkin was a student at Moscow University, he attended

Israel Gelfand Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (, , ; – 5 October 2009) was a prominent Soviet and American mathematician, one of the greatest mathematicians of the 20th century, biologist, teache ...

's seminar on

s. In 1944, Gelfand asked him to prepare a survey on the structure and classification of semisimple Lie groups, based on the papers by

Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...

and

Bartel Leendert van der Waerden Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amste ...

. Dynkin found the papers difficult to read, and in an attempt to better understand the results, he invented the notion of a "simple root" in a

root system In mathematics, a root system is a configuration of vector space, vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras, especially the classification and ...

. He represented the pairwise angles between these simple roots in the form of a

. In this way he obtained a cleaner exposition of the classification of complex semisimple Lie algebras. Of Dynkin's 1947 paper "Structure of semisimple Lie algebras", Bertram Kostant wrote: Dynkin's 1952 influential paper "Semisimple subalgebras of semisimple Lie algebras", contained large tables and lists, and studied the subalgebras of the exceptional Lie algebras.

Probability theory

Dynkin is considered one of the founders of the modern theory of

es. The results obtained by Dynkin and other participants of his seminar at Moscow University were summarized in two books. The first of these, "Theory of Markov Processes", was published in 1959, and laid the foundations of the theory. Dynkin's one-hour talk at the 1962

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

Stockholm Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately ...

, was delivered by Kolmogorov, since prior to his emigration, Dynkin was never permitted to travel to

the West West is a cardinal direction or compass point. West or The West may also refer to: Geography and locations Global context * The Western world * Western culture and Western civilization in general * The Western Bloc, countries allied with NAT ...

. This talk was titled "Markov processes and problems in analysis".

Prizes and awards

*Prize of the Moscow Mathematical Society, 1951 *Institute of Mathematical Statistics, Fellow, 1962 *American Academy of Arts and Sciences, Fellow, 1978 *National Academy of Sciences of the USA, Member, 1985 *American Mathematical Society, Leroy P. Steele Prize for Total Mathematical Work, 1993 *Moscow Mathematical Society, Honorary Member, 1995 *Doctor Honoris Causa of the Pierre and Marie Curie University (Paris 6), 1997 *Doctor of Science (honoris causa) of the

University of Warwick The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands and Warwickshire, England. The university was founded in 1965 as part of ...

, 2003. *Doctor Honoris Causa of the Independent Moscow University (Russia), 2003 *Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, 2012

Publications

* * * * * * * *

Notes

External links

* *
Department listing at Cornell UniversityPersonal web pageCollection of interviews assembled by Dynkin
{{DEFAULTSORT:Dynkin, Eugene B. 1924 births 2014 deaths American atheists Fellows of the American Mathematical Society Members of the United States National Academy of Sciences 20th-century Russian mathematicians 20th-century American mathematicians 21st-century American mathematicians Soviet mathematicians Cornell University faculty Jewish American atheists Russian atheists Russian Jews Mathematicians from Saint Petersburg Algebraists Probability theorists Soviet emigrants to the United States Moscow State University alumni People from Saint Petersburg Measure theorists Russian scientists