Saturday, May 8, 2010

Seventy years in mathematics

While yesterday Cornell students celebrated Slope Day - the last day of classes for 2009-10 academic year, mathematicians gathered in 251 Malott Hall for the lecture "Seventy years in mathematics" which was also an opening for the 48th Topology Festival..

Audience was certainly more than 100 people, all seats were full and many were standing or sitting simply on a floor.

We all came to listen to a man who has spent 70 years in mathematics.
Here he is - Prof. Eugene Dynkin or as his original Russian name sounds Jevgenij Borisovich Dynkin. In couple days - on May 11 he will turn 86 and he is no retiring. While people were looking for seats in the packed room he was quietly looking through his slide and concentrating for his lecture as he had done countless times in his life.

He was born in Leningrad, now St. Petersburg in 1924 in Jewish family. In 1935 his father was declared "an enemy of the people", family was exiled to Kazahstan, and in 1937 his father was arrested. As his mother was told -"he was sentenced for 10 years without any rights of correspondence". Only after perestroika they learned that it was a code name used for those who were shot immediately. His mother with a teenage boy managed to return to Moscow and he graduated a year early from a high school with all A in his high school diploma. Holders of such diploma did not have to pass entrance exams in the university but they had to have an interview. Dynkin was lucky to have an interviewer Alexander Gelfond who immediately recognized teenagers talent in mathematics. 
In 1940 he became a student of the Department of Mechanics and Mathematics in Moscow State University or as it is known in the whole world - Mekhmat in MGU. From this year he counts started his life in mathematics.
Prof. Sofja Janovskaja noticed the talented freshman and took care of him, including taking him and his mother to live with her, so that he would be able to concentrate on mathematics.
And he really started to work very seriously. Two most memorable courses from the freshman year in MGU for him are linear algebra which Israel Gelfand taught in a spirit of functional analysis, and Kolmogorov's lectures in set theory. As Dynkin remembered - Kolmogorov had an obvious ability to overestimate his students. Dynkin admitted that he had trouble following Kolmogorov's lectures, but he decided to work harder. So he found Hausdorf's monograph on a set theory and studied it so that he would be prepared for the next lecture.
When Nazi German attacked Soviet Union in 1941, Dynkin evacuated to Perm (then called Molotov) and continued his studies there was couple years. He returned back to MGU in 1943, and that was a time when Gelfand seminars started.  

In one of those seminars Dynkin had to present something from Van der Warden's monograph but he could not understand the material. He started to approach in his own way, and the result was what is now called Dynkin Diagrams. When Dynkin in 1976 left Soviet Union, all algebra textbooks were edited to  "diagrams of simple roots" to erase his name. When asked how did he come with this idea he said - it was just so much simplier! This was not the only result he talked in his lecture about which I noticed that a great role to come up   with simple idea was his excellent background in elementary geometry. Even now he said - but those are the things that everybody knows! Not so true, unfortunately, for graduates of American high schools...
Until he arrived in USA, he did not know that these diagrams are widely used by physicists - in 1960-70 they were playing a significant role in mathematical aspects of particle physics.

The other seminar Dynkin started to attend as an undergraduate was led by Kolmogorov on Markov Chains.
This was another result obtained by an undergraduate Dynkin - Kolmogorov in 1945 had posed a problem of describing all eigenvalues of nxn stochastic matrices. Dmitriev and Dynkin partially solved it. The rest of it was added by the very talented student of Dynkin's - Karpelevich. More about him later. As Dynkin noted here about Dmitriev - Andrei Sakharov in his memirs called Dmitriev a mathematician who could solve any mathematical problem need to be solved when they were developing Soviet hydrogen bomb.

Eventually (with great help from Kolmogorov to overcome anti-semitism) Dynkin became Kolmogorov's graduate student and completed his PhD thesis Explicit form of Campbell-Hausdorf formula and its applications in 1948. He became an assistant professor in Mekhmat. he defended his second thesis in 1951 but could become a full professor only after Stalin's death when the situation in Russia eased. He was a professor in Mekhmat until 1968 when he was forced to resign for political reasons - he was transferred to the Moscow Central Institute of Mathematics and Economics. (In 1967 Dynkin signed a petition letter in defense of Yuri Galanskov and Alexander Ginzburg. ) Dynkin was invited to give a lecture in International Congress of mathematicians in 1962 held in Stockholm but he was denied visa, so he asked Kolmogorov to read his talk at the congress 

An hour has already passed - the usual time slot for talks -but Professor Dynkin realizes that he has covered only the first 15 years in mathematics. he has tried to explain his work in Soviet Union and his results very accessibly, mainly speaking to the large crowd of young people in the audience. 

About his move to USA he says simply - in 1976 I became a professor of mathematics in Cornell University. And then he adds - so people here know what I have been doing, let us just summarize 3 directions:
1. Markov processes as a tool in theory of random fields - this was inspired by quantum theory.
2. Superbrownian motion and its applications to partial differential equations.
3. In 2007 return to Lie algebras with enhanced Dynkin diagrams and Weyl orbits.
He wrote a monograph but at the end there was still an open question left. In couple years a very talented mathematician Benoit Mselati who he heard later became a banker, no word is he as successful in banking as in math yet.
Topology festival people are becoming impatient because the time of their banquet is approaching, and Dynkin says that his mathematical talk is about his 70 years is over, so people who have to leave can leave. But those who are interested to see some pictures can stay a bit. 

The second half of his talk is something about which his face really lits up - he can talk about his students and it is obvious that he is very proud about their achievements. Dynkin was in his senior year when he became a leader of his "math circle" - selected students from Moscow high schools who were interested and talented in mathematics. As he put it                      already earlier - there were two activities where people could feel free under Soviets - math and chess.

Dynkin apologizes for the quality of the slide but these are some of his first students. First from the left is F.I. Karpelevich (1927-2000) - one of his brightest students ever.

When Karpelevich graduated from high school he told Dynkin that he is not going to apply to university but instead will go to work in a factory. Dynkin was very disappointed and asked why, so Karpelevich explained that his family is very poor. He had two other siblings and a mother who cared for them as a single parent working a low payed job in a factory. (from Lie Groups and Symmetric Spaces:in memory of F.I.Karpelevich,vol.210)

In 1947 several participants of this first Dynkin math circle were admitted to the Department of Mechanics and Mathematics at Moscow State University and the circle transformed into the seminar "Selected Problems of Contemporary Mathematics" for freshmen. Under various names this seminar continued for several years. In 1955 it was divided in two "daughter seminars" - seminar in algebra and seminar in probability theory. Participants of these seminars were encouraged not only to solve various problems (several of them were previously unsolved problems) but also to prepare their results for publications. Karpelevich made his first serious contribution in mathematics when he was sophomore. Kolmogorov in 1945 had posed a problem about n x n stochastic matrices which partially was solved by Dmitriev and Dynkin, Karpelevich managed to find a final solution for this problem. His result was published in Russian and then translated in English and published in AMS Notices. He was one of the brightest students in his class, however after he graduated from the university in 1952 there was no chance for him to be admitted in graduate school because of him being a Jew, the State commission responsible for assigning jobs to university graduates ordered him to go and teach mathematics in Novocherkassk (at the level of community college). He became seriously ill there and was permitted to return to Moscow a year later. With his return he was able again to join Dynkin's seminars and eventually to complete his PhD work.

I am recognizing a teenager second in a lower row - I knew him in 1980 as Professor Vladimir Andrejevich Uspenskij when I was taking his class in algorithm theory in MGU during a semester I was there.

Dynkin is recognized by many of his students as a wonderful and engaging teacher, there are many mathematicians who grew out of his math seminars for high school students. It was his great disappointment to find out that this practice did not work when he arrived in Ithaca. He tried to organize a math circle in Ithaca High School in 1977 but students could not stay after school because they had to have their parents to drive them if they missed school bus. There was not possible to keep in touch after they graduated from the school because they went to different places. I can share this sentiment with Dynkin - there are nothing like bonds between students and teachers in former Soviet Union. It was something I missed in US also.
But that is another story.
This was a story about the man who yesterday celebrated his seventy years in mathematics.
Happy 86th birthday, Evgenij Borisovich!


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  2. Tried to listen to the podcast but due to poor quality and accent of prof Dynkin, I cannot make it. I am thankful that you summarized the talk well for me to understand his achievements.

    I studied math in the U and am still interested to know more about the current trends and developments