This months issue of Notices of the American Mathematical Society (Vol. 62, No. 2, Feb. 2015 pp. 152 – 160) contains an interview with Professor Yakov Sinai. The interview occurred because he won an award called the Abel prize. The interview contains a large number references to A. N. Kolmogorov! Here are a few interesting quotes,
Regarding having Kolmogorov as an adviser,
Kolmogorov had many students, and I became one of them. His students had complete freedom to work on any problem. Kolmogorov loved to discuss their results. There were several cases when Kolmogorov wrote their papers in order to teach them how to write mathematical texts.
It seems that Kolmogorov did more than most to protect his students,
The other case arose with my entrance examination to graduate school. This exam was about the history of the Communist Party; I was very bad in this topic and failed the exam (I don’t want to discuss the details). But P. S. Alexandrov, who was head of the mathematical department at Moscow State University, together with Kolmogorov, visited the head of the Chair of the History of the Party and asked her to allow me to have another attempt.
Perhaps the most important excerpt might be,
At a certain time, Kolmogorov decided that the Soviet Union did not have enough applied statistics. He worked on theoretical statistics and found many beautiful and deep results, but he was not satisfied with the fact that the theorems in applied statistics were not used for practical purposes. (…) He wanted us to work on this problem and invited a very good geophysicist, Yevgeny Fyodorov, who was one of the main experts in this field. We were sitting there; Kolmogorov and Fyodorov were present. Kolmogorov said, “Look at these people; they prefer to write a paper for Doklady instead of doing something useful” (Doklady was the leading Russian journal). In our joint paper (by M. Arató, A. Kolmogorov, and me) written on this occasion, practically everything was done and written by Kolmogorov.
One might take away from this that we should focus on producing quality research, instead of focusing on placing articles in high level journals. This might be lost on many people today, especially with the publish or perish attitude so prevalent in academic circles. In the end creating high quality works, even just one over a lifetime, is more valuable than having countless articles in any publication. The point after all is to discover or explain something that has never been thought of before.