Gnedenko: On the past and future

The paper is published in:
Theory of Probability and Mathematical Statistics, 1995, vol. 49

... In April 1945 I was informed by wire on my nomination as a corresponding member of the Ukrainian Academy of Sciences. In June, my lectures at the University over, we packed our belongings and went to Kiev. We spent only several days in Kiev as the Academy Presidium sent me to Lvov to fulfill two main tasks: 1) organize the mathematics section at the Academy Branch and 2) to recreate the mathematical activities at Lvov University to the best of my abilities. My responsibility for the future was increased manifolds, as I knew quite well what a wonderful school of mathematics they used to have in Lvov before the war.

... by the time of my arrival S. Banach was extremely ill (throat cancer) and was living trough his last weeks. H. Steinhaus survived only because he had been placed at one of the monasteries. After the liberation of Poland he moved to Wroclaw and started energetically renewing the former strength of the mathematical school, which would be appropriate to call the Lvov mathematical school. In doing so he was counting on the gifted young people that came to Wroclaw University. To considerable extent he managed to put his idea into practice and Wroclaw became a mathematical center. This also included organization of publishing activity.

Mazur was the chairman of the Polish National Committee, which was in charge of repatriation of many dosens of thousands of Poles to Poland. Among the surviving former professors was also Zielinski --- an excellent teacher...

I had an excellent relationship with Banach, Mazur and Zielinski. Unfortunately I had no opportunity to work with the outstanding scientist S. Banach, as he died in August 1945 and was buried at Lychakovskoye Cemetery in Lvov. In commemoration of Banach one of the streets in Lvov was named after him...

...In 1950 the Presidium of the Academy of Sciences moved me to Kiev and I've got my first pupils at Kiev University. V. S. Korolyuk was the first among them and later V. S. Mikhalevich, A. V. Skorokhod, and G. N. Sakovich joined in...

In 1950 A. N. Kolmogorov organized a meeting in Moscow dedicated to the problems of quality control of mass industrial production. I took an active part in the sessions; since the war I have been interested in quality control problems and have myself beeof the problem.n engaged in the application aspect of this subject. As all the speakers were making assumptions concerning the distribution of the dimensions, determining the quality, I posed the problem differently: is it possible to find a parameter-free criterion, in which closeness of distributions could be estimated supposing nothing but their continuity? I involved my pupils --- V. S. Korolyuk, V. S. Mikhalevich, Ye. L. Rvachova, Ya. P. Studnev, I. D. Kvit, Kh. L. Berlyand and B. I. Yaroshevskii --- in solving this problem. I.~I.~Gikhman joined us as well. Later, the topic of his doctoral thesis grew out of this subject. My young people and myself were enthusiastically involved in solving our problems, for which purpose the transparent track method was developed.

At the same time I returned to my longtime interest in telephone problems. I delivered a course in queuing theory and started a seminar. In our work on these problems we were joined by my new pupils I. N. Kovalenko and T. P. Maryanovich. Many problems were arising and we readily shared them with anybody willing to participate in our research.

Apart from the University, I gave a course in queuing theory with possible military applications at the Kiev Higher Radio Engineering School. The students quickly familiarized themselves with the main aspects of the theory and noted their usefulness in solving practical problems. As a result they started to publish the lectures in separate issues. The first two issues were written by myself alone, and the third --- together with I. N. Kovalenko. These lectures became the basis for a book \cite 1, twice published in Moscow and twice --- in English --- in Israel and Switzerland. In addition to the mathematical theory, the wide range of its possible applications is represented in this monograph.

Speaking about books, my work on the textbook ``A Course of Probability Theory'' \cite 2 and the monograph ``Limit distributions for the sums of independent summands'' \cite 3 was already done in Lvov. The first of these books has had six Russian editions and at least eleven German and six American ones; it has been published also in Ukrainian, Japanese, French, Italian, Vietnamese, Chinese and Arabic languages. This book has been recommended as a main textbook in a number of countries, including England. More or less significant changes were introduced to every edition. In the last Russian, German and Arabic editions we put a large essay on the history of probability theory. This essay is based on the studies of the original works and in no way is a copy of any other writing.

The second of the books mentioned, which was written together with A. N. Kolmogorov , was given an excellent reception by specialists and also was translated into a number of European and Asian languages. Presently, its second, revised and updated edition, is being prepared.

I am still very disappointed that the work on applied statistics, computer engineering and medicine was not realized to the full extent. It was conducted in Kiev by a group including E. A. Shkabara , N. M. Amosov , M. A. Kulikov and myself in the field of objective diagnosis of heart disease, and in the construction of a machine capable of diagnosing a disease as the symptoms, observed by a doctor in a patient, are put in. Mathematical statistics was assigned a considerable role in this research. We built a model of the first machine, which showed that we are moving in the right direction. The demonstration of the possibilities of the machine was approved by a large number of physicians of various specialties, who took part in the lengthy demonstration of the machine and followed the subsequent discussions of its possibilities. E. A. Shkabara was the soul of this research. Owing to her energy, selflessness and courage the idea expressed by us at the sitting of the Ukrainian Republic Therapeutic Society was materialized. A. N. Kolmogorov enthusiastically supported our initiative. However, the situation around computational technology at that time, stopped the promising research work and forced me to leave Kiev. At that time we did not manage to put together even such a small group to continue this research in Moscow...