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
... by the time of my arrival S. Banach was
extremely ill (throat cancer) and was living trough his last
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,
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
...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
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 ---
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...