Problems of Information Transmission, Vol. 38, No. 1, 2002, pp. 96–97. Translated from Problemy Peredachi Informatsii, No. 1, 2002, pp. 108–110.
Original Russian Text Copyright
2002 by the Editorial Board.
On the 100th Anniversary since the Birth
of Andrei Nikolaevich Kolmogorov
In Nikolaev, en route
March 2, 1962
I began editing your paper of last year
and found plenty of unﬁnished things there. For
example, when building spirals (1) one has to explain why each component of a level curve reaches
the next C
Such an explanation is possible (for a suﬃciently small
): in case (2) it is possible to draw a com-
ponent (punched line) around a component of level curve
passing through P
, which will have a non-connected
intersection with C
. But nothing has been said about it!
There are many other imperfections as well.
As far as I can see, they can all be ﬁxed but there will
be a lot of work here.
This will be a good paper after all (in the sense that the
arguments are interesting and neat). Of course, it would be
better if you wrote it yourself at the proper time. However,
ﬁrst, Volodya Tikhomirov, whom I have considered the se-
nior person responsible for you, failed me. Then I broke
away from this subject completely.
Now I feel that I have been a bad supervisor of your
work (and the work of others). As you know, there were
“objective” reasons for that. Not only have I been over-
whelmed by an excessive amount of duties, but also my in-
terest in reﬂecting on quite general and semi-philosophical
matters took more energy and time from me than one might
In such a development of the most general views, the
outcome of your eﬀorts consists not in a formulation of pre-
cisely stated “results” but rather in a general reconstruction of your mind and in placing things
there in a proper perspective. That is why it may turn out that one has not discovered anything
This letter was written by A.N. Kolmogorov to L.A. Bassalygo on board the steamboat “Sergei Kirov”
when Kolmogorov was on his way to India. He was the scientiﬁc supervisor of Bassalygo, then a 5th year
student at the Mathematics and Mechanics Department of Moscow State University.
The paper is “On Representation of Continuous Functions of Two Variables by Means of Continuous
Functions of One Variable.” It was published in the journal Vestnik Mosk. Gos. Univ., Ser. 1, Mat.,
Mekh. (1966, no. 1, pp. 58–63) and shows that for any three continuous on a square functions ϕ
there is a continuous function ϕ(x, y) that cannot be represented as
(x, y)) for any continuous
,k=1, 2, 3.
2002 MAIK “Nauka/Interperiodica”