*May
8.*

During this week nothing particular has happened. Again I took the exam
in

astronomy, but the professor told me that he could not give me more than
four.

It so discouraged me, that I did not take any more exams. Now I am going
to leave [...] At the vacation I plan to
train my dog Milord.

Recently I have made an interesting observation. For a whole week I have
been

in a special mood, being dissatisfied with myself. But it can be well understood.
My condition is rather uncomely when seen from outside! The exams I do not
take, have tried to take one, but failed. All these things are strongly
dispiriting me [...]

* * * * * * * * * * *

**1888**

* Sunday, December 4.*

Last Friday I had my debut at the mathematical circle and together with other
observations reported a proof of one property of Bernoulli numbers, which I
propose.

For introduction I gave the definition of according to
Bernoulli's method.

Professor Markov treated my presentation very favourably for me, and
when one

of the students tried to raise objections, he almost snubbed him. Once I
had

proposed him a method of differentiation at proving some theorems, and
he

recalled it now and said that it could be especially appropriate here. I
replied him I had not wanted to come out of the frames of finite differences and
therefore had changed the method of proof.

When the opposed student remarked that something could be changed in the
proof, he almost cried: "What could be changed? There is another method,
and the author of this one knows about it, but he prefers on some reasons
another method, proposed by him."

When I expounded the method of proof of properties of Bernoulli numbers,
he said in conclusion that he recalled having seen in memoirs of either Academician
Ostrogradsky or Melmsten an indication for a possibility of such a proof and he
advised me to have a look at them […]

*Friday,
December 23*.

A strange thing, yesterday I could not make out what was happening to
me. On Wednesday I had a talk with my friend Smirnov about one theorem which I was
so eager to prove and which I had mentioned in my diary. I told him I did not
imagine how possible it was to be proved without inventing some way, and almost
on the same day, without inventing, I proved it! What a lot of work had I spent
for proving other theorems and it so often came to nothing, but here I up and
it's ready! Only a single thought was needed, and then it did not cost anything
to complete.

I should be rejoiced and triumphant, but I was feeling crest-fallen all
the day and instead of going on with my investigation I went to the opera for
"Traviata". My comrade told me that I in my state attracted attention
of his neighbour who told his companion: "Here is a student who looks like
a martyr". Indeed I was jaded completely. Whatever posture I would take I
could feel nothing but fatigue. And today this depressed mood is prevailing.
For the whole day I did not manage to do anything, but it was already because I
was hindered.

The obtained result is the following: I've shown that if the index is a prime number,
then the numerator of is divided by

[This
assertion was stated by Adams (J. reine angew.
Math., **85**). Adams also indicated the
following proposition in his paper: "If is a prime divisor of and it is not a factor
of the denominator of the -th Bernoulli number, then
the numerator of is divided by ". In this connection Adams
noted: "I have not succeeded however, in
obtaining a general proof of this proposition, though I have no doubt of its truth".
In his next notation on December 25 (see below), Voronoi stated that he had
proved this second Adams' proposition and gave
his proof.]

*Sunday,
December 25.*

Yesterday I completed my proof of the Adams
theorem, who had told about the last theorem that he could not prove it, but
did not doubt it is true. I proved it in a quite strict manner, so that what
had been outlined before was a particular case, but I had to add one lemma
[...]

The proof of this lemma is not quite worked out, because it is not refined.

( Just now I thought of another) [...]

*December
31, 1888.*

[...] Well, this year has passed not in vain for me! I have been working
a lot,

a big lot, and made certain that I can work and, it seems to me,
succeeded in making certain of it others.

At this time last year I had expressed about it in the diary only a
timid wish, and now I see it has come
true: the thing, which I was afraid of, does not exist: I know, I do believe,
that on the ground of science work and
only on it I shall find my good luck [...] I am not a poet and I do not know the inspiration which poets describe, but I know minutes not of
complacency, not of pride ─ they all come later ─ but moments when the mind
completely grips the idea which before kept slipping off like a small ball. Then I would forget about
my existence [...]

I firmly believe that the new year will bring me still more joy in this respect,
because I noticed that for my latest successes I am obliged to a habit of
thinking without a pen and paper. All assertions, which I proved, occurred to
me quite independently, and I had only to verify them. I hope this habit to
think in such a way will stand me in good stead [...]

* * * * * * * * * * *

**1889**

*Monday, January 9, 1889*.

I did not want to begin my diary until I knew for certain that the
paper, submitted by me to Markov, had been approved by him. I could not write anything,
as I did not want to write about it and could not about anything else. Yesterday I called on Markov and now feel
quite quiet.

He told me that if the literature on this problem were looked into, my paper
could be published, say, in "Communications of Kharkov Mathematical Society".
I told him I would like to wait for a while, as I was going on with my work. He
told me he had looked through the table of Bernoulli numbers and doubted if it
is possible to find the law of numerator, because it presents very big simple
quantities. On response I presented the theorem which introduced these simple quantities
[...]

Markov was greatly interested by it, as the theorem which I had
presented to him before gave nothing of the kind. I told I had no so far the
full proof of that theorem, but I hope to prove it soon [...]

I came home feeling quite jaded, unwilling to do anything, and I felt at
this time the whole burden of solitude, but the habit insisted on its own, I
went to bed soon, and today from 6 o'clock I have been working to prove that
proposition. If anybody asked me, where I had taken that theorem from, I should
certainly find difficulty in replying. I did not invent it, only proved, but in
leaps, and filled gaps between them by imagination. But then I checked it on
very big examples and never got a contradicting result. Even today when I felt
some doubt I checked its correctness with the help of the 44th Bernoulli
number, which has 70 figures in the numerator, though the probability of a
mistake was only $(1/17)$, but just with selected conditions which made me
doubt, and again I got confirmation of my theorem. Had there been any misprint
in the 70-figure number, it would have grieved me so deep, but fortunately it
did not happen. Now I shall set to
proving the theorem even with more energy, as it is quite difficult to doubt
its correctness.

*Tuesday,
January 17. *

Today I got up at half past five AM and sat down to read up on my
mechanics, but my progress in it was poor and I gave it up for a time; lately I
managed to move much farther on the issue I am occupied with, though not so far
as I should wish, and only the urgent need to read up made me give up this work
[...]

I have already been quite calmed
down and even gave the last proof to Professor Markov, and now I am eager to
know what his opinion about it is. I am very near to deciding, if his answer is
favourable, to request him to let me proceed with my studies at his chair in
the University.

*March 3.*

I do not know how to explain it, but my progress in the studies these
last days was exceedingly slow, and the main thing is that I am doing nothing
but studying. Therefore I have become very irritable and just cannot understand
what is going with me. I avoid classes, I am angry with myself because of it, I
feel upset even more, go to bed and instead of 5 AM get up at 7, again I lose
the morning and so on; I am told I have grown thin, and it seems to me rather
natural. I do not know what means I should take [...]

I seem to be slightly ill, but only not in body. I don't feel quite myself,
I wish I could have a talk with somebody, not a heart-to-heart talk, but one which
leaves warm feeling, because I feel an aching void in my soul. I understand
quite well that this wish is impossible to fulfil, but all the same I would run
about the College, drop in here and there, listen for a while and then leave at
once, I must have offended many people in this manner.

An idea flashed across my mind: why shouldn't I busy myself with some
problem

in mathematics -- it seemed a ray of light fell on me, but went out at
once: I can't, no time (though I do nothing all the same).