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 [...]

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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 [...]

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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).