Diaries, 1943–1945

Note on the Text#

A translation in progress of Book 3 of Kolmogorov, the three-volume jubilee edition (Moscow: Fizmatlit, 2003), edited by A. N. Shiryaev — the diaries of 1 August 1943 to 12 March 1945. It is made from the printed pages of that edition; we have not seen the manuscript. A register of everyone named in the diary — with dates, household names, and a note on each — is kept separately.

Translated from: А. Н. Колмогоров, Звуков сердца тихое эхо… (Дневники 1943–1945), в кн.: Колмогоров. Юбилейное издание в трёх книгах, Книга 3, под ред. А. Н. Ширяева, Физматлит, Москва, 2003.

The printed page is the arbiter. Where he is inconsistent — dates headed one way and then another, a line of Goethe departing from the standard text because he was copying from a friend’s pocket edition — we transcribe what is printed and do not normalise. Errors of transmission we correct silently; errors in the ink we keep, because they are evidence.

Brackets. Angle brackets ⟨ ⟩ mark what the 2003 editors supplied — a reconstructed date, a traced citation. It is their convention and we have kept it; a reader who knows the Leiden system should note that there ⟨ ⟩ marks an editor’s restoration of a scribal omission, whereas here it marks editorial supply of any kind. Square brackets are ours. A bracketed word followed by a question mark — [greenish?] — is a doubtful reading of the page; uncertainty about a translation is never bracketed, but discussed in the margin.

Four voices in the margin. An unmarked note is the translator, glossing; [Translator’s note:] is the translator on the source and its transmission; [Editor’s note:] is the 2003 editors, translated; [Author’s note:] is Kolmogorov’s own footnotes to his own diary; [In the margin:] is something he wrote in the margin. Anything we add inside an editors’ note is marked —Trans.

Where the diary’s subject is language itself — where he scans a line’s metre, or weighs a translation — the passage stays in its own language, since that is what his marks describe, with a plain English crib set immediately below it. Goethe and Mann, whom he quotes in German, likewise stand as he wrote them, cribbed. The editors’ notes to the diary are translated, all of them; but the 2003 edition’s own Russian renderings of his German — made for that edition, by B. V. Zakhoder, Yu. M. Smirnov and N. G. Khimchenko, to do for a Russian reader what our English does for ours — are not reproduced. Where a Russian rendering is instead a fact of the diary’s world — something sung, recited, or argued over — it is content, and translated.

The drawings are text. Roughly a quarter of these folios carry his own hand — diagrams, sketches, facsimiles — and much of it is invisible to the scanned text layer. Those pages are reproduced as figures. On 1 January 1944 the drawing is the entry.

Third-party material: the entry of 6 September 1943 reproduces poems by Yu. M. Smirnov, copied out and scanned by Kolmogorov; they remain their author’s. See the register for a note on permission.

1943: August–December#

Das Erlebte weiss jeder zu schätzen, am meisten der Denkende und Nachsinnende im Alter; er fühlt, mit Zuversicht und Behaglichkeit, dass ihm das niemand rauben kann.

— Goethe

Alles Gescheite ist schon gedacht worden, man muss nur versuchen es noch einmal zu denken.

— Goethe

Dedicated to myself on my eightieth birthday, with the wish that by then I shall have kept sense enough, at least, to understand the writings of my own self — the forty-year-old — and to judge them with sympathy, but also with severity.

Kh.G., entering upon the “Olympiad of Flourishing” (1943–1947) [Editor’s note:] Kh.G. — this abbreviated signature beneath the dedication stands for Kholmogorsky Gus, the Kholmogory Goose, the household name of A. N. Kolmogorov. We leave without comment why Andrei Nikolaevich declares the coming four-year period (1943–1947) an Olympiad of Flourishing. The Kholmogory goose is a real Russian breed, and the name puns on his own surname. An Olympiad [Olimpiada] is, in classical reckoning, not a contest but the four-year interval between the Games, used by the Greek historians as a unit of dating — and 1943–1947 is exactly four years. The joke is compounded by the setting: a man announcing his own four-year plan, in the country of the Five-Year Plan. The same word returns in its ordinary modern sense on the diary’s very last page, where he is setting problems for the Moscow schools Mathematical Olympiad, which he founded. [Editor’s note:] On 25 April 1943 A. N. Kolmogorov turned forty.

Das Beste

Wenn dir’s in Kopf und Herzen schwirrt, Was willst du Bess’res haben! Wer nicht mehr liebt und nicht mehr irrt, Der lasse sich begraben.

— Goethe

August 1943#

Sunday, 1 August 1943#

New moon

Half past six in the morning. A slightly misty, but still sunny morning. Pusya[Editor’s note:] Pusya — the household name of Pavel Sergeevich Alexandrov. and Oleg have run off to bathe, while I sit at home on account of ill health (which is ending).

Anya again has a working day, and she will not come. I feel on this account both vexation and awkwardness (for the second time our Sunday “readings” will take place without Anya). [Editor’s note:] Anya — Anna Dmitrievna Kolmogorova (Egorova) — the wife of A. N. Kolmogorov.

Why does this notebook begin precisely now?

There are two reasonable grounds for it:

1. The idea of a diary as a disciplining device has long attracted me. To record what has been done, what one wants to change in one’s life, what needs to be done, and then to check the execution — the idea is not new, but it is equally useful at 16 and at 40.

2. Towards forty I have begun to feel more keenly how life flows ... and passes away; how far what has been lived through already has a value of its own in comparison with what still lies ahead (at 16, and indeed at 30, everything still presents itself as a preparation for a more significant future). Hence there has arisen the need to fix the present at the very moment of its passing over out of non-being, as that which has not yet been, into non-being, as that which has already gone by.

It is possible that a third ground, a more doubtful one, joins itself to these:

3. It has been decided that the period of “psychological investigations” which began in February (see Kh.G., P.I.Ch. — “Love and Creative Work”)A bibliographic self-citation, in scholarly form, to his own unpublished manuscript: author (Kh.G. — the Kholmogory Goose, his household self-name), short title (P.I.Ch.), subtitle. The initials decode only through transliteration: Pyotr Ilyich Chaikovskii — the composer whose name English spells with a T. The deadpan is the form; he footnotes himself in his own private diary, under a joke pseudonym.[Editor’s note:] Kh.G., P.I.Ch. — a composition by A. N. Kolmogorov: Pyotr Ilyich Tchaikovsky. Love and Creative Work (written in connection with the fiftieth anniversary of the composer’s death, dedicated to P. S. Alexandrov; unpublished). is time to bring to a close. In July it brought both Pusya and me to a certain slackness. And so the setting-up of a diary, while pursuing the aims of the restoration of discipline, gives at the same time a more organised and regulated outlet to this passion for psychological investigations. Only let there not be too many of them!

Gradually there may appear in this notebook, besides the current short entries, memoirs too, and reflections, and psychological analyses — but only after order has been brought into life.

For now the immediate tasks are:

I) Quickly to deal with the immediate small jobs (gunnery, acceptance sampling, Lobachevsky). [Editor’s note:] Gunnery, acceptance sampling, Lobachevsky — see the Note to the entries of 16 August and 19 October 1943. Brakovka, here and throughout, is acceptance sampling — the problem, as the editors’ forward note of 19 October 1943 defines it, of constructing economical plans for inspecting batches of production, weighing two kinds of loss: accepting defective batches, and rejecting good ones. It is never defined in this month’s apparatus, only deferred forward.

II) To carry through smoothly all the family and household rearrangements (to bring Vera[Editor’s note:] Vera, Varya, Nadya — the sisters of Maria Yakovlevna Kolmogorova, Andrei Nikolaevich’s mother. Vera and Varya had to be brought from Kazan, where they had remained in the evacuation. and Varya, to take Varya to Nadya, to get Anya away from her job, and so on). [Editor’s note:] Yakov Stepanovich and Yuliya Ivanovna Kolmogorov had seven children — six daughters: Sofya, Vera, Nadezhda, Lyubov, Varvara, Maria, and a son, Stepan.

III) To establish constant and calm work on the great designs (the analysis course, turbulence, spectra).

And only then — the joining of mathematics with all the wealth of purely personal human interests and enthusiasms that has flourished these last two years.

For now, though, the main thing is:

1. Discipline in the carrying out of boring work.

2. Confident and consistent clearing of the ground for calm work on the great designs.

3. The struggle with “temptations” (sweets, reading at the wrong time), including immoderate writing in this notebook. (An agreement with Pusya on the limitation of chatter!)

And where, then, is love (Christian and non-Christian), on which I reflect so much and of which I perhaps talk too much (to Oleg, for instance)? But it seems that it is precisely for its sake that one must now concentrate on the disciplinary rules set out above! These two paragraphs are not typeset in the 2003 edition: they are reproduced photographically, as a facsimile of the notebook page in Kolmogorov’s hand, and so are absent from the text layer of the scan. He underlines love himself. The word answers the three numbered points above it — the whole disciplinary programme is declared to be for love’s sake — and it is the same word that titles the Tchaikovsky essay cited three paragraphs earlier, and the same word he will pursue through Mann for the rest of the month.

And so, enough of reasoning! But to record not only labour feats, but analyses too, and shades of mood (briefly!) — is not forbidden. Trudovye podvigi, “labour feats” — the Stakhanovite phrase of the Soviet production campaign, applied to his own desk work. Of a piece with the “output” of 3 August and the “norm” of 2 August.

Monday, 2 August 1943#

On Sunday from the morning, after breakfast, I sat down to occupy myself with the problems of acceptance sampling, but soon Anya arrived (the fears that this Sunday too would be declared a working day at Lyublino[Editor’s note:] At Lyublino was situated the Laboratory attached to the Lyublino filtration fields, in which A. D. Kolmogorova worked in those years. were not borne out). We walked down along the Klyazma[Editor’s note:] Klyazma — the next station (from Moscow) after Tarasovka on this line. In the settlement of Klyazma A.N. and P.S. lived (in the Alexandrovs’ family house, 27 Nekrasovskaya, or in the half of a house rented from V. A. Ponomareva) for several years before the purchase of the house at Komarovka. as far as the ski slopes, sat on the bank, bathed.

Before and after dinner I read “Tonio Kröger” to Anya and Oleg. We got as far as Tonio’s departure from his native town, further north. Anya was charmed at once by the first chapter (Hans Hansen). Then, probably, the “crumb of contempt” for people, so characteristic not only of Tonio but of Mann himself, disturbed Anya somewhat, but in conclusion she said that she “had not thought such works were possible in contemporary literature”.[Author’s note:] Just before this, on our walk, Anya was asking whether she was right in thinking that Russian literature of the nineteenth century (Turgenev, Tolstoy, Dostoevsky) is “special” and differs in principle from Western literature. [Translator’s note:] Kolmogorov footnotes himself with *) markers throughout the notebook, ruling the notes off below the entry. They are given here as [Author’s note:] sidenotes at their anchors; the sidenote number absorbs his asterisk. Krokhotka prezreniia — a crumb of contempt. He is quoting the Russian translation he is reading aloud; the diminutive krokhotka (“little crumb”) is the Russian translator’s vividness. He will quote Mann’s own German for the same phrase on 6 August, where it reads ein klein wenig Verachtung — “a little contempt”. The crumb is the translator’s, and he keeps it.

Oleg’s impressions of “Tonio Kröger” are not yet clear to me: I am afraid that he is too much inclined to judge a work by the “ideas” plainly expressed in it, and with such an attitude to the matter one can only get tangled up in Tonio’s utterances to Lizaveta Ivanovna. [Editor’s note:] Lizaveta Ivanovna — a character in Thomas Mann’s novella “Tonio Kröger”.

Pusya meanwhile was writing Lobachevsky. [Editor’s note:] Pusya was writing Lobachevsky — different things may be meant here: first, in 1943 there appeared a booklet by P. S. Alexandrov and A. N. Kolmogorov, Nikolai Ivanovich Lobachevsky. 1793–1943 (Moscow–Leningrad: GTTI); secondly, in the entry of 9 August 1943 an article by P. S. Alexandrov on the geometry of Lobachevsky is mentioned. Finally, on 6 October 1943 a lecture by P. S. Alexandrov on N. I. Lobachevsky took place at the Moscow House of Scientists, the written text of which is preserved in P.S.'s archive.

Subsequently it was proposed to publish this lecture in a mass edition (for schoolchildren), in connection with which the Central Committee of the Komsomol asked Academician N. N. Luzin to express his opinion of this lecture. In P. S. Alexandrov’s archive there is preserved a typewritten text of 5 pages under the title: “Remarks on the lecture of the Stalin Prize laureate, corresponding member of the USSR Academy of Sciences P. S. Alexandrov, ‘The great Russian mathematician Lobachevsky’, by Academician N. N. Luzin”. The text consists of 12 points and a conclusion, which we give here in full: “All the passages noted in Pavel Sergeevich’s lecture are especially telling, and combine a high contemporary scientific quality with the property of a beneficial influence upon young minds. The scientific quality, the pictorial vividness and the ‘accessibility’ to the consciousness of the listeners make Pavel Sergeevich’s lecture a valuable invention and an unconditional contribution to our national literature” (5 November 1945).

We dined with Pusya at the sanatorium. Then I fed Anya and Oleg at home. [Editor’s note:] At the sanatorium “Sosnovy Bor”, next to the Komarovka house, A. N. Kolmogorov and P. S. Alexandrov took their meals during the war on coupons (against their food ration cards).

Briefly discussed various provisioning matters with Anya. To Margarita Mikhailovna, on Anya’s proposal, her August dry dinner ration is being handed over, against July and August. This both corresponds to the established “norm” and removes the necessity of deciding what exactly to give away. Unfortunately, in the taking of such decisions jointly there is not to be observed in us a sufficient simplicity. I am perhaps insufficiently tactful, but Anya, unexpectedly given her extreme selflessness, displays a (in its essence highly egoistic) persistent wish not to soil herself in dry and calculating activity of this kind. [Editor’s note:] Margarita Mikhailovna (Egorova) — the mother of Anna Dmitrievna Kolmogorova (Egorova).

Incidentally, Anya about her “egoism”, and I about her “aristocratism of a special kind”, were talking in the morning apropos of her aversion to a bathing costume.

(Of Anya’s impressions of “Arrowsmith” later, when she finishes reading.)

I saw Anya off to Tarasovka for the 18.50 train almost as far as the footbridge. I went back because of the rain that was starting, while Oleg ran on barefoot with Anya further towards Tarasovka. [Editor’s note:] Tarasovka — the station nearest to Komarovka on the main branch of the Yaroslavl direction.

Then I saw Pusya off to Klyazma, had supper at the sanatorium, received S. V. Fomin (was somewhat excitedly talkative with him, as, for that matter, with many people just now), fed Oleg sour milk.

In conclusion of the day we cheerfully sawed and chopped firewood with Oleg and Shurka. [Editor’s note:] Marina — M. A. Kozlova, help with the household at the Komarovka house from the moment of its purchase. Shurka — her husband.

Oleg on this visit is livelier and more sure of himself. He managed his affairs of the preceding week well, once went to Lyublino to work (without Anya’s pressure, apparently). He has tanned a little and is coming little by little to a taste for going barefoot, for running, for demonstrating to Shurka and Marina his skill at sawing and chopping firewood. Sometimes he shows off a little, both with his tramp-like appearance with darned trousers and with his frightful tarpaulin coat.

Oleg’s declaration that among his comrades at Voskresenskoye[Editor’s note:] Voskresenskoye — a settlement in Bashkiria where Oleg Ivashev-Musatov was in the evacuation with the Moscow Art School at which he was studying. a “Karamazov spirit” prevailed, and that the majority of them had lost the human likeness just as Fyodor Pavlovich had (it was I who in conversation had insisted on the difference between Mitya, for example, and Fyodor Pavlovich[Editor’s note:] Fyodor Pavlovich, Mitya — characters in F. M. Dostoevsky’s “The Brothers Karamazov”. — whereas Oleg “likes nobody” there), alarmed both Pusya and me somewhat.

I asked Oleg whether he had read the “Gospel”. It turned out — no (so much for the absurdity of Seryozha‘s “religious-philosophical-ethical” upbringing!). [Editor’s note:] Seryozha — Sergei Nikolaevich (by passport Mikhailovich) Musatov — a painter, Oleg’s father. From 1936 he officially bore the surname Ivashev-Musatov (Ivasheva being his mother’s maiden name); he always signed his pictures “S. Musatov”.

After the somewhat offensive letter sent last Monday, I sent Seryozha a note with an invitation to come to Komarovka some time. [Editor’s note:] Komarovka is so situated that from Moscow one could get there by various means and routes: along the main line of the Northern (Yaroslavl) railway as far as Tarasovka station or Klyazma station; along the Shchelkovo branch of that line — as far as Bolshevo station, and then by the little steam train (the “cuckoo”) that runs to Ivanteevka. Nowadays a branch runs from Moscow through Bolshevo to Fryazino, and one can reach Komarovka by electric train, getting off at the platform “Fabrika 1 Maya”. In those days, though, the way from Tarasovka or from Klyazma (and often from Bolshevo too) was covered on foot. The inhabitants of Komarovka, as a rule, met their guests and saw them off to the station. Mentions of this occur often in the “Diaries”.

Towards dark Pusya came. Talked with him about his prospective doctoral candidates. Doktoranty — not doctoral students in the English sense. Under the Soviet two-doctorate system a doktorant already holds the kandidat degree and is working towards the higher doctorate, the doktor nauk. Fomin in 1943 already held the kandidat.

Tuesday, 3 August 1943#

After the long wet from Monday morning, it is clear and sunny. Today the morning is cold and extraordinarily transparent (already autumnal), and in the daytime a heat.

In two days I have written 20 pages of “The Choice of a Rational System of Acceptance Sampling — I”. [Editor’s note:] “The Choice of a Rational System of Acceptance Sampling” — see the Note to the entry of 19 October 1943.

This is adequate output, but with my affairs in their neglected state one wants to work faster still. We bathe, we run, I chop firewood. On the whole, I am satisfied with these two days.

Pusya is writing Lobachevsky very slowly and with difficulty; for some reason he has come to loathe him utterly.

Today Spitsyn and his friend restored the electricity at Komarovka; at this moment he is sitting in the kitchen and trying to swindle us over the payment. How much more trouble and unpleasantness will this electricity cause? [Editor’s note:] Spitsyn, Nikolai Ivanovich — a neighbour at Komarovka, who sometimes helped with the household work.

Also — an exact regime of nutrition and physical culture is needed, so that there should be neither colitis, nor nervous “perfatigation”, nor sleeplessness! Perfatigatsiia — a macaronic mock-Latin coinage of his own (per-, thoroughly + fatigare, to weary), dressed as a clinical diagnosis and set between a real colitis and a real insomnia. The scare quotes are his: he knows it is not a word.

Friday, 6 August 1943#

Wednesday <4 August>#

Morning — collection of provisions on the limits;

evening — the faculty council with the defence of Perepelkin’s doctoral dissertation, and a visit from Oleg with Yura[Editor’s note:] Yura — Yuri Mikhailovich Smirnov.. Limity — a privileged entitlement booklet issued to academicians and others of comparable standing, against which special provisions could be drawn. Not an ordinary ration book: the privilege is the point. The first of two Yuras in this household. This one is Yu. M. Smirnov — the topologist, the translator of Goethe whose verses Alexandrov edits through this month, and the Strausenok or “Little Ostrich” of the parody on 16 August. The editors gloss a second Yura on folio 43 — Yuri Andreevich Egorov, Anya’s nephew. In August every Yura named in the diary is Smirnov.

Thursday <5 August>#

Morning — earthing up the potatoes and bathing with Oleg on the Sparrow Hills;

day — the savings bank, dinner at the House of Scientists, the library, Borya;

evening — “Le Verre d’eau” at the Maly Theatre (with Natasha[Editor’s note:] Natasha — Natalya Konstantinovna Gnedenko. and Borya[Editor’s note:] Borya — Boris Vladimirovich Gnedenko.).

At dinner at the House of Scientists I conversed with the younger Meiman (the mathematician), taking him for the elder (the political economist).

Friday (today)#

Morning — nonsense with the warm things; left for Komarovka by the 10.40 train.

Before dinner, conversations with Pusya on the bank of the little river, and bathing with a wash with soap; dinner at the sanatorium (I alone, Pusya’s term has already ended).

With Anya it is all the same: away from home she is bold (she neatly put down an insolent captain in the metro), but she is afraid of me and closes up. And when her unspoken grievances break through, she takes fright all the more and will say nothing by way of explanation. At this I get extraordinarily angry. So it was this morning too (with the warm things).

What does Anya like in “The Knight in the Panther’s Skin”? One would have thought this work was not in her style.

In general, apropos of Anya and Borya (with his Jerome K. Jerome), I reflected sadly on solitude and on my own fate. Probably, I am not “a bourgeois gone astray”, but, perhaps, “a mathematician gone astray (in the ‘worlds of love’)”...

(Pusya claims that he, on the contrary, is a dweller in those worlds gone astray in mathematics.) Lisaveta Ivanovna’s verdict on Tonio Kröger is ein verirrter Bürger, “a bourgeois gone astray” — a Bürger who strayed into art. Kolmogorov inverts it for himself, and Alexandrov inverts it once more. One verb carries all three. Alexandrov’s wit turns on the last word: obyvatel, “bourgeois”, literally means “one who dwells”, and the Russian switches to zhitel, “dweller”, at exactly that point.

Apparently one must, at last, begin to occupy oneself with mathematics and to preserve one’s own “Sehnsucht ist darin und schwermütiger Neid und ein klein wenig Verachtung und eine ganze keusche Seligkeit”. “Longing is in it, and melancholy envy, and a little contempt, and a whole chaste bliss.” From Mann’s “Tonio Kröger”. Ein klein wenig Verachtung — “a little contempt” — is the phrase he quoted on 2 August, in Russian, as a “crumb of contempt”: the crumb was the Russian translator’s touch, and he adopted it.

“Was ich getan habe, ist nichts, nicht viel, so gut wie nichts. Ich werde Besseres machen, Lisaweta, — dies ist ein Versprechen. Während ich schreibe, rauscht das Meer zu mir herauf, und ich schließe die Augen. Ich schaue in eine ungeborene und schemenhafte Welt hinein, die geordnet und gebildet sein will, ich sehe in ein Gewimmel von Schatten menschlicher Gestalten, die mir winken, daß ich sie banne und erlöse: tragische und lächerliche und solche, die beides zugleich sind, — und diesen bin ich sehr zugetan. Aber meine tiefste und verstohlenste Liebe gehört den Blonden und Blauäugigen, den hellen Lebendigen, den Glücklichen, Liebenswürdigen und Gewöhnlichen.” “What I have done is nothing, not much, as good as nothing. I shall do better, Lisaveta — this is a promise. While I write, the sea roars up to me, and I close my eyes. I look into an unborn and shadowy world that wants to be ordered and given form; I look into a swarming of shadows of human figures who beckon me to bind and redeem them: tragic and ridiculous, and some that are both at once — and to these I am much devoted. But my deepest and most secret love belongs to the fair-haired and blue-eyed, the bright living ones, the happy, the loveable and the ordinary.” From “Tonio Kröger”. The unborn world “that wants to be ordered and given form” is a design in his sense of the word: it stands to Mann’s writer exactly as the analysis course, turbulence and the spectra stand to him.

“Alle Wärme, alle Güte, aller Humor kommt aus ihr, und fast will mir scheinen, als sei sie jene Liebe selbst, von der geschrieben steht, daß einer mit Menschen- und Engelszungen reden könne und ohne sie doch nur ein tönendes Erz und eine klingende Schelle sei.” “All warmth, all goodness, all humour comes from it, and it almost seems to me as if it were that very love itself of which it is written that a man might speak with the tongues of men and of angels and yet, without it, be only a sounding brass and a tinkling cymbal.” From “Tonio Kröger”. [Translator’s note:] The pronoun dangles in Kolmogorov’s excerpt as it does not in Mann. Ihr and sie refer back to diese meine Bürgerliebe zum Menschlichen — “this bourgeois love of mine for the human” — which stands a few lines above the passage he copied out and is not reproduced here. Mann’s closing clause echoes 1 Corinthians 13:1; the English follows the Authorised Version’s “sounding brass” and “tinkling cymbal”, but keeps love, which is Luther’s Liebe and Mann’s word, rather than the Authorised Version’s “charity”.

I regret not having gone to the concert (I am not working anyway, and have polished off a bar of chocolate):

P. I. Tchaikovsky — Second Suite. Music for “The Snow Maiden”. Variations on a Rococo Theme. First Piano Concerto.

Oleg on the Sparrow Hills.

His fantasy (?) about our walk on the Sparrow Hills (some five years ago), when I astonished him by racing him.

Oleg worked sluggishly at the earthing up and the weeding (perhaps I had “talked him out”). It was hot. He tanned considerably in a single morning.

Verse, by his own admission, he knows little of. He loves Pushkin’s “Anchar”, and A. Tolstoy’s “Ilya Muromets” and “Potok-bogatyr”! More he cannot name.

Of a boy’s life with riding and vagabondage he “was envious at first, but then stopped”.

“Although I studied badly, I decided at once that I was cleverer than everybody.”

The view of Moscow from the Sparrow Hills was news to Oleg: “I didn’t think Moscow was so big” (!)

I read M. A. Kreines’s dissertation, “The Synthesis of Regular Toothed Mechanisms” — good, though elementary, new ideas.

At Pusya’s today S. V. Fomin — they will not release him to the doctorate until the end of the war.

A letter from Varvara Sergeevna. [Editor’s note:] Varvara Sergeevna Alexandrova — the sister of P. S. Alexandrov; at that time she remained in the evacuation in Kazan.

The transport in August only on the 10th–15th. From 1 August they have stopped giving dinners in the canteen to V.Ya. and V.Ya. [Editor’s note:] V.Ya. and V.Ya. — Vera Yakovlevna and Varvara Yakovlevna Kolmogorova, Andrei Nikolaevich’s aunts, were also in Kazan. What is meant is the necessity of transporting them back to Moscow.

How is all this return to Moscow to be organised?

Saturday, 7 August 1943#

A somewhat misty, milky-sunny, warm day.

Over the morning and after dinner I edited the first 15 pages of Gubler’s work (wrote seven anew). Worked satisfactorily. [Editor’s note:] What is meant is I. A. Gubler’s article “The solution of the problem of firing with artificial dispersion for certain cases”. Published in the “Collection of articles on the theory of gunnery. I” under the editorship of A. N. Kolmogorov (A.N. calls it the “Gunnery Collection”). — Transactions of the V. A. Steklov Mathematical Institute of the USSR Academy of Sciences, 1945, vol. 12, pp. 67–94.

Pusya sluggishly writes Lobachevsky, edits Yura’s verses, and grieves over the Kazan difficulties.

Marina fell ill, and Shurka took her to the hospital in a droshky, accompanied by Spitsyn.

From Sergei Musatov a letter with notice of the possibility of coming to Komarovka only in a month, and of an intention to write to me further “on the questions raised”.

Monday, 9 August 1943#

Today a day of complete collapse: I saw Pusya and Oleg[Editor’s note:] Oleg — Oleg Sergeevich Ivashev-Musatov — the son of Anna Dmitrievna by her first marriage, to S. Ivashev-Musatov. off, read “Arrowsmith”, and did very little of Pusya’s article on the geometry of Lobachevsky. [Editor’s note:] The article on the geometry of Lobachevsky — what is meant is P. S. Alexandrov’s article “What is non-Euclidean geometry” in the book: Nikolai Ivanovich Lobachevsky. 1793–1943 (see also the Note to the entry of 2 August 1943).

After dinner I terribly wanted to sleep. Meanwhile, despite the fact that I got up at 5.30, I had slept not a little (on Sunday Oleg and I went to bed very early). Oleg turned up on Saturday from the cuckoo that comes in at eight o’clock, Anya — very late. So I fed them, each separately, Anya — having already got out of bed. The “cuckoo” — the little local steam train, named for its whistle, which ran from Bolshevo to Ivanteevka. Kept here as he has it: the 7.30 cuckoo, the 8.39 cuckoo.

Apparently Sunday tired me.

I acknowledge this as a fact and describe Sunday.

On Sunday I got up at half past five. The sun was only just breaking through the mist. I raised Oleg and took him bathing. With Pusya we prepared breakfast.

Then I worked for four hours. In four hours (8.30–12.30) I edited another 24 pages of Gubler (of them seven written anew).

Anya meanwhile kept house with taste and with pleasure, as she knows how.

Oleg puzzled a little over the conclusion of “Tonio Kröger”, copied out for him in German, and then ... dug out of the cupboard the fourth volume of Plato, which opens with the “Phaedrus”. Pusya came to inform me of this not entirely happy choice, but I could not find a way to intervene. When I passed through the library terrace where Oleg was sitting, he quickly hid the book.

I observed further that Oleg was standing under the birch in gloomy pensiveness. Soon, however, he had already passed on to the Small Soviet Encyclopaedia and the like. It has not so far been established whether it is connected with the reading of the “Phaedrus” that for the rest of the day Oleg was very animated and cheerful, but from time to time covered his face with his hands and then looked up at me in astonishment.

Then I finished reading “Tonio Kröger” to Anya and Oleg.

The dinner prepared by Anya (warmed-up soup, sanatorium leftovers, fried eggs with bread) was a success. At dinner Anya said that all the time, listening to “Tonio Kröger”, she had been waiting for “them, in the end, to throw themselves into each other’s arms”. Pusya and I could not restrain ourselves and asked with one voice: “And who are ‘they’?”

I took Anya bathing and saw her off to the 19.30 cuckoo before the sanatorium supper.

On the way to the cuckoo Anya asked seriously whether I love her. I said that if I get so angry and swear so, it is precisely because I love her.

After supper we sawed firewood with Oleg and bathed.

Before supper there had also been a thunderstorm — in general, the days are very colourful!

This morning at half past five we set off into a still greater mist to bathe. The blue mists in the west and the golden ones in the east, pierced through with sun, were really fine. Oleg settled himself many times, shading his eyes with his hand, standing and squatting, to examine them, having declared that “some savage might think that the end of the world was there”.

Then we swam downstream (towards the sun) as far as the fallen birch.

Swimming back, I examined Oleg, sitting against the background of the sunny mist with his feet in the water and smeared with duckweed — really, rather like a savage.

If only he could be like that more often!

With the 8.39 cuckoo Pusya and Oleg left together.

Anya found that in “Arrowsmith” “the problem of joining scientific work with family life is not solved”. Apropos of Gottlieb she pronounced: “It must be very interesting to work with passion like that”, but then dragged in Pavlov with his “modesty”.

She seriously hopes that S. P. Stroganov will be elected to the Academy of Sciences and is “sure that then they will set up a laboratory attached to the Academy”. There she would like to work.

This last week Anya has been occupied at Lyublino only with “the river”, i.e. the dissertation, but so far tells me nothing about it. I only fished out of her that she has decided to replace the “literature review” with the “present state of the question”.

Tuesday, 10 August 1943#

Comrade Kolmogorov!

Your acquaintance military technician Seliverstov, Nikolai Alexandrovich, was killed in the performance of his official duties on 22.07.43. His relatives have been informed.

Clerk of unit No. 92966 Sergeant-major

25.07.43[Editor’s note:] Seliverstov, Nikolai Alexandrovich (1902–1943), whom the death notice calls an “acquaintance”, was in fact a comrade and classmate of A. N. Kolmogorov at the gymnasium. Andrei Nikolaevich was especially close friends with his brother, Gleb Alexandrovich Seliverstov (he later worked with him jointly on the theory of trigonometric series; the result of that work was the well-known Kolmogorov–Seliverstov theorem). Both brothers were called up into the army, and both were killed. A. N. Kolmogorov corresponded with the Seliverstov brothers and kept their letters, visited their parents and helped them.

(The last (unsent) letter of Andrei Nikolaevich to Nikolai Seliverstov, which seems to us consonant with the diary entries of this time:) This parenthesis is the editors’ own voice, printed inside the body of the diary. The letter that follows was placed here by them, not by Kolmogorov: he did not file his dead friend’s unsent letter into his own notebook.

A letter of A. N. Kolmogorov to N. A. Seliverstov

(Typed, on two sides of half a sheet)

Komarovka, 12 July 1943

Dear Kolya!

To my last two letters I have had no answer from you, whether because they were lost, or because you have no time to write just now. I have only now realised that, not being prompted by the receipt of letters from you, I have not written to you for a very long time.

My life flows on as before. Tomorrow and the day after are the last examinations at the university. Then I shall be finishing off a piece of military-scientific work, and in August, presumably, I shall go to Kazan, in order to bring Vera and Varvara Yakovlevna from there to Moscow by the beginning of September.

Our life together with Anya has, over the past year, quite taken shape, but it will receive more final forms when, with Vera Yakovlevna’s arrival, Anya leaves her job at Lyublino (such are our plans); whereas for the present, despite our complete inner unity, we simply spend too little time together.

Anya’s relations with Vera Yakovlevna will undoubtedly turn out very good. The relations arising out of our joint existence at Komarovka with Pavel Sergeevich have, in essence, been established as good from the very beginning; the household details arising out of the undividedness of property that formerly existed between Pavel Sergeevich and myself are being put in order: at present, with my having the most various material obligations that do not concern Pavel Sergeevich, such undividedness would be burdensome to me.

Less satisfying to me are my relations with the Musatov family. These relations are unavoidably rather close, since Oleg lives with Polina Alexandrovna and studies painting with Seryozha, but is supplied with a money and food allowance and with clothing, and also has his washing done — by Anya and me. He spends Sundays with us at Komarovka, and approximately once a week, on a weekday, works with us on our vegetable plots (at Lyublino and on the Sparrow Hills).

The boy I have quite sincerely come to love, but to have to do with a fifteen-year-old person who, for example, at the present time:

1. is himself reading “The Brothers Karamazov”,

2. at his grandmother’s listens to a reading aloud of Anatole France’s “Thaïs” (I do not know how Polina Alexandrovna swallows and arranges it all there, but in reality “Thaïs” is a brilliant treatise on psychiatry, in which it is convincingly recounted how the whole frenzy of Christianity, with its self-tortures, its standing for years on a pillar, its mystical visions and diabolical wiles, arises on the soil of sexual experiences that find no outlet — such is precisely Anatole France’s design, and not my interpretation),

3. at Seryozha’s listens to “philosophical readings” from the writings of Vladimir Solovyov and the dialogues of Plato,

— is, as you yourself understand, not simple.

To tear him away from Polina Alexandrovna would probably be quite difficult. It is consoling that he treats her in many respects protectively, is very solicitous of her — this last month he cooked dinner daily for the whole dear family, and of Polina Alexandrovna he is continuously solicitous in all such respects. At present the family has divided into two parts, living in different places and with a strictly separate household: Seryozha with Alla, and Oleg — with Polina Alexandrovna.

For now I finish, and shall write about more abstract matters separately. I was at Alexander Nikolaevich’s and Nina Vasilievna’s a fortnight ago. With the coming of summer they (like all of us, to some degree) are naturally anxious about you and Gleb especially, but there is nothing to be done about that.

Write. Anya sends her greetings.

Your Andrei

Wednesday, 11 August 1943#

I still cannot master myself and work properly.

Not even because of Kolya (although I think much about his death!), but because of a feeling of uncertainty in my family affairs.

I intend to ask Anya orally (and, for exactness, in writing too) approximately the following:

Dear Anya!

You and I intend to live together another forty years or so, if not more. Permit me therefore, in answer to your question (whether I really love you), to put a question to you as well, concerning these coming forty years:

Do you picture your future life in such a way that at the centre of it stand:

1. our common personal life together and our family,

2. our common circle of friends, including my closest comrades at work and my pupils,

3. my work, which you support by your cares,

or do you picture it somehow otherwise?

This “query” is made, to a known degree, in cancellation of my excessive nervousness and heat over various current occasions.

Saturday, 14 August 1943#

2 p.m.

Yesterday I left Moscow by the 21.54 train.

The full moon approaches. The moon lit the little river at Tarasovka and the forest glades along the road to us most fantastically through the rapidly thickening mist.

I slept in until 10 in the morning, glancing out of the window at the poplars: at first they showed grey in the mist, quite colourless, then they drew themselves more clearly against a pale blue sky with cloudlets pink from the dawn, then the distant ones (Spitsyn’s) were lit by the sun; I got up when the forest behind the poplars was already being veiled in the haze proper to a hot day.

Marks on points 1)–3) (p. 4 [p. 28 in this edition]) for 1–14 August. The bracketed cross-reference is the editors’, mapping his notebook’s page 4 onto the printed edition’s page 28 — where the numbered points 1)–3) of 1 August indeed stand.

1. fair, [Author’s note:] See the current entries above.

2. good, [Author’s note:] That is, I took no new burdens upon myself.

3. poor. [Author’s note:] Immoderate consumption of sweets, writing in this notebook, and daydreaming at the wrong time.

To be added:

4. regular physical culture, correct nutrition.

On Tuesday and Wednesday I finished Gubler, worked a little on my old gunnery writings.

On Wednesday I made my own dinner (Masha was away, Pusya in Moscow). [Editor’s note:] Masha (Marina) — M. A. Kozlova — help with the household at the Komarovka house from the moment of its purchase.

To Anya at Lyublino I came by 16.30. We observed on the little potato plot a potato jungle without the slightest sign of tubers: instead of forming tubers, the roots come out again to the surface and form green shoots with leaves. We earthed up and weeded the cabbage, which grows well. Anya recounted that her Tanya is being left by her husband (a university soil scientist who always seemed to me rather disgusting — and now his first name, patronymic and surname have slipped my mind). [Editor’s note:] Anya’s Tanya — apparently T. Nikolskaya — the niece of Nina Petrovna Nikolskaya, an acquaintance of A. D. Kolmogorova who looked after Oleg.

By Anya’s account, P.S. and Oleg do nothing but say “how Andrei, how Andrei”.

On Thursday with Oleg we quickly (by 11) finished the earthing up and the weeding, then bathed. With greater ease than before Oleg talked about Seryozha, Alla and so on. [Editor’s note:] Alla — the second wife of S. Musatov.

Called in at the institute, spoke with Bermant and Vasilkov, received money.

Dined at the House of Scientists. Was at Oleg’s with Polina[Editor’s note:] Polina Alexandrovna, P.A. — the mother of S. M. Musatov, Oleg’s grandmother. Ivasheva by birth, Musatova by her husband, from 1936 — Ivasheva-Musatova. Alexandrovna. (Oleg’s sketches for a “composition”, Seryozha’s spring landscape of 1941.) [Editor’s note:] Oleg Ivashev-Musatov intended to become, like his father, a painter, and studied at the Moscow Art School. Hence here and subsequently his artistic compositions are discussed.

At the Academy of Sciences spoke with Bruevich (acceptance sampling [see the Note to the entry of 19 Oct. 1943] — a report for Wednesday 25 August, the election of academicians, Anya’s safety in the event of her leaving her job, the flat).

On Friday we met Varvara Sergeevna. Pusya made a scene with Sergei[Editor’s note:] Sergei Lvovich — S. L. Sobolev. Lvovich. Was at the university at Azarov’s (Pusya’s room). Petrovsky is satisfied with the faculty’s affairs (112 people admitted, and so on). Dined, was at the Nyubergs’ (Kolya’s dissertation), at the philological faculty at Dean Gudzy’s on Lyova[Editor’s note:] Lyova — Lev Dmitrievich Egorov, the brother of A. D. Kolmogorova (Egorova).‘s affairs (Gudzy was deferential before an academician to the point of indecency), at Trubnikovsky Lane (handed over the paper for the house manager), at the Seliverstovs’ (did not find them in), at Varvara Sergeevna’s. [Editor’s note:] Yura — Yuri Andreevich Egorov, the nephew of A. D. Kolmogorova (Egorova). [Translator’s note:] The editors’ note on Yura is printed at the foot of this page, but no Yura occurs anywhere on it — the printed page confirms this is not a defect of the scan. It is given here at the Egorov family’s only mention. This second Yura, Anya’s nephew, is not the Yura of 4 and 7 August, who is Yu. M. Smirnov. [Editor’s note:] The Seliverstovs — Alexander Nikolaevich and Nina Vasilievna — the parents of Nikolai and Gleb Seliverstov, friends of A.N. since his gymnasium years. “Kolya’s dissertation” is unglossed, and the Kolya meant is presumably one of the Nyubergs — not the Kolya whose death notice stands three pages earlier.

For insufficient energy over Thursday–Friday I cannot reproach myself, although I still had to ask Oleg today to run to Gudzy and to the Academy of Sciences, and to leave Anya and Oleg on their own to collect on the ration cards.

Today over the morning I only wrote letters to Varya and Petya and inserted the formulae into the report on Nyuberg’s dissertation. [Editor’s note:] Petya — Pyotr Savvich Kuznetsov (1899–1968) — philologist, professor of Moscow State University, was brought up together with A.N. in his grandfather’s house from early childhood and then studied at the same gymnasium.

Monday, 16 August 1943#

Sunday — a muddled day, ending with a certain scene between Pusya and me (see our picture-book). [Editor’s note:] Our picture-book — what is meant is one of the “artistic notebooks” (many of them survive in the Komarovka house), filled with pen drawings. Andrei Nikolaevich loved to draw in this way, and Pavel Sergeevich — to look these drawings over.

The conversation with Anya on the theme marked out earlier (see the entry for Wednesday, 11 August) went well. An affirmative answer seemed to Anya self-evident, and my doubts — idle.

But it was precisely our sitting shut away over this conversation at the moment of Varvara Sergeevna’s arrival that seemed to Pusya an inadmissible inattention to her.

Afterwards we sat very well, the three of us (with Anya and Oleg), over tea. With Pusya a complete reconciliation.

This morning rain and cold. We ran with Oleg to bathe by the little bridge (Pusya has boils on his leg). We wrestled. Oleg took “Arrowsmith” away to read.

I worked middlingly today — drew up the plan of the article “The number of hits with several shots and the general principles of assessing the effectiveness of a system of fire”.

It is coming out beautifully and interestingly. I wrote five pages and arranged ten out of the old material. The article ought to go first in the collection with which I am so tediously fussing.

Pusya in the daytime read Yura’s verses (his selection and light editing, 25 items).

Really, it seems to me precisely that which ought imperceptibly to take shape in contemporary good young people, and, consequently, being well made, to carry them along too. [Editor’s note:] The Collection of articles on the theory of gunnery appeared as a separate volume of the Transactions of the V. A. Steklov Mathematical Institute with the subtitle: “Collection of articles on the theory of gunnery. I” under the editorship of A. N. Kolmogorov (Leningrad–Moscow: USSR Academy of Sciences Press, 1945; 106 pp.). As Andrei Nikolaevich planned, the collection consists of four articles, a preface (unsigned) and an appendix (tables and diagrams). We give the titles of these articles: A. N. Kolmogorov, The number of hits with several shots and the general principles of assessing the effectiveness of a system of fire; A. N. Kolmogorov, Artificial dispersion in the case of destruction by a single hit and dispersion in one dimension; A. A. Sveshnikov, The determination of the best method of laying with artificial dispersion in firing (for certain particular cases); I. A. Gubler, The solution of the problem of firing with artificial dispersion for certain cases.

Where armfuls of autumn leaves The sunrise waters with red water, A little ostrich chick scrubs its feet Diligently with a loofah.[Editor’s note:] Strausenok [“Little Ostrich”] — the household name of Yu. M. Smirnov. [Editor’s note:] Here A.N. has made over Yesenin’s quatrain:

There, where the cabbage beds The sunrise waters with red water, A little maple chick sucks At its mother’s green udder. [Translator’s note:] The parody keeps Yesenin’s second line verbatim and twists the other three. Its hinge is a pun that cannot be carried across: Yesenin’s klenyonochek, “little maple chick”, becomes strausenochek, “little ostrich chick” — and Strausenok, “Little Ostrich”, is Yuri Smirnov’s household name, so the verses Alexandrov was editing that afternoon become the creature washing its feet. Both quatrains are anapaestic and rhyme akhapki/lapki, voskhod/tryot; the English keeps the sense and the bathos, not the metre.

September 1943#

Monday, 6 September 1943#

From the Poems of the Little Ostrich (August–September 1943)#

. . . . . . . . . . . . . . . . . . . .

Я прошагиваю улицу За воротами ворота, ⁠ Дом за домом. Надо мною вечер хмурится ⁠ В небе черном.

Я жалею о потерянном И грущу, о чем не знаю сам. Я иду путем рассеянным Голошеим глупым страусом.

... Снова ранние зори Освещают леса и поля. В бледно-синем, чуть желтом просторе Розовеют, цветут тополя. ⁠ Снова ветер, прохладный и свежий... ⁠ Белой пеной плывут облака, ⁠ Слыша зовы морских побережий... ⁠ Им дорога вольна и легка.

Мне двадцать один год. Мне жить бы, влюбляясь и радуясь! Смотреть бы только вперед, ⁠ Не оглядываясь! Мне двадцать один год, А ветер свистит, непоседа, И в дальние страны зовет, ⁠ Меня, соседа...

От дум тяжелых не уйти Они стоят и смотрят строго: Беда и горе впереди, Тоска и дальняя дорога.

За туманными далями снов Дни за днями упрямо толкутся...

. . . . . . . . . . . . . . . . . . . .

⇑

⁠ Этим утром покой и прохлада. ⁠ Побыстрее, сестренка, вставай! ⁠ За окном суета и трамвай, ⁠ И людей беспокойное стадо.

⁠ И спешить нам не нужно на службу: ⁠ Ведь сегодня у нас выходной! ⁠ Проведем его вместе с тобой, ⁠ Обновим нашу старую дружбу!

⁠ Нам бы жить, чудакам, и смеяться... ⁠ Дай, покрепче тебя обниму! ⁠ Вижу, знаю: опять одному ⁠ Вдалеке мне придется скитаться.

⁠ Погляди — распахнулось окно ⁠ В мир иной без тоски и печали... ⁠ Что таят недоступные дали, ⁠ Нам с тобою узнать не дано.

Если сердцу очень больно, Если сердцу тяжело, Друг обидел ли невольно, Заупрямился ль назло, ⁠ Это все — ничего!

⁠ К берегам пойду зеленым, ⁠ Где под солнечным лучом ⁠ Летом знойным, опаленным, Хорошо — горячо!

Забияка-ветер гонит Стаи легких облаков, И березка ветки клонит ⁠ Надо мной — высоко!

⁠ Все обиды и печали ⁠ Улетают тихо вдаль. ⁠ Вот и звезды заблистали И река — как сталь!

Каждую ночь барабанит дождь, И каждую ночь я слышу (Сквозь сон), как небо — лохматый пес — Когтями скребется в крышу.

⁠ Бездомный бродяга, холодный нос, ⁠ Скулит, напевает тоскливо, ⁠ И крупные капли собачьих слез ⁠ По кровле бегут торопливо.

И странные сны, занятней задач, Каждую ночь мне снятся, Что будто по лестнице из неудач Упрямо хочу подняться.

⁠ Туда, где воля любым мечтам: ⁠ Писать ли стихи иль влюбляться ⁠ (Но чаще всего смеются там)... ⁠ Ах, нужно только подняться!

⁠ Я уезжать собрался. ⁠ Недолго здесь прожил. ⁠ Все нужные мне вещи ⁠ В мешок свой уложил

⁠ Белье, бумаги, книжки, ⁠ Соль, мыло и табак — ⁠ Взял все, что очень нужно, ⁠ А что и просто так.

⁠ Но самой нужной вещи ⁠ Потерян даже след: ⁠ Оставил где-то сердце — ⁠ Назад дороги нет.

Monday, 13 September 1943. Kazan#

I left Moscow by the Academy carriage on the evening of the 6th.

Twenty days (16 August – 6 September) in Moscow and Komarovka were muddled and wearisome, though not so useless in the sense of work and of the stabilisation of family affairs as it seemed in the course of those days themselves.

1. I gave lectures on acceptance sampling at the Mathematical Institute and at Bruevich’s. Beyond that I have not yet worked. [Editor’s note:] The Collection of articles on the theory of gunnery — see the Note to the entry of 16 August 1943.

2. After a fashion I finished the collection of articles on the theory of gunnery, out of four articles (2 — mine, 1 — Sveshnikov’s, 1 — Gubler’s, my preface).

3. I wrote my own part (rather tedious, but it seems not useless) of Pusya‘s and my little book on Lobachevsky. [Editor’s note:] The little book on Lobachevsky came out in that same year, 1943: P. S. Alexandrov and A. N. Kolmogorov, Nikolai Ivanovich Lobachevsky. 1793–1943 (Moscow–Leningrad: Gostekhizdat, 1943, 100 pp.); the collection consists of two articles by P. S. Alexandrov (“Nikolai Ivanovich Lobachevsky. A short sketch of his life and activity” and “What is non-Euclidean geometry?”) and an article by A. N. Kolmogorov (“Lobachevsky and the mathematical thinking of the nineteenth century”).

4. I fussed a great deal over Yurka‘s poems. I even wrote him a whole treatise on the foundations of Russian versification, as an appendix to a letter. The treatise is mentioned, not reproduced; nothing of it survives in the notebook. The verses of the 6 September entry are its occasion.

5. Anya and I in Staropimenovsky moved into the former rooms of Mikhail Semyonovich, settled in there well, celebrated the house-warming, joined with our wedding anniversary, received Seryozha with Alla. [Editor’s note:] A. N. Kolmogorov and A. D. Egorova were married on 3 September 1942.

6. On one of the Sundays (4 September) with Borya[Editor’s note:] Borya — Boris Dmitrievich Egorov, the brother of A. D. Kolmogorova.‘s help we stacked the firewood Pusya had bought. Not the Borya of August, who is B. V. Gnedenko. From here to the end of the month every Borya is Anya’s brother.

7. I spent a very great deal of nervous energy on inducing Anya to occupy herself seriously with getting away from Lyublino. Just before my departure I was at Bruevich’s on this account, and he promised to sign the corresponding letter. Earlier Anya and I had been to S. N. Stroganov’s.

8. I was angry at the drag over Oleg‘s “holidays” at Komarovka. I was worried about his flu and the “complications on the heart” from that flu.

On the road and here I have read Lion Feuchtwanger’s “The Jewish War”. The modernisation of the ancient world is witty and, apparently, well-grounded: Editions which “sell out” in 300 or 4200 copies; the case of three innocent old men, like the case of the six Negro youths from Scarboro; universities, artillery, telegraphists — all this is sufficiently documented.

Pictures, of the sort of Josephus wandering about Jerusalem with the right of life for 70 people, are very vivid.

But on the whole — a repellent book, and the general conception

is narrow: against a refined Judaism there comes forward only a coarse Rome, and not Turkey,

⁠ there is no Christianity at all.

The philosophy of the word, hostile to the visual and tangible image, is interesting. Josephus himself is extremely repellent, and, to my mind, it is difficult to find a more intelligent antisemitic book than this one. [Translator’s note:] The book is Lion Feuchtwanger’s Der jüdische Krieg (1932), the first novel of his Josephus trilogy, which Kolmogorov read in the Russian translation. Feuchtwanger (1884–1958) was a German-Jewish émigré antifascist, widely translated and celebrated in the USSR, and the novel’s design is philosemitic; Kolmogorov’s verdict inverts the book’s intention. Whether he means that the book is so intelligent that it serves antisemitism despite itself, or that it is intelligent and antisemitic in tendency, the sentence does not resolve. The centred lines are his summary of Feuchtwanger’s conception, which he calls narrow in the same sentence; they are not a schema of his own, and the sentence runs through them without resuming after the second. Iudeistvo in the display is the civilisational term, “Jewry”; iudaizm in the next clause is the religion, “Judaism” — the distinction is his. The “six Negro youths from Scarboro” is almost certainly the Scottsboro case (Alabama, 1931), which concerned nine defendants; the number and the spelling are as printed.

In Kazan the first days I slept myself out, packed things, was angry at the dirt and disorder at Vera and Varya‘s, though sometimes I talked well with them, was once at the Kazanka, talked with Anatoly Ivanovich about all sorts of things, and, on the whole, rested and came to myself. [Editor’s note:] Anatoly Ivanovich — A. I. Maltsev.

Yesterday I was at “La Traviata”. They sang decently.

Today I wrote letters to Petya, Pusya, Anya, Nadya.

Today I give a lecture on acceptance sampling at the local branch of the Institute.

I have re-read the preceding pages from 1 August. Interesting. To strain to restore the omitted days (were they not omitted because of Oleg’s flu?) in more detail is not worth while; better simply to write on. A four-sided ruled box. The diary auditing itself, a fortnight in: he reads his own notebook back from its first page and decides against backfilling. The days he means are 16 August – 6 September, which the numbered list above has just covered.

Tuesday, 14 September 1943. Kazan#

Morning. Under the sun’s rays the hoar-frost is melting on the neighbouring roofs. It seems that at last there will be a clear sunny day.

Yesterday I appended to my lecture a little moral about applied mathematics:

Chebotaryov naturally observed that there is no such thing as any consecutive development of mathematics “in layers”, but that the researcher at random “bites into” some point of the region of the “unknown”, separate from everything known before. Vgryzaetsia — to bite or gnaw one’s way in; vgryzat’sia v porodu is what a drill or a miner does to a rock face. Kolmogorov lays down a stratum, Chebotaryov bites through it. Both halves of a mining image, split between two men, in scare quotes on both sides.

In the evening, however, Anatoly Ivanovich and I discussed the question of how long one would have had to wait for this or that mathematical discovery, if it had not been made by precisely the given mathematician.

Pro domo mea, I expressed the opinion that without me the everywhere-divergent Fourier–Lebesgue series would not have been constructed at all in the past 20 years. Pro domo mea — Latin, “as regards myself”; literally, “in defence of my own house”. The editors gloss it in Russian for their reader; the gloss is dropped and this is ours. He writes the surnames in Latin script and hangs a Russian case-ending on them with an apostrophe: ряд Fourier—Lebesgue’а, and below книгу Weyl’я, по Weyl’ю; on 29 September, со Schnellverschluss’ом. English has no equivalent gesture and the device is simply lost in translation. Noted once here.

As a more significant and more long-drawn-out example A.I. puts forward Hilbert’s theorem on a finite system of invariants.

A.I. (following Weyl) told of the general problem of a finite system of invariants for any group of linear transformations.

Wednesday, 15 September 1943. Kazan#

Bekehrte

Bei dem Glanz der Abendröthe Ging ich stillen Wald entlang, Damon sass und blies die Flöte, Dass es von den Felsen klang. ⁠ So la la! le rala! Und er zog mich zu sich nieder Küsste mich so hold, so süss. Und ich sagte: blase wieder! Und der gute Junge blies. ⁠ So la la! le rala! Meine Ruh’ ist nun verloren, Meine Freude floh davon, Und ich hör’ vor meinen Ohren, Immer nur den alten Ton, ⁠ So la la! le rala!

⁠ Goethe

Eigenthum

Ich weiss, das ich nichts angehört, Als der Gedanke, der ungestört Aus meiner Seele will fliessen, Und jeder günstige Augenblick, Den mich ein liebendes Geschick Von Grund aus lässt geniessen.

⁠ Goethe

Thursday, 16 September 1943. Kazan#

Vier Jahreszeiten (Sommer)

⁠ 19. Grausam erweiset sich Amor an mir! O, spielet, ihr Musen, Mit den Schmerzen, die er, spielend, im Busen erregt! ⁠ 35. Warum bin ich vergänglich, o Zeus? So fragte die Schönheit. Macht’ ich doch, sagte der Gott, nur das Vergängliche schön. ⁠ 36. Und die Liebe, die Blumen, der Thau und die Jugend vernahmen’s; Alle gingen sie weg, weinend, von Jupiters Thron. ⁠ 37. Leben muss man und lieben; es endet Leben und Liebe. Schnittest du, Parze, doch nur beiden die Fäden zugleich!Four Seasons (Summer). — 19. “Cruelly does Amor show himself to me! O play, you Muses, with the pains that he, in play, stirs up in the breast!” 35. “Why am I transient, o Zeus? So asked Beauty. — Why, said the god, I made only the transient beautiful.” 36. “And Love, the flowers, the dew and Youth heard it; all of them went away, weeping, from Jupiter’s throne.” 37. “One must live and love; life and love come to an end. Would that you, Parca, cut both their threads at once!” ⟨Goethes Werke: I, 1 (1887), S. 348, 350⟩. He takes four epigrams out of the sequence and keeps Goethe’s numbers; the two page-references are for the two places he took them from. (Sommer) is letter-spaced in the source — the Russian razryadka, an emphasis device with no English equivalent; it is given as italics here, as everywhere in this edition.

Dieselbe

Nur wer die Sehnsucht kennt Weiss, was ich leide! Allein und abgetrennt Von aller Freude, Seh’ ich an’s Firmament, Nach jener Seite. Ach! Der mich liebt und kennt. Ist in der Weite. Es schwindelt mir, es brennt Mein Eingemeide. Nur wer die Sehnsucht kennt. Weiss, was ich leide![In the margin:] This is always sung by Pusya.

These last three days I have been sitting over Goethe’s verses (from Pusya‘s little book with the photograph of the flood of the Dnieper at Smolensk).

And the form too is astonishing! I am especially privately proud of the discovery of the unbroken dactyl [bespereboinyi daktil’] in “Rastlose Liebe”: Bez- (“without”) + pereboi. A pereboi is an interruption of a regular series of beats: of an engine, a misfire; of a pulse, an arrhythmia — pereboi v serdtse is the everyday Russian for heart palpitations; and in verse theory, a rhythmic inversion that breaks the established metre. So: a dactyl with no arrhythmia, in a month whose pages carry Oleg’s “complications on the heart”, “poor Oleshka with his heart”, Mandelstam speaking “with pain in his heart”, and an acute endocarditis — in a volume called The quiet sound of the heart. Offered as the translator’s inference, not asserted.

Dem Schnee, dem Regen, Dem Wind entgegen, Im Dampf der Klüfte, Durch Nebeldüfte, ⁠ Immer zu! ⁠ Immer zu! ⁠ Ohne Rast und Ruh’!

Lieber durch Leiden Möcht’ ich mich schlagen, Als so viel Freuden des Lebens ertragen. Alle das Neigen von Herzen zu Herzen, Ach, wie so eigen Schaffet das Schmerzen!

Wie soll ich fliehen? Wälderwärts ziehen? Alles vergebens! Krone des Lebens, Glück ohne Ruh’, Liebe, bist du!

I wrote Yura a letter about the translations of Goethe’s verses.

It is possible that this is only a literary form, and that in fact it will not even be sent, as one already has been rejected [zabrakovano], written before my departure from Moscow. The verb is that of brakovka, acceptance sampling — the culling of defective goods — and he is applying it to his own letter, in the same week he lectures on acceptance sampling twice.

Saturday, 18 September 1943. On the road to Moscow#

We travelled on a beautiful, sunny day.

The Volga, the Chuvash oak forests, the Observatory stay in the memory.

I read Vera Goethe’s verses — she knows them and loves them, with a good selection.

Sunday, 26 September 1943. Moscow#

Early morning. I sit at the open window in the Moscow room.

By the little piece of sky visible on the right — pink clouds in little fleeces. Anya is still asleep.

Over the floor of the room is scattered the potato brought yesterday. On the table a disorder, among which the recently acquired “Problems of Form in the Fine Arts” of Hildebrand and “Bondage and Bondmen in the Muscovite State in the 17th Century” of Yakovlev. Adolf von Hildebrand, Das Problem der Form in der bildenden Kunst (1893); A. I. Yakovlev, Kholopstvo i kholopy v Moskovskom gosudarstve XVII v. (1943).

A goose, rather [brown?], with its middle taken out — it too stands on the table and serves as a stand for pens and pencils:

Yesterday may be counted a success. In the morning with Anya, Borya and Tatyana (spouse No. 2 of B. Egorov) we dug the potatoes on the Sparrow Hills. [Translator’s note:] This band of the page is not typeset: two pen drawings of a goose — the first hollowed out into an open oval, the second with two pens stuck into it — and three lines of Kolmogorov’s hand between them, reproduced photographically and therefore invisible to the scan’s text layer. The colon introduces the second drawing: text and drawing are one sentence. Tatyana, whom the next typeset paragraph discusses, is named nowhere but here. The word after “rather” will not resolve at any available resolution between buryi (“brown”) and burnyi (“stormy, wild”); sense favours the first, the strokes may favour the second, and it wants the original notebook. The Kholmogory Goose is his own emblem and his signature: here it is a piece of furniture on his desk, holding his pens.

Tatyana — a creature with painted little lips and a snub-nosed, though comely, physiognomy. On her return from the trip (Krasnodar, the Kuban stanitsas, Gelendzhik on the eve of the taking of Novorossiysk, Rostov-on-Don) she tries very hard to “enter into the family”. She has a good attitude to Dima. By the same thing is explained her readiness to go with us too. Having got herself up in a ski suit and flirting with her own appearance with a spade, [Editor’s note:] Tatyana — B. D. Egorov’s second wife. Dima — B. D. Egorov’s son by his first marriage.

she worked, however, well. With enthusiasm she told of the pleasures of camp and country life; asserted that she wants to live in the provinces (“if Boris agrees”).

The autumn day, damp and somewhat misty on the Sparrow Hills, was also very fine. And poor Oleshka with his heart and the prohibition of physical work stood all day in the queue at the Chief Administration of the Militia for permission for Vera Yakovlevna’s residence registration. [Editor’s note:] What is meant is the final return to Moscow from the evacuation to Kazan, where until this time Vera Yakovlevna and Varvara Yakovlevna had remained. The August errand, completed: on 1 August the second of his immediate tasks was “to bring Vera and Varya”. Oleshka is a new diminutive; August has only Oleg.

We caught a lorry and brought everything home (for 400 r.). I immediately changed and went off to the House of Scientists.

With Papaleksi and Fesenkov I was on the tellers’ committee.

In snatches during the sitting I dined.

Although the result of the elections is satisfactory, the impression from our public life [obshchestvennost’] is a sad one. And not only from the group now ruling (A. F. Ioffe), but from the old men too, of the sort of Bernstein and Mandelstam, who cannot rise above defending their personal candidates by every means. O.Yu[Editor’s note:] O.Yu. — Otto Yulievich Schmidt.. was effective, but demagogic (in the question of Kurchatov). Obshchestvennost’ is the collective body of the professionally engaged, the “public” acting as a body — not publika, the audience, and not obshchestvo, society at large.

We supped with Kapitsa and Sobolev. With Kapitsa it is all the same easier to come to an agreement on a line of principle.

At the general assembly the only interesting thing was Asratian’s speech with a criticism of L. S. Stern (whose works were highly assessed in Bruevich’s report) and Frumkin’s subsequent proposal to approve the report only “in the main”. On this occasion Baikov showed himself a coarse and unintelligent boss, but Bruevich and Komarov turned out to be cleverer.

Monday, 27 September 1943#

The election of full members.#

Alikhanov — 77 of 95 ( — 18 party members?) Ivanov 55 Korneichuk 52 Sergeev-Tsensky — 56[Editor’s note:] ⟨Here are given the results of the elections at the general assembly of the Academy.⟩ A block set between two rules. His parenthetical aside is as printed.

S. N. Bernstein’s speech and the shameful spectacle Abram Fedorovich made. Pozorishche — pozor, “shame”, with an augmentative suffix; but the archaic pozorishche is “a spectacle” (from the root “to see”), and the older sense is still audible. Ioffe’s performance was both a sight and a disgrace.

In the evening — the enlarged expert commission. Unanimously they earmarked Kurchatov for the second place in nuclear physics. [Editor’s note:] ⟨On the supplementary election of full members.⟩ [Translator’s note:] Kurchatov had lost the ordinary ballot the day before, placing fourth in all three rounds; the expert commission now creates a second nuclear-physics seat and puts him in it unanimously, and on 28 September he is elected 13 of 14. This is the documented 1943 engineering of his election, and he was by then head of the Soviet atomic project.

For the second place in applied mathematics, after a short discussion, Abram Fedorovich’s roll-call vote proceeded thus:

Vavilov — Smirnov

Mandelstam — Smirnov

Bernstein — Smirnov

I — Lavrentiev

Kapitsa — Smirnov, since Lavrentiev is a Ukrainian academician

Sobolev — abstains

Fock — Smirnov

Vul — abstains

Ioffe — Smirnov.Every name in the roll-call is underlined in the source, including his own — the same device that on the previous folio marks who was elected, here marking who is speaking. It is invisible to the scan’s text layer in both places.

I declared after this that, to avoid splitting the vote, I would support Smirnov.

Then I waited for Anya a long time senselessly, in order to go to Sergei Ivanovich Preobrazhensky’s, thinking that she was listening to the reports of Obruchev and Pavlovsky.

Tuesday, 28 September 1943#

The assembly of the Division at the Neskuchny.#

I was somewhat late. Before my arrival Ivan[Editor’s note:] Ivan Matveevich — I. M. Vinogradov. Matveevich had spoken sharply against V. I. Smirnov and for Mikh. Aleks. Lavrentiev. [Editor’s note:] The Neskuchny ⟨palace⟩ — so A.N. calls the building of the Presidium of the USSR Academy of Sciences at 14 Bolshaya Kaluzhskaya Street. The adjoining part of the Gorky Park of Culture and Rest has always been called the Neskuchny Garden.

The candidates for corresponding membership had been arranged the day before thus:

S. N. Bernstein spoke for Kuzmin, considering him no worse than Petrovsky and referring to A. N. Krylov’s opinion. I, for my part, gave my opinion of him as the strongest mathematician in the USSR of a purely “sporting” type (number theory, trigonometric series, interpolations and mechanical quadratures — the latter, however, in a style far from the needs of practice).

At the general assembly of the Division Nikolai Mitrofanovich ⟨Krylov⟩ spoke yet again, extremely plaintively and at the same time pretentiously, for N. N. Bogolyubov. It was I, again, who answered (extremely amiably and gently). Two Krylovs on one page: A. N. Krylov the naval architect, cited above for his opinion of Kuzmin, and N. M. Krylov, the Ukrainian mathematician, whose surname the editors supply in the body in angle brackets.

In the first round were elected:

Petrovsky Kikoin Mikhailov Kibel Kobeko Keldysh Alexandrov

It remained to elect

a) Andronov or Kravets b) Orlov or Mansurov.

Mandelstam, though with pain in his heart, spoke out for Kravets, which decided the matter, notwithstanding my own, Sergei Lvovich’s and Lev Semyonovich’s speeches.

In the second round were elected:

Kravets, Orlov.

In the evening Anya and I were at Sergei Ivanovich’s. He is a sensible and pleasant man, a doctor, apparently decent, but no more. He approved the appeal to Tareev, supported sponging-down with room-temperature water and moderate hardening [Editor’s note:] Sergei Ivanovich — S. I. Preobrazhensky.

and training in the future. The acute endocarditis he ascribes to the flu. It is astonishing how far both Sergei Ivanovich and his spouse look at everything through Polina Alexandrovna’s eyes (and Elizaveta Rodionovna likewise!). [Editor’s note:] Elizaveta Rodionovna — the mother of D. D. Romashov (Dimetrusya).

I got excessively heated and expressed my whole attitude to Polina Alexandrovna. Needlessly, perhaps, I also declared my intentions of taking Polina Alexandrovna to live with us. The latter, however, called forth warm sympathy.

Wednesday, 29 September 1943#

The supplementary election of academicians and the confirmation of corresponding members at the general assembly.#

My speech on the subject of mechanics, Ilyushin and Chetaev.

A. Ya. Vyshinsky’s remark: “A strange speech!” (The result of a confusion of two Ilyushins? — if so, then everything has been explained to Vyshinsky by Nikolai Ivanovich Muskhelishvili and others.). Helpless speeches (on the subject of Chetaev) by Terpigorev and Galerkin. The two Ilyushins are A. A. Ilyushin (1911–1998), the mechanician, who headed the Moscow University chair of elasticity theory and was elected a corresponding member in this very election, and S. V. Ilyushin (1894–1977), the aircraft designer. Kolmogorov’s conjecture is that Vyshinsky took the one for the other. The question mark is his. A. Ya. Vyshinsky (1883–1954) — Procurator General of the USSR and the prosecutor of the Moscow Trials, at this date a Deputy People’s Commissar for Foreign Affairs and an academician since 1939.

On a separate vote I insist only in application to Chetaev: 7 against, including Orbeli, 17 — abstained.

In the evening Oleg at the reports of Terenin, Kapitsa and Speransky.

I preferred Shirinsky’s concert.

The first half from Asafiev, Prokofiev and Shostakovich.

In the second half Tchaikovsky, Mussorgsky. The piano part was performed by Jacobson — very beautiful, “with the face of a medusa”, a very spiteful one, according to the remark of S. N. Nyberg, who was sitting next to me. Specially for the Tchaikovsky a handsome sixteen-year-old fair-haired boy in a short jacket with a Schnellverschluss came to turn the music for her. Schnellverschluss — German, a zip fastener. The editors gloss it in Russian in the body; the gloss is dropped and this is ours.

The “Variations on a Rococo Theme” (for cello) in the first redaction made a great impression.

With them I left, not staying for the Mussorgsky.

October 1943#

Friday, 1 October 1943. Komarovka#

Schwimme, du mächtige Scholle, nur hin! Und kommst du als Scholle Nicht hinunter, du kommst doch wohl als Tropfen in’s Meer.

⁠ Goethe, Vier Jahreszeiten (Winter). 99.

Winterreise#

Яркий снег, и солнце в небе; Путь далекий. Облака. Хорошо мне, сердце в неге, И душа, как снег, легка!

Темной улицей пустынной Я ищу твой огонек, И дороги этой длинной Темный смысл мне невдомек.

Комнатка эта такая уютная, И самовар зашумел на столе; Быстро исчезла усталость минутная, Радость так тихо подкралась ко мне.

Ах, хоть нежностью бывалой Расцвечен вновь твой венок — Чую, путник запоздалый, Что опять я одинок...

Утро. Мы идем в конюшню, Лошадям даем овса. Снежным кружевом воздушным Вновь подернулись леса.

...Кто меня, как ты, согреет?.. Ехать надо, уж пора! Снова солнце, ветер веет, Небо, снежные поля...

Vier Jahreszeiten (Herbst)#

Wisst ihr, wie auch der Kleine was ist? Er macht das Kleine Recht; der Grosse begehrt just so das Grosse zu thun.

Was ist heilig? Das ist’s, was viele Seelen zusammen Bindet; band’ es auch nur leicht, wie die Binse den Kranz.

Was ist das Heiligste? Das, was heut und ewig die Geister, Tiefer und tiefer gefühlt, immer nur einiger macht.

⁠ Goethe

Continuation#

I spent the morning idling at Komarovka.

I came by three o’clock to Anya‘s festive dinner (with Vera Yakovlevna and Oleshka) and her pies. For the tea that followed the dinner Pusya arrived with Varvara Sergeevna. [Editor’s note:] 1 October is the birthday of Anna Dmitrievna Kolmogorova. In 1943 she turned 40.

In the evening, The Snow Maiden (Varvara Sergeevna, Pusya, Vera Yakovlevna, I, Anya, Oleshka). A good voice from the young singer who performed the Snow Maiden.

The general impression, however, was for everyone a moderate one: many good places, but the whole does not grip.

Tuesday, 5 October 1943#

Saturday, 2 October#

In the morning and afternoon I sorted potatoes, missing the Higher Attestation Commission. VAK — the Vysshaia attestatsionnaia komissiia, the body that confirmed academic degrees and titles.

We left for Komarovka with Oleg on the 20.00 train.

With pleasure I washed and took a shower.

Sunday, 3 October#

A walk with Oleg to the far Ucha. After dinner I read (to Vera Yakovlevna, V.S. and Oleg) “The Solitary Little House on Vasilyevsky” — a tale of A. S. Pushkin’s as recorded by V. P. Titov.

Night of 3–4 October#

At Alikhanov’s (with Pusya and Anya). [Editor’s note:] The reception at Alikhanov’s evidently took place in connection with his election as a full member of the USSR Academy of Sciences.

A disappointment — the excellent quality of the wines apart — an ordinary Soviet spree (with Landau and Nemenov; the promised Ios. Abg. Orbeli and Nik. Iv. Muskhelishvili were not there).

Monday, 4 October#

Ration-card and residence-registration affairs at the Institute. Departure for Komarovka.

Today#

Mainly, the editing of Yura’s poem:

Помнится... Редкая сетка веток, Слабо краснея, дрожит в отдаленье. Взор ожиданья порывист и меток . . . . . . . . . . . . . . . . . . . .

Principles of criticism: the joint epistle to Yurka, Pusya’s and mine — a success, it seems.

At last I have slept myself thoroughly out. I am in bliss on a diet of potato and carrot with butter, coffee with milk in the mornings and chocolate (2 bars!).

I am quickly coming back into form, physically and mentally.

Wednesday, 6 October 1943#

On Sunday, 26 September in the morning I was at Polina Alexandrovna’s and Oleg‘s.

Before Pusya‘s lecture we walked with Oleg as far as the Crimean Bridge — we talked of the possibility of a joint life, his and mine, Anya‘s and Polina Alexandrovna’s. It somewhat surprised me that the very idea of such an arrangement was taken by Oleg without the least embarrassment: at once he passed to the question of whether it would be convenient for P.A. to travel to her institute from Kaluzhskaya. [Editor’s note:] Kaluzhskaya — on B. Kaluzhskaya St. (now Leninsky Prospekt), in house No. 13, the so-called “House of Academicians”, flat 144, where the Kolmogorovs then lived. The windows of the Kolmogorov flat gave onto Vystavochny Lane — now Academician Petrovsky Street, after Petrovsky, who lived in the same house. In answer to his question about the causes of the ill-feeling between Anya and Polina Alexandrovna I suddenly resolved to tell him of my own understanding of the shift in P.A.'s exclusive attachments (first to Seryozha, then to Oleg himself) and of the whole of P.A.'s attitude to Anya in the distant past. All such things Oleg grasps very quickly and seriously. [Translator’s note:] “P.A.” here is Polina Alexandrovna (Ivasheva-Musatova), Oleg’s grandmother — not Pusya (P. S. Alexandrov), and not A. P. Alexandrov. She is female and a different person; the abbreviation is the single easiest catastrophic misreading in the entry. “Pusya’s lecture” below is P. S. Alexandrov’s.

By twelve o’clock we came to the House of Scientists. At first they did not want to let Oleshka in on his guest ticket. [Editor’s note:] The House of Scientists — both A. N. Kolmogorov and P. S. Alexandrov were long-standing members of the Moscow House of Scientists (Andrei Nikolaevich held membership card No. 5422, Pavel Sergeevich No. 6044).

V. L. Komarov’s lecture on Timiryazev was read in the absence of V. L. himself.

Pusya’s lecture exceeded all expectations in the richness and variety of its content (from Tyutchev’s verse to the thieving of the apparatus functionaries within the walls of Kazan University), the elevation of the general tone and the mastery of the delivery. The audience listened attentively and responded vividly to the hints scattered through the lecture. They clapped long and warmly. Afterwards Abram Fedorovich shook Pusya’s hand for a long time and, in his own words, declared that “only now have I understood what mathematics is”. [Editor’s note:] Abram Fedorovich — A. F. Ioffe.

Maria Fedorovna Andreeva congratulated him on the success, “like an old actress”.

Into the lecture there had also been inserted an exact exposition of the Kleinian interpretation of Lobachevsky’s plane geometry, which took some five minutes of the fifty.

For me, however, this lecture was hard, simply to the point of tears. So agitated and captivating an exposition of Lobachevsky’s scholarly and educational ideals (that is, strictly, of Pusya’s, or of his and mine in common) before the Presidium of the Academy (and the lecturer addressed himself much to the Presidium precisely!) rang wild. I was troubled, too, by the thought of whether the listeners might not take the emotional tone of the lecture as a manifestation of the lecturer’s hurt and bitterness over his own non-recognition (and non-election...). [Editor’s note:] P. S. Alexandrov was elected a corresponding member of the USSR Academy of Sciences in 1929, and a full member (academician) only in 1953.

After the lecture Anya and Oleg set off to dine at Polina Alexandrovna’s, and I stayed to dine at the House of Scientists. For a long time they searched for my dinner coupon, which I had by mistake handed in that same morning for breakfast.

Because of this I was late to P.A.'s, and Anya and Oleg had left for Lyublino without me. I came to them already at dusk. In the dark Anya and I carried across all the cabbage from the near plot, which Oleshka had been cutting (he, after all, is not allowed to carry more than 15 pounds!). [Editor’s note:] Lyublino — in this then-suburban settlement (now a district of Moscow, Verkhnie Polya St.) was the Filtration Laboratory attached to the aeration fields, where Anna Dmitrievna worked. There too were the garden plots of the Laboratory’s staff.

Friday, 8 October 1943#

Wednesday#

I corrected the stenogram of my speech at the general assembly ⟨of the Academy⟩, wrote a short letter to A. Ya. Vyshinsky. [Editor’s note:] The letter to Vyshinsky — see the Note to the entry of 29 September 1943.

The Mathematical Society — O. Yu. Schmidt, Gelfand and Raikov (the theorem on the existence of irreducible representations of locally bicompact groups by unitary operators in Hilbert space).

The Board (of the Mathematical Society) (the problem of the approaching re-elections).

At S. Musatov’s.

Thursday#

At Borya’s (a son!). [Editor’s note:] Borya — B. V. Gnedenko. The son is Dima (D. B. Gnedenko), born 1943.

At the Mathematical Institute I got stuck on the jury for the socialist competition.

At the philology faculty, at Prof. Vinokur’s, on Petya‘s business.

Friday morning#

Again at the philology faculty and on Trubnikovsky (also Petya’s business). [Editor’s note:] Petya’s business — Andrei Nikolaevich was at that time petitioning for a post at the Philology Faculty of Moscow University, and for a residence registration with his aunts in Trubnikovsky Lane, for Petr Savvich Kuznetsov, who had returned from evacuation.

At Oleg‘s — ill with mumps? Swollen on both cheeks, temperature 37.2. He says he always feels especially well when he is ill (?!). He is reading about the principle of relativity. My explanations he listens to sensibly.

A multitude of new projects for a military composition, among them a slain youth with his head tipped back into the water, with grass and water-lilies all around.

“The funeral service for the slain man” — the priest’s head is good — but the author insists stubbornly that this is exclusively “an analysis of form”.

Besides which, at my commission, he is copying Michelangelo’s “Adam”.

In watercolour — some very colourful dancing couples with generals, and the Presidium of the Academy at Pusya‘s lecture.

At last I have got to Komarovka for a good while: Saturday to Wednesday — five working days!

Saturday, 9 October 1943#

In the morning Pusya and I bathed, drank coffee.

Then I did many small jobs: I looked through the notes submitted to the DAN, wrote the report of the chairman of the state examination commission, drew the diagram for Pusya’s lecture on Lobachevsky. [Editor’s note:] DAN — the journal Reports of the Academy of Sciences of the USSR (in the case where the author is not a member of the Academy, his note must be presented by one of the academicians). [Editor’s note:] The diagram for Pusya’s lecture — Andrei Nikolaevich liked to make diagrams; in P. S. Alexandrov’s monograph Combinatorial Topology many of the diagrams were done by Kolmogorov.

I worked rather lazily, reading in passing Plato (“Alcibiades I”), Goethe and Bogdanovich’s “Dushenka”.

In the evening we carried across the newly acquired firewood. In the course of it I felt a kind of faintness (?).

Seryozha says that in reading Hegel he is not too much occupied by the literal logical sense of Hegel’s assertions, but is carried away by the grandeur of the Hegelian spirit. Hegel’s works he compares with Beethoven’s symphonies, and even indicates which of them is analogous to which symphony. Pusya found this “verbiage”. The category of “mental onanism” (O. Yu.'s) came into my head too, independently. This rapture before the grandiosity and greatness of ideas independently of their content is, perhaps, Seryozha’s basic, fatal weakness. [Editor’s note:] Seryozha — S. M. Ivashev-Musatov. [Translator’s note:] The edition prints Sergei Ivashev-Musatov’s patronymic inconsistently: here and in the note on folio 74 the page-foot notes give “S. M.” (Mikhailovich, his passport patronymic), but the Index of Names heads his entry “Sergei Nikolaevich” (S. N.). The discrepancy is the edition’s own and is left unresolved; his initials are reproduced folio by folio as printed, not normalised. Verbiage renders slovobludie — slovo “word” + blud- “fornication, going astray” (the root of zabludivshiisia, “gone astray”); the pejorative is vivid, closer to “word-whoring”. Mental onanism is O. Yu. Schmidt’s phrase, which Kolmogorov here reports adopting. “Independently of their content” is underlined.

Oleg’s markings in “Paul et Virginie”#

“The courage that pushes us towards death lasts only a minute. It is often aroused by vain human praise. But there is another courage, rarer and more precious, which helps us to bear, daily, without praise and without witnesses, all life’s adversities — this is patience.

It is sustained in us not by others’ opinion and a momentary impulse, but by the will of God.”

“So many passions stir us that reason is often darkened and troubled by them; but we have a beacon at which we can rekindle its torch, namely — science.”

“Science, my son, is a true help from on high.”[Translator’s note:] The two quotations are the passages Oleg marked in his copy of Bernardin de Saint-Pierre’s Paul et Virginie, transcribed here by Kolmogorov under the heading above; each is flagged in the left margin by a boxed NB — Oleg’s mark, not Kolmogorov’s. Rendered into English as Russian prose, since they carry no metre.

Sunday, 10 October 1943#

Bekehrte#

Monday, 11 October 1943#

Petrov brought Pusya the four-volume collected works of Esenin (GIZ, 1926–27).

Есть в дружбе счастье оголтелое И судорога буйных чувств — Огонь растапливает тело, Как стеариновую свечу. ⁠ Возлюбленный мой! Дай мне руки — ⁠ Я по-иному не привык, — ⁠ Хочу омыть их в час разлуки ⁠ Я желтой пеной головы. Ах, Толя, Толя, ты ли, ты ли, В который миг, в который раз — Опять, как молоко, застыли Круги недвижущихся глаз. ⁠ Прощай, прощай. В пожарах лунных ⁠ Дождусь ли радостного дня? ⁠ Среди прославленных и юных ⁠ Ты был всех лучше для меня. В такой-то срок, в таком-то годе Мы встретимся, быть может, вновь... Мне страшно, — ведь душа проходит, Как молодость и как любовь.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Прощай, прощай! В пожарах лунных Не зреть мне радостного дня, Но все ж средь трепетных и юных Ты был всех лучше для меня.

And so the whole myth of my awakening to a pagan-beautiful sensuous life, which so occupied me since last autumn, comes to an end!

В неизведанный небес простор Грустный ветер листья с клена мечет И со мной заводит разговор, Ласково обняв меня за плечи:

Неужели тоже Вы поэт? Сколько повидал я вас на свете! Вам, как мне, наверно, тесен свет, Что порой так радостен и светел. Я привык: ведь издавна слыву Средь людей мечтателем суровым; Грустью и печалью лишь живу, Да с тоски кручу хвосты коровам!.. ⁠ А бывает, слишком рассердясь ⁠ (Над собою тоже я не властен), ⁠ Грозной бурей смешиваю в грязь ⁠ Человечьи мелочные страсти... Нам обоим дар мечтаний дан: Вместе с Вами то смеюсь, то плачу; Наш отец — бескрайний Океан, А подруга наша — Неудача! ⁠ Он замолк, а вечер заливал ⁠ Даль небес осеннею прохладой. ⁠ Факел солнца тихо догорал ⁠ За лесною синею оградой.

Мы теперь уходим понемногу В ту страну, где тишь и благодать. Может быть, и скоро мне в дорогу Бренные пожитки собирать. ⁠ Милые березовые чащи! ⁠ Ты, земля! И вы, равнин пески! ⁠ Перед этим сонмом уходящих ⁠ Я не в силах скрыть моей тоски. Слишком я любил на этом свете Все, что душу облекает в плоть. Мир осинам, что, раскинув ветви, Загляделись в розовую водь! ⁠ Много дум я в тишине продумал, ⁠ Много песен про себя сложил, ⁠ И на этой на земле угрюмой ⁠ Счастлив тем, что я дышал и жил. Счастлив тем, что целовал я женщин, Мял цветы, валялся на траве И зверьё, как братьев наших меньших, Никогда не бил по голове.

Знаю я, что не цветут там чащи, Не звенит лебяжьей шеей рожь. Оттого пред сонмом уходящих Я всегда испытываю дрожь. Знаю я, что в той стране не будет Этих нив, златящихся во мгле. Оттого и дороги мне люди, Что живут со мною на земле.

⁠ С. Есенин

Tuesday, 12 October 1943#

A smoky-sunny (Parisian) autumn day.

I am settling in for the winter in my room.

After breakfast Pusya and I walked down along the Klyazma, looked at the trees wrenched out by the hurricane (among them our two pines by the shore).

Vera Yakovlevna sits in turn in the different rooms and reckons up or recalls something. Just now she has gone to Pervomaiskaya.

To the preceding reflections I here append the letter to Pusya of 6 February, which was written, in large measure, for myself (for want, that spring, of this notebook). This letter was itself the end of a whole period of life that had begun in the summer of 1942. [Editor’s note:] The letter of 6 February 1943 is glued into this notebook. It is printed in full in the book Selected Passages from the Correspondence of A. N. Kolmogorov and P. S. Alexandrov of the present edition (pp. 587–593).

After that, in February, I wrote my notes on P.I.Ch. [Editor’s note:] The notes on P.I.Ch. — see the Note to the entry of 1 August 1943 (p. 28). [Translator’s note:] The facsimile is the typeset cover of his own essay on Tchaikovsky, now in print: “Kh.G. / PYOTR ILYICH TCHAIKOVSKY / Love and Creative Work / G.P.D. / 1943”. “P.I.Ch.” are Tchaikovsky’s initials (Chaikovskii by transliteration); “Kh.G.” is the Kholmogory Goose, his own pen-name. The caption is his. “G.P.D.” is an unresolved mock-imprint, left as printed.

The mood was analogous to the present one. Only now there would be added the evening bathes by the Komarovka bridge after the first trip with Oleg to Lyublino, with talk of nature, Plato and the like.

Friday, 15 October 1943#

Wednesday morning I spent on a letter to Sergei Musatov about Oleshka (there is a copy). [Editor’s note:] ⟨A copy of the letter to S. Musatov has not been found.⟩

Then I drove Vera Yakovlevna to Moscow.

I was at the defence of Kreines’s dissertation, on the synthesis of gear mechanisms. Ilyushin, in his general irritation at the mathematicians, started up a scandal, supported by Kosmodemyansky, Filonenko and, in part, Artobolevsky. Ilyushin here is A. A. Ilyushin, the mechanician — not S. V. Ilyushin, the aircraft designer; the same collision Kolmogorov himself flagged on 29 September.

I spoke a good deal, on the whole to good effect.

Result: for — 27, against — 5, abstained — 2.

Only by ten o’clock did I get to Seryozha‘s. What was essential in the conversations that took place there will go into the next letter to him. It is worth going to Seryozha’s, though, not to converse but to hear the four-hand playing (Mozart, Schubert, Gluck). [Editor’s note:] For four hands — S. M. Ivashev-Musatov played the piano with his wife Alla. (The note stands at the foot of folio 74, keyed back to this page.) —Trans.

I got home just after twelve.

Thursday#

The class L of functions

for which the number N(λ) of those k with |λ_k| < λ satisfies the condition

A function from L is uniquely determined by its values on an interval of length 2π !!Reconstructed from the image. These are almost-periodic functions (Bohr): a trigonometric sum over a discrete spectrum {λ_k}, with a counting condition on how the spectrum thins out. The “lim” is underlined on the page — the lower limit, liminf, set here as \varliminf; it is not modernised with a λ→∞ subscript, which the page does not carry. The doubled exclamation is his. The thread — stationarity, homogeneity, spectra — is item II of the “big jobs” list four days on.

Oleshka’s note:

Dear Andrei!

Many thanks for the book. It interested me exceedingly, but I could not get on with it, since my brains will not work and my temperature is rising. Everyone laughed a great deal when they read the captions and looked at the little added drawings. I live now as if in non-being — I lie down and do nothing. I lie from morning till evening, only now opening my eyes, now closing them.

Well, forgive me, I can write no more, I have a temperature of 40 just now.

Oleg.

I have no appetite at all. I lie all day and eat nothing. Only now and then I take a gulp of water. If I do eat (because one must) — in the morning a morsel with hot tea, and in the evening some soup-broth. Only hot tea or boiled water do I drink with pleasure.

I sent Oleg “The Voyage of Captain Scott” with penguins drawn in.

I got to Komarovka around midnight. Full moon, stars, mist.

Today is sunny and fine. I got up at 9 o’clock.

Vier Jahreszeiten (Winter)#

Fallen ist der Sterblichen Loos. So fällt hier der Schüler, Wie der Meister; doch stürzt dieser gefährlicher hin.

Vieles gibt uns die Zeit#

Vieles gibt uns die Zeit und nimmt’s auch, ⁠ aber der Bessern Holde Neigung sei ewig dir froher Besitz.

Man mag nicht mit jedem leben, und so kann man auch nicht für jeden leben; wer das recht einsieht wird seine Freunde höchlich zu schätzen wissen, seine Feinde nicht hassen noch verfolgen, ...

⁠ Goethe

I keep sitting and idling over this notebook, over Goethe in various editions, over Oleshka’s few letters and notes.

I shall go now for a bathe!

. . . . . . . . . . . . . . . . . . . . Молкнет язык мой, и тонкое пламя Льется по членам моим, начинает Звон раздаваться в ушах, пред глазами Ночь наступает. Праздность, Катулл, насылает мытарства, Праздность и блажь на тебя напустила; Праздность царей и блаженные царства Часто губила.

⁠ Катулл ⁠ (Подражание Сафо).

I ought to have gone with Anya to cart the cabbage out of Lyublino, instead of pretending to be very busy at Komarovka with scholarly labours.

Sunday, 17 October 1943#

Yurka‘s “Little Song”, composed on 6 October in Kursk.

Небо сонное надо мной. Месяц плавает золотой. ⁠ Время позднее. ⁠ Искры звездные Над прохладной водой.

⟨з а ч е р к н у т о⟩ ⁠ Чутко слушаю, ⁠ Все я думаю: ⟨в с т а в л е н о⟩ ⁠ Берег спит, молчит, ⁠ Сердце мне стучит: Где, любимый ты мой?

Ветер песенку мне поет, Что любимый ко мне придет. ⁠ И звенит волна, ⁠ Бьет о борт челна... Только он не идет! ⁠ И печально мне, ⁠ А в туманной мгле ⁠ [В непроглядной тьме] Звезды вьют хоровод.

Friday, Saturday and Sunday I reflected, without positive results, on the spectra of stationary random functions and related questions.

I bathed, read Goethe, Plato. I drew penguins and, in general, idly amused myself between times.

To spend time so is vexing and, perhaps, stupid, but one must also enter into an unconstrained occupation with real science, and without such unconstrained, dreamy days that does not come off.

I read Brehm on birds and, as many times before, gave myself over to reflections on whether there are objective grounds for reckoning birds (even from the “spiritual”, though not specifically “intellectual”, side!) lower than people.

However ridiculous it sounds, sometimes I am seriously perplexed.

Monday, 18 October 1943#

The day again fine, sunny.

I saw Anya off to Bolshevo — she had come the evening before — and Pusya to Tarasovka.

I read Turing and Van der Waerden’s “Gruppen von Linearen Transformationen”.

I dined alone.

In the evening, Obukhov.

I also read Gelfand and Raikov on the irreducible unitary representations of locally bicompact groups in Hilbert space.

I remain all the while in dread that I have unlearned how to work with concentration (in mathematics proper, that is!).

Sitz’ ich allein, Wo kann ich besser sein? Meinen Wein Trink’ ich allein, Niemand setzt mir Schranken, Ich hab’ so meine eignen Gedanken.

⁠ Goethe

Well, well! — the poor Goose with his big family. His own emblem again — the Kholmogory Goose (Kh.G.), set against Goethe’s solitary wine-drinker.

Tuesday, 19 October 1943#

Immediate jobs:

Ugh! Again for several months! — Markov, Lobachevsky, acceptance sampling, gunnery (2nd instalment), probability theory (book), crystallization. Must study: group theory (representations, Lie groups). [Translator’s note:] On the page these stand in three columns: far left his aside “Ugh! Again for several months!”; in the centre the list of immediate jobs; on the right, boxed off, “Must study: group theory (representations, Lie groups).” Brakovka is rendered throughout as acceptance sampling (Dodge–Romig lot inspection — never “rejection sampling”, which is a different thing); strel’ba as gunnery. The Gelfand–Raikov theorem of folio 66 is behind the group-theory note.

The big jobs [bol’shie dela]:

Saturday, 23 October 1943#

Tuesday, 19 October, evening#

Nina Dorliak — sings well, dresses (in Anya‘s opinion) “much too cleverly” (a gold transparent wrap over a black dress) and carries herself somewhat pretentiously.

The concert began with “Believe me not, my friend, when in excess of grief” (1869), but Anya, through the first half, was more occupied with external impressions (how she carries herself, how she sings) than with Tchaikovsky. Very fine is the romance to Tyutchev’s words, “As over the hot ash” (1874), which I had not heard before.

The second half began with “Was I not a little blade of grass in the field” (words by Surikov, 1880) — very fine, and it carried Anya over, it seems, to the perception of the music itself.

Fine is “In the dark hell underground...” (words by Maikov, 1872).

There stayed in the memory the performance of the familiar “Bear my heart away into the ringing distance” (1873) and “Alone again, as before” (1893).

For the encores all sorts of nonsense was sung — well, though.

Pusya scolded me for applauding over “So what, then?” (words by P. I. Tchaikovsky, 1872).

Wednesday, 20 October#

12 o’clock. The editorial board of Matematicheskii Sbornik.

Otto Yulievich presides brilliantly, but knows the business not at all and is not in the least embarrassed by it. [Editor’s note:] Otto Yulievich — O. Yu. Schmidt was then editor-in-chief of the journal Matematicheskii Sbornik; P. S. Alexandrov and A. N. Kolmogorov were on the editorial board.

I talked with S.N. in his office at the Academy institute and along the way, as far as the Crimean Bridge. [Editor’s note:] S.N. — Sergei Natanovich Bernstein.

N. V. Smirnov and P. S. Novikov took our and Pusya’s books, potatoes and Varvara Sergeevna’s things from Kapitsa’s out of the Mathematical Institute and brought them to us. (Both are pleased, since, apparently, without cooperation with us they would not have got a vehicle.)

At 6 o’clock — the Mathematical Society.

O. Yu. presided not only brilliantly but with a charming humour.

Re-elections:

The officer slate continues: Secretary — A. I. Maltsev, 20 (V. V. Nemytskii — 9); Treasurer — S. A. Galpern; Librarian — A. G. Kurosh; Members of the Board: A. Ya. Khinchin, O. Yu. Schmidt, L. A. Lyusternik, I. G. Petrovsky, L. S. Pontryagin. Maltsev’s count (20) is underlined, elected; Nemytskii’s (9), parenthesised, is the runner-up.

The roughly 50 members of the Society who had gathered belonged, for the most part, to the core of Moscow university mathematics in the good sense of the word (from the academic institute — Gelfand, Lyusternik, Plessner; of the geometers — Rashevsky alone); the “throbbing of hearts” and the diplomacy around the candidacy of V. V. Stepanov. “University” is underlined. “The throbbing of hearts” — his scare-quoted name for the pre-election lobbying, tied to the volume’s heart-motif (the title, The Quiet Sound of the Heart).

Discussions about the accessibility of talks.

Thursday, 21 October#

Cabbage affairs at Margarita Mikhailovna’s.

At Borya’s (a son, Natasha’s mother). Two Natashas run in these weeks: here, N. K. Gnedenko, Borya’s wife (“Natasha’s mother” — i.e. mother of the newborn); and, folios 81–82, a portrait model who is a friend of S. Musatov.

At the Academy of Sciences institute. The reception of doctoral candidates.

Lev Semyonovich, as chairman of the postgraduate commission, is occupied for the most part with psychology: he strives to guess who praises his candidates sincerely and honestly, and who does not.

Admitted: Shilov, Tolstov, Kulikov, Volkovyskii, Verchenko and Kozlov.

Bernstein is greatly aggrieved on behalf of his Sarmanov.

On all three sittings, on Wednesday and Thursday, I demonstrated, with complete success but perhaps with excessive pressure, my superiority in the knowledge of the essence of the matter.

Concert of Sofronitsky (Schumann)#

Encores: Chopin — a Nocturne and two mazurkas; Schumann — the Finale of “Kreisleriana” (1838).

The performance was severe, though also very rhythmically accented and full of contrast.

Pusya remarked that the Finale of “Kreisleriana” was performed in a peculiar way — “with a strong bringing-out of the left hand”.

Vera Yakovlevna found many little pieces from “Carnaval” familiar, and was pleased.

Anya took in the merits of Sofronitsky’s performance; Schumann she praised, but, it seems, more from a wish to give me pleasure by it.

Borya very much liked the idea of the procession of the “March of the Davidsbündler” over the transfinite numbers, but how far he really needs Schumann is doubtful.

Anya reported that Oleg is well, animated, drawing scenes of the crossing of the Dnieper, and eager for Komarovka, in particular for the sake of the morning on the river. Even Anya considers that, having lost weight, he has grown better-looking and carries himself more “smartly”.

On Friday ⟨22 October⟩ in the morning we sorted potatoes.

I went to the Shtekkers’ to find out the prospects for a vehicle to Komarovka. Ekaterina Dmitrievna received me very kindly. The domestic Shtekker museum keeps on growing. [Editor’s note:] The Shtekkers — Georgy Andreevich and Ekaterina Dmitrievna — neighbours (former owners) at the “Komarovka house”.

I got to Komarovka after five.

I read Fet, in the edition Pusya bought in place of my Petersburg one (1926 — at 30 kopecks a pound). By the chronological index we read the years 1840, 1842 and ... 1891–1892. [Author’s note:] This index makes unnecessary the little sheet of “old age” I recently drew up, which I am throwing away.

Besides the beginning and the end, a time of flowering was also the year 1857 (here now simply the lawful wife ⟨of A. Fet⟩, Maria Petrovna Botkina, the marriage with whom was concluded in Paris on 16 August 1857).

Pusya is wholly absorbed by Yurka‘s arrival (this evening?). [Editor’s note:] Boris (Borya) — B. V. Gnedenko. Yu. M. Smirnov — returned from a posting to Kursk on the business of his military service.

Monday, 25 October 1943#

On Saturday I read L. I. Sedov’s article on turbulence and did various small jobs. [Editor’s note:] The article on turbulence — most probably this concerns L. I. Sedov’s article “The planar problem of planing on the surface of a heavy fluid” (Proceedings of the conference on the theory of wave resistance, Moscow: TsAGI, 1937, pp. 7–30).

In the evening Anya and Oleg arrived, soon Pusya, and then Yura.

Sunday#

Conversations with Anya — most of all about Seryozha. She told much of interest about him: how resolutely he refused military service; how, guarding firewood, he let an old woman steal it; how he courted Dimetrusya; how he consoled someone, saving them from an attempt at suicide (even two of them). Then again, he once asked Anya for poison from the laboratory, for someone, at some family misfortune (?!). [Editor’s note:] Dimetrusya — D. D. Romashov — a gymnasium friend of A. N. and A. D. Kolmogorov and of S. M. Musatov.

Having received my little note about the material affairs of Polina Alexandrovna, he began to lament to Anya, in Oleg’s presence, that they are still feeding Natasha. [Editor’s note:] Natasha — a friend of S. Musatov, whose portrait he was painting at the time.

We walked along the forest edge as far as Tarasovka with Oleshka.

We talked, setting out from “Paul et Virginie”, of the simple life and of culture (self-simplification and a return to nature Oleg resolutely rejects), of love of all and love of the elect (he wishes that, in the main, it should be the former, but does not venture to deny the rights of the latter). About Polina Alexandrovna and Seryozha he understands everything, but Seryozha’s great possibilities in painting (and precisely as a painter-”theorist”) he naturally does not wish to yield. Is it good that I talk with him of all this?.. Self-simplification renders oproshchenie — the settled Russian term for Tolstoy’s doctrine of the simple life, the educated man renouncing comfort to live and labour like a peasant; a reflexive social-ethical programme, not mere “simplicity”. Paired with “a return to nature”. Oleg rejects the doctrine, not just a preference.

A ceremonial dinner in honour of Yura#

Fet:

1. 1842,
2. 1891–92,

Gumilyov and, for his “annihilation”, Pushkin. [Author’s note:] Oleg recently took a liking to “The Worker” and “You and I”, read to him by Seryozha. “The Trees” was intensively discussed among us, and pleased everyone (Varvara Sergeevna in particular), except Pusya. “For his annihilation” — the Gumilyov, that is, to be countered by the Pushkin poem copied next. “The Worker”, “You and I” and “The Trees” are Gumilyov’s.

Пора, мой друг, пора! Покоя сердце просит, Летят за днями дни, и каждый час уносит Частичку бытия, а мы с тобой вдвоем Предполагаем жить, и глядь — как раз — умрем. На свете счастья нет, а есть покой и воля. Давно завидная мечтается мне доля —

Давно усталый раб, замыслил я побег В обитель дальнюю трудов и чистых нег.

The *) footnote (Oleg’s Gumilyov reading) belongs to the “Gumilyov” line above.

This morning Oleg quickly made a study of our riverbank with its fallen birch.

I, for my part, found an elegant solution of the simplest of Lemmlein’s crystallographic problems.

The Yagloms were here — to sign me up for the goods-lottery and to take advice about the physicist-brother’s admission to the postgraduate course. [Editor’s note:] The Yagloms — the twin brothers Akiva Moiseevich and Isaak Moiseevich.

Today, in general, I languish and idle.

To A. S. Pushkin#

Она улыбкою своей Поэта в жертвы пригласила, Но не любовь, ответом ей Взор ясный думой осенила.

Нет, это был сей легкий сон, Сей тонкий сон воображенья, Что посылает Аполлон Не для любви — для вдохновенья.

⁠ Баратынский, 1837.

Tuesday, 26 October 1943#

On the death of Goethe#

. . . . . . . . . . . . . . . . . . . . Погас! Но ничто не оставлено им ⁠ Под солнцем живым без привета; На все отозвался он сердцем своим, ⁠ Что просит у сердца ответа: Крылатою мыслью он мир облетел, В одном беспредельном нашел ей предел.

Все дух в нем питало: труды мудрецов, ⁠ Искусств вдохновенных созданья, Преданья, заветы минувших веков, ⁠ Цветущих времен упованья; Мечтою по воле проникнуть он мог И в нищую хату, и в царский чертог.

С природой одною он жизнью дышал: ⁠ Ручья разумел лепетанье, И говор древесных листов понимал, ⁠ И чувствовал трав прозябанье; Была ему звездная книга ясна, И с ним говорила морская волна.

Изведан, испытан им весь человек! ⁠ И ежели жизнью земною Творец ограничил летучий наш век, ⁠ И нас за могильной доскою, За миром явлений не ждет ничего, — Творца оправдает могила его.

И если загробная жизнь нам дана, ⁠ Он, здешней вполне отдышавший, И в звучных, глубоких отзывах сполна ⁠ Все дольное долу отдавший, К предвечному легкой душой возлетит, И в небе земное его не смутит.

⁠ Баратынский, 1832

However, over the poetry I overlooked that yesterday’s solution of Lemmlein’s needle problem is mistaken.

In reality, the matter reduces to the integral equation

where P(α,l) is the probability that a needle, deflected by an angle α from the vertical, will grow to height l, and k is the mean density of needle-nuclei. Reconstructed from the image, his notation kept. Zarodysh — literally a “begotten little thing”, a germ or seed at the moment of coming into being; the technical term is nucleus, and “the mean density of needle-nuclei” is the seeding rate of the crystal needles whose growth the equation describes. This is Lemmlein’s crystallization problem — the “elegant solution” of the day before (folio 82) which he now finds wrong; it feeds item V of the “big jobs”, “the foundations of statistics”.

In the evening we walked with Pusya, drank tea and finished off the “Saamo” we had started with Yura on Sunday.

Wednesday, 27 October 1943#

This morning −6°. A winter dawn all round the sky and a dazzling sunrise.

I saw Pusya off and looked over Leonardo da Vinci, Raphael, Titian and so on. In reality, though, I am awaiting the evening in Moscow with Oleg (he is to come and show his new drawings, if they do not put him on duty at school).

What, then, is the matter: whence my disquiet and impatience?

I think it is not in “greed”, nor in the insufficiency of the time Oleg spends with me, but in irritation at my own powerlessness to bring him out of his present state, and in disquiet over whether I have set about the business rightly.

Meanwhile, I must still prepare tomorrow’s report at ANIMI. [Editor’s note:] ANIMI — the Artillery Naval Research Institute — in this Institute joint research on the theory of gunnery was carried out with the V. A. Steklov Mathematical Institute of the USSR Academy of Sciences, under the direction and with the direct participation of A. N. Kolmogorov.

November 1943#

Monday, 1 November 1943#

Thursday ⟨28 October⟩#

Lemmlein.

I cancelled the report at ANIMI.

At the AS institute, a discussion of the prospects for the development of the departments.

In the evening at Pusya‘s, Yura and Myasoedov. [Editor’s note:] Myasoedov — the head of a military depot at which Yu. M. Smirnov, being liable for military service, was on duty.

Friday ⟨29 October⟩#

A senseless day.

Saturday ⟨30 October⟩#

Even more so: I sat in Moscow and waited for the vehicle that Shurka had promised to send for the cabbage and the things. Anya read Gumilyov well to Vera Yakovlevna and me (“Lake Chad”, “The Rhinoceros” and the like — she especially loves “Mick”). Oleg on Saturday and Sunday is busy in Moscow laying the stove.

Sunday ⟨31 October⟩#

In the morning I reflected on the representations [predstavlenie] of groups. “Representations of groups by unitary operators” — the campaign that runs, all but continuously, through the rest of the month (folios 89, 92, 95–97, 99, 101–109): his attempt to build a theory of unitary representations of infinite groups. See the entry of 16 November.

In the evening I finished the article on Lobachevsky for Izvestia. [Editor’s note:] Izvestia — here the central newspaper, in which on 2 November 1943 there appeared A. N. Kolmogorov’s article “A great Russian scholar-innovator: on the 150th anniversary of the birth of N. I. Lobachevsky”.

Anya spent only Saturday evening and Sunday morning at Komarovka. I saw her off to Tarasovka.

Monday ⟨1 November⟩#

In the morning I wrote yet another letter to S. Musatov — in the main, about himself.

This, I hope, is the last.

Pusya, to the utter shaming of my weakness, obtained without difficulty from Bruevich an order to give a vehicle for transporting our things to Komarovka.

Saturday, 6 November 1943#

Tuesday ⟨2 November⟩#

In the morning I went to Moscow and learned of Varya‘s grave condition. [Editor’s note:] Varya — Varvara Yakovlevna Kolmogorova, Andrei Nikolaevich’s aunt, his mother’s sister; after her return from Kazan she lived in Trubnikovsky Lane. [Translator’s note:] Varya (Varvara Yakovlevna Kolmogorova, 1869–1943), who dies here, is not Varvara Sergeevna Alexandrova (V.S.), who is alive and appears a few folios on, beginning work at the sanatorium and moving into Marina’s room. Two Varvaras; one dies, one lives. Note likewise, later, V.Ya. = Vera Yakovlevna, his other, surviving aunt, against V.S. = Varvara Sergeevna. I myself went back with the things and the cabbage, and sent Anya to Varya. I meant to go to Moscow in the evening, but missed the train.

Wednesday ⟨3 November⟩#

On Trubnikovsky.

My report “Visual non-Euclidean geometry” at the Mathematical Society (a session in memory of N. I. Lobachevsky, jointly with the Faculty).

Thursday ⟨4 November⟩#

Piskunov. [Editor’s note:] Piskunov, Nikolai Semyonovich — in 1937 A. N. Kolmogorov, jointly with I. G. Petrovsky and N. S. Piskunov, published in the Bulletin of MGU the “KPP” paper that became widely known, “A study of the diffusion equation coupled with an increase in the quantity of matter, and its application to a biological problem” (also published in the book: A. N. Kolmogorov. Selected Works. Mathematics and Mechanics. — M.: Nauka, 1985, pp. 221–246).

At Bruevich’s (a conference on the AS editions connected with the Lobachevsky jubilee). [Editor’s note:] The jubilee of N. I. Lobachevsky — in 1943 the 150th anniversary of the birth of N. I. Lobachevsky was marked. Among the editions connected with this jubilee should be counted also the collection of articles by P. S. Alexandrov and A. N. Kolmogorov “Nikolai Ivanovich Lobachevsky. 1793–1943” (M.–L.: GTTI, 1943).

Friday ⟨5 November⟩#

Plato ([Philebus?], Euthyphro). [Translator’s note:] The page reads «Фалеб» — almost certainly Филеб, the Philebus, paired here with «Евтифрон», the Euthyphro. Kept as a doubtful reading of the printed form.

Yura’s verses.

Saturday ⟨6 November⟩#

Sorting out my things.

I am going to Moscow to buy tickets for the concerts (Tchaikovsky) and to take Oleg to Tareev.

Varvara Sergeevna has begun work at the Sanatorium and has settled into Marina‘s room. [Editor’s note:] The Sanatorium where V. S. Alexandrova began work — the sanatorium “Sosnovy Bor” (formerly under the KSU), was at Bolshevo, near Komarovka.

Tuesday, 9 November 1943#

Saturday ⟨6 November⟩#

The tickets for the 16th (the Sixth Symphony) proved to be all sold out. I bought for the 13th and the 18th. I was briefly at Borya’s. By six o’clock I went to the polyclinic. Poor Oleg stood on the street by the doors and said that he had made a mistake and was down for the 13th, not for today. We went to our home. We drank tea. Disputes about the mind and feeling. Oleg hopes (!) that his heart will turn out bad enough for him to be released from school physical training. Talk about the connection of the spiritual and the physical — Oleg digs in his heels, but unexpectedly became very interested in Beethoven’s passion for brisk walking, and so on.

We set off with Anya for Komarovka late.

Sunday ⟨7 November⟩#

I inserted formulas into the English text of the “Stationary Sequences” — I corrected many misprints and small errors in the Russian text. [Editor’s note:] “Stationary Sequences” — this concerns A. N. Kolmogorov’s paper “Stationary sequences in Hilbert space”, published in 1941 in the journal Bulletin of MGU. Mathematics, vol. 2, issue 6, 1941, pp. 1–40, and also in the book: Kolmogorov A. N. Probability Theory and Mathematical Statistics. — M.: Nauka, 1986, pp. 215–255. An English translation of this paper, it seems, then never saw the light.

Then we sawed and split firewood with Yura and Pusya.

After dinner we read Hoffmann’s “Sanctus” together.

With Anya I read the “Symposium” (we finished on Monday). Much in it frightens her, she is displeased that nothing is said there about the family (!), but some attractiveness and poetry she too felt.

We read besides, in addition, the beginning and end of “Alcibiades I”.

Apropos of the “Symposium” we looked (in my little guidebook) at Rodin’s “La mort d’Alceste” and some of his other things. For sculptures, like the Alcestis, Anya has good taste.

We looked too at Lysippus’s Socrates, since Anya remembered only Antokolsky’s Socrates.

Yura is on duty every third day and is much at Komarovka. On Sunday and Monday, with Pusya’s help, he set about translating Goethe. The first little attempt is good. In general, Yura flourishes. Physically, though thin and a little pale, he has grown even sturdier since Kursk.

Monday ⟨8 November⟩#

I continued the “Stationary Sequences”.

I read Trubetskoy on Socrates and Plato.

In the evening at the concert of Oistrakh and Oborin:

• Beethoven’s 10th sonata for violin and piano (1812).
• Schumann’s Fantasy.
• Franck’s Sonata (A-dur) ⟨also for violin and piano⟩.

Everything pleased both me and Anya very much. They performed well and with enthusiasm. Under Beethoven I dreamed, after my new custom (a bad one or a good?): morning at Komarovka, the poplars in my windows, Oleg sleeping and waking, Anya in the evening... Franck seemed very fine, but, indeed, “Christianly detached” (Gleb). [Editor’s note:] Gleb — G. A. Seliverstov.

At the concert there sat before us Kishkina and a charming senior lieutenant. Anya had earlier imagined Kishkina to be like Tatyana Borisovna Gendlina (!?).

Demuth. Seh’ ich die Werke der Meister an, Sî seh’ ich das, was sie gethan; Betracht’ ich meine Siebensachen, Seh’ ich, was ich hätt’ sollen machen.

⁠ Goethe

I, at all events, look sadly at the little boxes with my 70 opuses. Having got out of the habit of regular work these last years, I snatch now at this, now at that, to no purpose. Time passes, already the first volume of the course of analysis, promised for next autumn, hangs as a threat that it can be written in time only by giving up everything else for that period. [Editor’s note:] Here is a play on words: in German “Siebensachen” means “belongings, chattels, all that one has acquired”. But if one writes it separately, “Sieben Sachen”, the result is “seven things”, which A. N. then plays on, speaking of his 70 opuses.

Tuesday, 16 November 1943#

I reflected on the representations of groups by unitary operators. Yesterday I busied myself with the construction of a “continuously-coordinated” Hilbert space:

How to arrange $d\theta = f\,d\psi$ so that the knowledge of $\theta$ would replace $\{f, \varphi\}$, and $\theta$ would coincide for equivalent ones?

For three mornings I corrected the English text of the “Stationary Sequences”. Every kind of work demands much time and application. That is why it is so hard for me now to take it up seriously: for that one must renounce an over-broad and philosophical flight of fancy.

And with the characters [kharakter] I have still not made out how they are distinguished from other positive-definite functions [polozhitel’no opredelionnaia funktsiia] on groups! Character, $\chi(g)$ — classically the trace of a representation. But the whole November campaign turns on his attempt to redefine it: «my definition of a character» (folio 95), «how they are distinguished from other positive-definite functions» (here). He is trying to define a character for infinite groups, where the classical trace fails, as a distinguished positive-definite function. “Character” throughout renders his word, but a reader who takes it as the settled textbook object misreads the month — this is his own generalisation-in-progress. A positive-definite function on a group is $\varphi(g) = (U_g x, x)$, the matrix coefficient of a unitary representation (Bochner’s theorem) — the central object of the whole month. And I have already fantasised much about what to replace them with when they are absent (for infinite-dimensional unitary representations) in the “usual” sense of the word.

What, then — to plunge, in earnest, into the representations of groups? [Editor’s note:] As far as we know, Andrei Nikolaevich came forward with the problematics of group representations at the Mathematical Society only once, on 2 February 1944, with a report on this theme (the report was called “Unitary representations of infinite groups”).

Saturday ⟨13 November⟩#

I was with Oleg at Tareev’s. Oleg is much disheartened that no endocarditis is to be found.

Then with Anya, Oleg and Varvara Sergeevna I listened to Tchaikovsky’s “Trio” (Oborin, Oistrakh, Knushevitsky) and various of his piano pieces (Oborin).

Anya finds Tchaikovsky “much too earthly”. There, after Wagner “one wants to do something great”, but after Tchaikovsky — no.

In the morning on Saturday I was also at the VAK.

Friday ⟨12 November⟩#

With Pusya we opened the skiing season (along the forest edge to Tarasovka).

I gathered for Oleg illustrations for my ideas about portrait painting.

Thursday ⟨11 November⟩#

I gave a report at ANIMI. At the university I examined the two Yagloms in probability theory.

Die Freude Es flattert um die Quelle Die wechselnde Libelle, Mich freut sie lange schon; Bald dunkel und bald helle, Wie der Chamäleon. Bald roth, bald blau, Bald blau, bald grün; O dass ich in der Nähe Doch ihre Farben sähe!

Sie schwirrt und schwebet, rastet nie! Doch still, sie setzt sich an die Weiden. Da hab’ ich sie! Da hab’ ich sie! Und nun betracht’ ich sie genau, Und seh’ ein traurig dunkles Blau.

So geht es dir, Zergliedrer deiner Freuden!

Wednesday ⟨10 November⟩#

As I was carrying in the pipes for the stove, I discovered at Oleshka’s, next to Plato, a Gospel. In the evening we looked over Oleg’s paintings and drawings with Anya and Pusya.

Seriously good in Oleg’s work:

1. Three portraits of 1941 (himself, Seryozha, Polina Alexandrovna);
2. The first experiments in oil painting (1941): a) pretzels, b) cups and a teapot with gold on red, c) a bottle, a basin, a knife and bread;
3. Watercolour landscapes (Voskresenskoye, spring 1943). Adjoining them is the last, the Komarovka one.

I also liked the view of winter from the window (1941, graphics).

Seryozha gave him much, the art school — almost nothing.

If he has something to express by his painting, then with the “how” he will, perhaps, cope worthily, but to shine by the “how” alone, even at the level of Sokolov-Skalya, he probably will not be able.

The composition with the crossing of the Dnieper may come out not badly, but it is an exercise in the “how”, and only that.

Sunday ⟨14 November⟩#

In the morning I worked, wrote letters and did small jobs, then we ran on skis over the heavy, sticky snow with Yura.

Dinner with pudding.

We began to read Ovid’s “Metamorphoses”, and the first book — very good.

With Anya we looked over Serov, Titian, Velázquez, Rubens.

Yura flourishes on his translations of Goethe (really very good — somehow I find it hard to get used to the idea that Yura has, it must be, seriously turned out a genuine and considerable person!).

Monday ⟨15 November⟩#

I worked in the morning.

After dinner we read Ovid (“Phaethon”), and then I reflected on the realisations of Hilbert space mentioned above.

I read Trubetskoy on Aristotle.

I dug up the translation for the Euthyphro: piety — ὅσια, impiety — ἀνόσια, The Greek is his, set letter-spaced on the page; he is making his own Russian-to-Greek gloss for the dialogue he means to expound to Oleg. ὅσια (holy, pious) and ἀνόσια (unholy, impious) are the terms the Euthyphro turns on. The edition sets them without breathings or accents — and the first word with a delta-like initial (δσια) — so they are restored here to the standard accented forms of those terms, not reproduced as the bare printed letters. but whether I shall carry out my intention to write about the Euthyphro, the psychology of Plato and the like for Oleshka — I do not know.

Overcast and warm. The snow has almost gone. From somewhere a multitude of tits has appeared.

They flit about the lilac bushes and now and then chirp.

Sunday and Monday — good days.

Today — reaction and anguish.

I am digging about in Plato, Aristotle, Xenophon, Thucydides and the encyclopaedias. Am I doing a serious thing thereby (clarifying and checking my own philosophical views, even if apropos of Oleg’s enthusiasms — the occasion is a good and serious one!) or am I simply filling with this digging my own bewilderment and incapacity for work — I do not yet understand properly.

Saturday, 20 November 1943#

An early pre-winter morning. The waning moon stands high, straight before my window. Beyond the poplars, on the green-blue sky, lilac-pink clouds glow ever brighter. The fields turn yellow and pink — on them only the remnants of snow.

Just now I put out the lamp. Pusya has run off, warmly dressed and with a ski-pole, to bathe. Varvara Sergeevna is getting up in the former little room of Marina‘s.

Wednesday ⟨17 November⟩#

I did, after all, work out how to build a Hilbert space out of pure set functions:

In the evening the Mathematical Society began at six o’clock, not at seven, as I had thought. So I missed Kurosh’s report. Kreines reported well. [Translator’s note:] Three Kreins run through these two folios and must be held apart: M. G. Krein, the author of the report on the moment problem below (and of the photograph); Selim = S. G. Krein, his younger brother; and Kreines = M. A. Kreines, whose dissertation on the synthesis of gear mechanisms is meant here (cf. folio 72).

At the board meeting the leadership of the abstracting section was discussed — Pusya announced that I do not decline to take it, and only asked whether there were any objections to this.

To Vyacheslav Vasilyevich they gave the school-olympiad activity. [Editor’s note:] Vyacheslav Vasilyevich — V. V. Stepanov.

Kurosh earned universal approval by his energy in the library affairs.

Thursday ⟨18 November⟩#

Kolya Nyuberg was here. As always, we chatted with him about everything. Interesting were the stories he passed on, of his friend, a sergeant from among the research workers, about his impressions of Stalingrad. Somewhat wearisome — talk of poetic affairs.

Kolya took up the morning. Then we dined, and at two o’clock Petrovsky came to consult about faculty affairs (the establishment of a chair of physics, the situation with hydromechanics, and the like). Now Petrovsky, to such a degree, has definite judgements about everything (usually correct ones, and in my opinion too) that he comes rather to check and confirm them than for advice in the proper sense of the word.

At the Mathematical Institute I received Lemmlein (he keeps drawing the growth of “needles” and crystals on enormous sheets).

Then there was a very interesting report by Krein on the “generalized problem of moments”. A continuer of the traditions of classical analysis (albeit complicated by all sorts of modernity), he is, it seems, the most remarkable among us. Selim looked charming, while Krein the elder, in relation to Gelfand and the rest, was somewhat provocative (concerning classical applications).

With Pusya together we rode on the tram, in a great crush, to the conservatory.

I dropped in on Borya to leave my briefcase with him. There everything is little baths and swaddling-clothes. The son is to be called “Dima”, not “Mitya”. He is healthy, resembles Borya. [Editor’s note:] “...dropped in on Borya” — B. V. Gnedenko, who at that time lived with his family in the university building on Mokhovaya, i.e. right next to the Conservatory. [Editor’s note:] Dima — Dmitry Borisovich Gnedenko (born 6 October 1943) — son of B. V. Gnedenko, now a docent of the chair of probability theory at MGU.

Meanwhile Pusya found, at the entrance to the conservatory, Yura — who thought that he had been invited to this concert and not to the next (the 24th) — and Anya, who had forgotten her ticket at home. For them and for himself he boldly begged a free pass (after a morning telephone call to the administrator, about him alone, from Mikhail Sergeevich, who had operated on the administrator’s wife). [Editor’s note:] Mikhail Sergeevich — M. S. Alexandrov — brother of P. S. Alexandrov, a well-known Moscow surgeon. Afterwards Pusya recounted, with pleasure, how Anya and Yura had a bewildered air and were ready to weep, looking at him with exactly the same eyes.

The “Concert Fantasia” (a composition of P. I. Tchaikovsky’s, Op. 56, for piano and orchestra) pleased me very much.

After it Igumnov played also a nocturne and a waltz from the music to “The Snow Maiden” (P. I. Tchaikovsky’s music for the dramatic production at the Maly Theatre after A. N. Ostrovsky’s play).

The Second Symphony (of P. I. Tchaikovsky), by its naive gaiety, put Anya in perplexity. More lyrical in it is only the second movement.

In the finale the “little goose Andryusha” unexpectedly breaks out of all the complexities and terrors and, ever more resonantly, scatters itself in one and the same theme of the “crane”. The Kholmogory Goose (Kh.G.) again — his own emblem and household self-name, a pun on his surname; it recurs through the diary. Here he hears himself in the finale of Tchaikovsky’s Second Symphony (the “Little Russian”), whose last movement is built on the folk-tune “The Crane”.

Ioanna’s aria (from P. I. Tchaikovsky’s opera “The Maid of Orleans”) Davydova also sang well.

Friday ⟨19 November⟩#

We walked with Borya to the Skalba (a little river in the environs of Komarovka).

We discussed our little book. [Editor’s note:] Our little book — most probably the book with B. V. Gnedenko, “Limit Distributions for Sums of Independent Random Variables”. — M.–L.: Gostekhizdat, 1949.

After dinner Borya hurriedly left to bathe his son.

In the evening we read, with Pusya and V.S., Xenophon’s “Banquet”.

Sunday, 21 November 1943#

At last, on the way home from Dimetrusya‘s, I resolved a somewhat naive perplexity concerning how the characters are distinguished from positive-definite functions (and why they are positive-definite at all — yesterday it turned out that I had not understood this before!).

Now it remains to make out just what representation is generated by $\chi(g)$ itself: will it not, for example, always be a representation in $E^{r^2}$?

My definition of a character, to all appearances, holds in the case of any locally-bicompact [bikompaktnyi] groups? Bicompact (бикомпакт) is P. S. Alexandrov’s period term for what is now simply a compact (Hausdorff) space; «bicompact extension» = a compactification. Kept as he wrote it — it is a datum about the mathematical culture he worked in — rather than silently modernised. Recurs on folios 102, 106. Gelfand, however, said something about the absence, for them (generally speaking), of an analogue of characters in the form of positive-definite functions.

Perhaps the means $\chi(g) = M\varphi(g)$ are discontinuous?

In any case, it is true (though the proof is so far less direct than one would wish):

Monday, 22 November 1943#

A direct proof of the last assertion.

1. $k > r$

and this means precisely that $V_g x$ is subject, independently of $g$, to linear conditions.

2. $k = r$

since

for any $y = y_1 \times y_2 \times \dots \times y_r$.

Proof.

By invariance,

And for $\alpha \ne \beta$

by analogous considerations.

Characters#

In the space $E^{r^2} = E^r \times E^r \times \dots \times E^r$ let us take

Let $U_g e_\alpha = \sum u_{\alpha\beta}(g) e_\beta$. Then

“Directions” in Hilbert space#

$\mathfrak{M} = \{M\}$ — the totality of finite-dimensional subspaces. For $M' \subset M$ the projections $P_{M'} M = M'$. A “direction” is the totality of vectors $x_M$ with $x_{M'} = P_{M'} x_M$ for $M' \subset M$.

Tuesday, 23 November 1943#

Saturday ⟨20 November⟩#

I occupied myself with the representations of groups.

In the afternoon Anya arrived, and in the evening we set off to the celebration of Dimetrusya‘s doctoral degree (Seryozha, Alla, Dubinin, two fish-breeders, Dimetrusya, Ksenia, Elizaveta Rodionovna, Anya, I). It was pleasant and merry. Dimetrusya got somewhat drunk, which he had best not do. One of the fish-breeders read a poem about “halves”.

Elizaveta Rodionovna’s culinary talents are fully at the proper height.

Sunday ⟨21 November⟩#

I occupied myself a little, read Anya some Voloshin (she finds it boring) and talked much with her about various things.

Oleg in the morning painted a good landscape.

Then we read the “Odyssey”.

I saw Oleg off to Tarasovka. I gave him algebraic problems, showed him photographs. He himself was reading “The Modern Architecture of the West”. Conversations about anything too philosophical (even about their Platonic readings) he keeps up with me reluctantly.

Yura has a new series of verses.

Monday ⟨22 November⟩#

I saw Anya off, then walked almost to Mytishchi.

In the evening I was at Dimetrusya’s in the sanatorium.

I reflected much about the representations (see above).

The same today#

I read a little Mayakovsky (“To Yesenin” — good, but even this is done slovenly, in spite of all his declarations of how carefully he composed!):

⁠ ...И мир, как море пред зарею, ⁠ И я иду по лону вод. ⁠ И подо мной, и надо мною ⁠ Трепещет звездный небосвод...

Wednesday, 24 November 1943#

Yesterday evening I received Dimetrusya, gave him tea with jam.

Again conversations about Sergei Musatov (rather at Dimetrusya’s initiative than mine).

In my interest in S.M.'s affairs there is, of course, an element of grievance at the arrogance of these “spiritual” people, who consider me — with my equanimity (particularly insistently demonstrated, however, by myself precisely to them, by contrast) — all the same earthbound.

In my own justification I may remark that this grievance is really felt keenly by me only because the said attitude to me estranges me from Oleg, and that is hardly of use to him himself either.

More on the representations of finite groups#

Let a representation be formed, for an irreducible representation in $E^r$, in

by the usual recipe.

Then, it appears, $x \in E^{kr}$ generates all of $E^{kr}$ if and only if $x_1, x_2, \dots, x_k$ ($x = x_1 \times x_2 \times \dots \times x_k$) are linearly independent.

The synthesis of a) and b) for the one-dimensional case is present in the harmonic analysis of N. Wiener.

Will not the solution of the problem so posed (even only for a one-parameter group!) lead also to the clarification of my problem of the spectral analysis of random stationary functions, with allowance for “phase shifts”?

Competition with Gelfand, indeed, in my present mood is useful, to drag me out of the state of indifference to mathematics.

As it were, the solution is given by the Hilbert space from the record of 20-XI-1943, but with finitely-additive functions. What family of sets is one to choose, to integrate over it?

Thursday, 25 November 1943#

Yesterday evening, a concert:

“The Tempest” Tchaikovsky: Duet of Romeo and Juliet, The Fifth Symphony.

“The Tempest” pleased Anya very much.

I dreamed, under it, of some forests, of thunderclouds over them, of steppes with luxuriant grass and the whistle of the wind. Then of my April–May journey through the Crimea. [Editor’s note:] The April–May journey through the Crimea — there is no clarity here. Judging by the letters and diaries of 1943, in May A. N. went to Kazan to fetch his aunts, and there is no mention of any journey through the Crimea preceding this (and it could hardly have taken place in 1943!). If the dreams were of the future, of 1944, then no letters of 1944 have yet been found at all, and the diary entries for that year break off on 24 April, and reveal no signs of a forthcoming journey. Perhaps Andrei Nikolaevich was recalling some much earlier, pre-war Crimean journey of his (for example, V. M. Tikhomirov, in his article “A word about the teacher” (collection “Kolmogorov in Reminiscence”. — M.: Nauka, 1993), mentions A. N.'s journey through the Crimea with pupils of the Potylikha school in 1924)...

To the Fifth Symphony I devised a programme: “Rejected — or love that has not justified its hopes, and yet all-devouring.”

Pusya, however, this time found this symphony brighter, and even more jubilant, than he had found it, it seems, before.

In reality, the Fifth Symphony, together with “Hamlet”, was written in the summer of 1888 at Frolovskoye, already after the infatuation (in the spring) with S. — evidently in the period of a wish to renounce personal life and only to work. Already in the autumn (again with S.) Tchaikovsky finds the symphony motley, insincere and long (2 Dec. 1888). Further vacillations.

This morning I went to the Leninsky district finance office to receive 600 rubles of overpaid military tax (without success — it must be done at one’s place of residence), received money at the AS savings-bank, and talked with Bermant about the prospects of Vinogradov’s return (Bermant is much taken with this idea of Pontryagin’s).

I dined with Anya and V.Ya., then left for here, feasted here alone on three pastries, read Hildebrand’s “Problem of Form” (clever, but ponderous), and am going to bed.

I keep thinking, however, stubbornly about the representations#

A function of the form $\varphi(g) = (U_g x, y)$ for some representation $U_g$, the corresponding topology, and the “charges” [zariad] of A. D. Alexandrov, and the passage from the (complex) charge $\mu(\varepsilon)$ to A charge (заряд) is A. D. Alexandrov’s term — the geometer, not P. S. Alexandrov (Pusya), nor the surgeon M. S. — for a signed (or complex) measure, a set function that may take either sign, like an electric charge. He keeps the scare-quotes. The whole construction of the next folios is: charges → the normalised $f(\varepsilon) = \mu(\varepsilon)/\sqrt{|\mu(\varepsilon)|}$ → a Hilbert space.

Friday, 26 November 1943[In the margin:] For the distant future.#

In the multiplication of positive-definite functions there result positive-definite functions (Schur — see Pólya and Szegő, II, p. 113, section VII, problem 35). [Editor’s note:] Pólya and Szegő — this refers to the book Pólya G., Szegő G. Aufgaben und Lehrsätze aus der Analysis. — Bd. II, Julius Springer, Berlin, 1925. (In the Russian translation, by D. A. Raikov: Pólya G., Szegő G. Problems and Theorems from Analysis. II. The name G. Pólya is erroneously transliterated in the Russian as Полиа; correctly — Пойа.)

Does this generate also some multiplication of representations?

— In the abelian case, yes!

A possible variant of a narrowed Čech extension [Chekhovskoe rasshirenie] of groups: after A. D. Alexandrov, starting from uniformly-continuous functions. Not “Chekhov”: Чеховский here = of Eduard Čech; the «Čech extension» is the Čech (Stone–Čech) compactification. [Editor’s note:] The Čech extension — on bicompact extensions (after E. Čech, M. Stone) see, for example, § 6 of chapter 6 of P. S. Alexandrov’s book “Introduction to Set Theory and General Topology” (M.: Nauka, 1977). But for us, a narrowing of the Čech extension is desirable already in the case of discrete groups.

Friday, evening.#

Hypothetical programme:

1). The ring $\Re$: the linear-uniform closure of the shifts ($\psi(g) = \varphi(hg)$) of positive-definite functions.

2). The corresponding topology (in the sense of A. D. Alexandrov?) and the bicompact extension $G^*$.

3). On this $G^*$, the functions with completely-additive square — the unitary space $\mathcal{H}$. In it, the fundamental representation $U$.

⟼ see the formulation of the problem on p. 99 (24 November).

Is it interesting whether it will all come out so or not?

And perhaps $G^*$ is constructed also in some still simpler way.

Finite groups again#

The fundamental representation in the space of $n$-dimensional vectors $x = (x_e, x_{g_2}, \dots, x_{g_n})$:

How to show that it contains a representation with any positive-definite function $\varphi(g)$:

This form is invariant.

The vector $\xi = (1, 0, 0, \dots, 0)$ (i.e. $\xi_e = 1, \xi_g = 0, g \ne e$) generates the whole space; $(U_g \xi, \xi)_\varphi = \varphi(g)$.

Mailied O Lieb, o Liebe! So golden schön Wie Morgenwolken Auf jenen Höhn!

Du segnest herrlich Das frische Feld Im Blüthendampfe Die volle Welt.

Sunday, 28 November 1943#

Майская песня О, как прекрасен Весь мир вокруг! Сверкает солнце, Смеется луг! ⁠ Взбухают почки ⁠ На всех ветвях, (сучкáх) ⁠ И птичьи стаи ⁠ Кричат в кустах; Блаженство, счастье (радость?) В груди моей; О лес, о солнце, О радость дней! ⁠ Как утром рано ⁠ Средь гор и круч ⁠ Там золотятся ⁠ Обрывки туч, Как солнцем залит Росистый луг, Весь мир объемлет Цветочный дух, Весенней страстью Цветет земля —Так ты прекрасна, Любовь моя!

Как, дорогая, Люблю тебя! Как глазки светят, Меня любя! ⁠ Так любят птички ⁠ Петь с высоты, ⁠ Дыханье утра ⁠ Впивать — цветы. И к новым песням И танцам вновь Дарит мне смелость Твоя любовь! ⁠ И с нею радость, ⁠ И с ней мечты! ⁠ Так будь счастлива, ⁠ Как любишь ты!

Continuation of p. 103.

The spaces $M_k$ are invariant (all $\lambda_k$ distinct).

This is not at all $U_g Lx = L U_g x$.

This is precisely what must be carried over to the infinite-dimensional case.

Multiplication of spaces#

To each $\alpha \in A$ there corresponds an $H_\alpha$. In $A$, a family $F$ of “measures” $\Theta(\mu)$, $\mu \in A$.

For the infinite-dimensional generalisation of the above, only the case of one-dimensional $H_\alpha$ is needed. But in multiplying irreducible representations, presumably, the case of general $H_\alpha$ is needed too.

For the future#

Does the von Neumann mean not always exist, for all positive-definite functions?

If this is so, then is an almost-periodic part singled out from them, with a remainder equal, on average, to zero?

Is the invariant measure on $G^*$ with $\mu(G^*) = 1$ unique, and coincident with the von Neumann density? In the absence of almost-periodic functions other than constants, this measure is very poor, but nothing prevents it from existing!

The simplest variant of the Milman–Krein theorem (applied, after Gelfand, to the case of discrete groups).

On a set $A$:

Functionals $f(x) = \sum f_\alpha x_\alpha$ with bounded $f_\alpha$,

The Tychonoff weak topology in $\{\|f\| \le c\}$: $f \in \bar{M}$ if, for any $\varepsilon$ and $\alpha_1, \alpha_2, \dots, \alpha_n$, there exists $f' \in M$ with $|f(\alpha_k) - f'(\alpha_k)| < \varepsilon$.

In this topology, the set $\Phi_0$ of all positive-definite functions $\varphi(g)$ with $|\varphi(e)| = 1$ is bicompact and convex. In fact: it is weakly closed, and all $f$ with $|f| \le 1$ form a bicompact space. The extremal positive-definite functions form the set $E_0$. All $\varphi$ from $\Phi_0$ are determined by measures on $E_0$ (perhaps, and not one-to-one).

The space $H$ from

Its subspaces invariant with respect to all the shifts $U_g x$: they always have an element that generates them, and consequently the positive-definite functions corresponding to them as well. [Editor’s note:] The Milman–Krein theorem (on the “convex hull and extreme points”) — see the work of these authors, On extreme points of regular convex sets // Studia Math., 1940, v. 9, p. 133–138.

Monday, 29 November 1943#

I must set the results down here more sparingly, and start a separate notebook for all sorts of wanderings in the representations.

Yesterday we walked with Anya, read together “Queen Pédauque” (Anya does not like it because of its indecency).

Her bad mood of these last weeks Anya explains by: 1) doubts (“is she not a bad wife”), 2) sufferings (from the “excessive” material well-being of ours).

For each positive-definite function $\varphi(g)$:

$M_\varphi$ is both right- and left-invariant, since $\varphi(g^{-1}) = \overline{\varphi(g)}$.

— since $M_\varphi$ and $L_\varphi$ are invariant. For $M_\varphi$ this is true, but for $L_\varphi$ it must be required. However, the extraction of the square root of non-negative operators is, it seems, unique.

Left and right shifts:

Positive-definite functions and invariant positive-definite Hermitian operators.

In the finite-dimensional case: to the one-to-one correspondence and multiplication

there corresponds the convolution [svortyvanie]

From the considerations on pp. 104–105, the extraction of the root is possible, and unique.

For characters, thus. The corresponding system of invariant spaces common to all $M_\varphi$ — ⟼ in the infinite-dimensional case it will first appear precisely from here!

Positive-definite functions of the form $\varphi(g) = (U_g x, x)$, for some vector $x = \{x_g\}$, coincide with those for which

— This is the case of bounded $M_\varphi$.

In fact, formally, $(U_g x, x) = \sum x_{g^{-1}h} \bar{x}_h$ and $y_h = \sum_g \varphi(h^{-1}g) x_g$ lead to this result from the theorem on convolution over the group. (Where is it, this theorem?)

Pusya set off yesterday for Moscow at Yura’s summons. Myasoedov is being posted for a month to Kiev, and Yura with him. Today he will learn everything more exactly.

Tuesday, 30 November 1943#

On the group of integers, besides $\mu(\varepsilon)$ = the number of elements of the set $\varepsilon$, or $\mu(\varepsilon)$ = the density of $\varepsilon$, there exist invariant “densities of fractional orders”:

Perhaps with these invariant measures one can somehow manage, for the generation of all positive-definite functions in the form

Basic hypotheses#

— without which all the rest becomes of little sense.

Kinds of representations:

1). Irreducible representations.

2). Those corresponding to powers of irreducible ones having a generating vector.

3). Representations with a generating vector.

4). ? ———— ?!

1. There exists a minimal representation which contains all representations with a generating vector.

2.

3.

So it is all in the extension of the space, after Naimark!?

? In order for a positive-definite invariant Hermitian operator $M$ to be an $M_\varphi$, it is necessary and sufficient that $(M e_g, e_h) \le C$.

! How might I get across to invariant unitary or isometric ones?

The conversion of finitely-additive functions into countably-additive ones by means of Fomin extensions [Fominskie rasshireniia]. The Fomin extensions are of S. V. Fomin (later Kolmogorov’s co-author on the Elements of the Theory of Functions) — not to be confused with the Naimark of the same folios, nor with the Neumann of folios 99/105: three near neighbours in transliteration, three different mathematicians.[Editor’s note:] The following two lines are added in red pencil, apparently later.

Will not the characters that do not exist in the form of positive-definite functions correspond, all the same, to operators $M_\varphi$?!

? Characters as positive-definite functions with $\varphi(h^{-1}gh) = \varphi(g)$.

I went to Moscow, to Feinberg’s concert (Beethoven, sonatas Nos. 17–22). With interest I listened to Nos. 17–18. I was enchanted by Nos. 19–20. I grew tired and listened poorly to Nos. 21–22. Anya liked Nos. 19–20. (Present were: Seryozha with Alla, Natasha and Oleg.) [Editor’s note:] “...after Naimark” — evidently the results of M. A. Naimark’s paper “Positive-definite operator functions on a commutative group” (Izvestia AN SSSR. Ser. mat., 1943, vol. 7, No. 5, pp. 237–244) are meant. [Editor’s note:] Corrections in red pencil occur on many pages (in the mathematical arguments) — one may suppose that all these corrections appeared at one time, on a re-reading of all the entries on group representations. [Translator’s note:] The facsimile pages are reproduced in greyscale, so the colour is lost: every ⟨...in red pencil...⟩ note is the only witness that a mark belongs to that later re-reading — a second stratum of the manuscript the image cannot show. [Editor’s note:] Natasha — an acquaintance of S. Musatov, whose portrait he was painting at the time. This month’s Natasha is his model, not N. K. Gnedenko.

December 1943#

Wednesday, 1 December 1943#

A concrete plan for how to become a great man, if there is enough desire and diligence for it. [Editor’s note:] Of this unique document much might be said, but we leave the reader the chance to acquaint himself with it in detail and to form his own opinion. Here we shall only draw attention to the fact that the Plan consists of two separate parts, which, it seems to us, may be entitled the plan of the “big” (the upper table) and the plan of the “small” (the lower table) jobs for the future. (The reader will, of course, have noticed too how and where Andrei Nikolaevich has placed the question marks and the omission marks (Z), and sometimes both together.) [Translator’s note:] The decade labels are transcribed here from the facsimile (folio 110), where they run 1944–1953 · 1954–1963 · 1964–1973 · 1974–1983 · 1984–1993 — confirmed at high magnification (the second row of the top table has an ink-blot over the first year but reads 1954–1963). The 2003 edition’s own typeset transcription on folio 111 misprints these labels, repeating “1964–1973” for the last three rows of both tables; that is a genuine error of the source edition, and the facsimile — not the flawed typeset — is followed here.

The plan of the “big” jobs:

The plan of the “small” jobs:

In the unitary representations these last days a hold-up — I am somewhat tired.

Yet another week of intense occupation with them must, however, be arranged, neglecting other affairs. If in a week nothing comes out, it will have to be put off a little.

On Friday, to begin with putting into order everything about the finite-dimensional case in a separate little notebook.

Today I did a large gymnastic session — this must be done daily. Now I take up Chetverukhin and the like. [Editor’s note:] The reference here is evidently to N. F. Chetverukhin’s paper “On the affine rigidity of polyhedra”, published in the Doklady of the USSR Academy of Sciences (1944, vol. 42, no. 1, pp. 3–6).

To each $n$-dimensional representation $U_g$ there corresponds a representation $F_g A = U_g A$ in the $n^2$-dimensional space of matrices.

More generally — in the $mn$-dimensional space of rectangular matrices. This is nothing other than the “$mn$-th power” of the representation $U_g$.

Generalise this operator-wise to the infinite-dimensional case!

In the finite-dimensional case the “subordination” of representations $U_g \prec U'_g$ is the finding of $U_g$ in some invariant subspace of $U'_g$. In the infinite-dimensional case there exists some extension $U_g \prec \bar{U}'_g$. (Can one, in doing so, give a direct sense to $\bar{U}'_g$ — see above.)

Presumably, $U_g \prec U'_g$ means that for the corresponding sets of positive-definite functions $\Phi \subset \bar{\Phi}'$. Is $\bar{U}'_g$ just $U_g$ with $\Phi = \bar{\Phi}'$?

The difficulty is that already in the simplest cases of infinite groups $\bar{U}'_g$ cannot have a generating vector — that is, a single one generating all the positive-definite functions.

Before setting off for the Mathematical Society:

4. See p. 109. Spaces in which any two vectors enter into the space generated by some third one.

Friday, 3 December 1943#

Hypothesis. If $\psi = \int_{E_0} \varphi\, d\mu$ ($\varphi$ — elementary positive-definite functions) and $\psi'$ is absolutely continuous with respect to $\mu$, then $\psi' \prec \psi$.

The mapping $E_0 \to M_0$ — the set of irreducible representations. $\mu$ on $E_0$ gives $\pi$ on $M_0$.

For representations with a “simple” spectrum, is everything determined by this $\pi$?

The algebraic side of the completion. Let $\varphi(g, h)$ ($g \in M$, $h \in M$) be positive-definite,

with the corresponding Hilbert space of the $\{c(g)\}$ — with termwise addition — for which there exists a $c > 0$ with positive-definiteness; the infimum of such $c$ is precisely $\|\{c(g)\}\|$. This is what gives the possibility of arranging $c(g)$ as a measurable function of $\varphi$ and then integrating over $\varphi$!

At the Mathematical Society on Wednesday, Lavrentiev’s report (the solvability and uniqueness of the problem of mapping a region onto a region for non-linear elliptic equations subject to certain conditions) was very interesting in conception, but Lavrentiev works crudely and untidily, and recounts things not yet verified. And in answering questions, it seems to me, he even fibs a little.

Thursday [2 December]#

In the morning Verchenko and Myshkis were at my place.

Then I was at the savings-bank (the lost suitcase, naturally, did not turn up) and at the exhibition in the Tretyakov Gallery (to record my impressions after a second visit!).

Pusya brought several issues of journals. In the Annals for 1942 there is a paper of H. B. Mann’s with a proof, on five pages, of the theorem on the addition of densities of sets of whole numbers. [Editor’s note:] The paper of H. B. Mann — this concerns the article H. B. Mann, “A proof of the fundamental theorem on the density of sums of sets of positive integers” // Ann. of Math., 1942, v. 43, no. 3, pp. 523–527. And various other interesting things besides.

“Formal theory of representations.”

Hypothesis ($\varphi$ — a positive-definite function). If $\varphi = \varphi_1 + \varphi_2$, then $\varphi_1 \prec \varphi$, $\varphi_2 \prec \varphi$.

Definition. A function $\varphi$ is called “complete” if from $\varphi' \prec \varphi$ there follows $\varphi + \varphi' \prec \varphi$.

Classes $\Phi = \{\varphi\}$ of equivalent $\varphi$. The relation of subordination $\Phi' \prec \Phi$.

Hypothesis. For any two $\Phi_1$ and $\Phi_2$ there exist $\varphi_1 \in \Phi_1$, $\varphi_2 \in \Phi_2$, such that for any $\varphi'_1 \in \Phi_1$, $\varphi'_2 \in \Phi_2$

The class generated by $\varphi_1 + \varphi_2$ is what is called $\Phi_1 + \Phi_2$.

In the night much snow was heaped up. Now a thaw threatens again.

Yura made Pusya a present of Rustaveli. I read Nutsubidze’s introduction on Georgian neo-Platonism.

Monday, 6 December 1943#

Saturday [4 December]#

From Komarovka we set off with Varvara Sergeevna for a concert.

• Tchaikovsky: The Florentine Sextet
• Nature and Love
• Night
• The Second Quartet.

At the Conservatory we met Anya, who bade me go, after the concert, to Petya ⟨Kuznetsov⟩, who had only just arrived. [Editor’s note:] Petya — P. S. Kuznetsov. Petya physically looks better than usual. He recounted how splendidly he had been seen off, and so on.

We left at 11.45. We went to Komarovka along the forest path through the snowdrifts.

Sunday [5 December]#

The whole day I killed on Chetverukhin (see the Note to the entry of 1 December 1943).

Interesting: is the condition $h = 4 - \alpha_0 + 2\alpha_1 - 3\alpha_2 \ge 0$ necessary and sufficient for affine rigidity? For dual polyhedra $h + h' = 0$.

On Sunday evening we read “Queen Pédauque” with Anya.

I keep feeling somehow out of sorts. The representations of groups have still not come out. Oleg is not here (he is puttying the windows at the school). With Anya and Pusya somehow it is all tea-and-coffee, dinners-and-grievances... Anya takes offence if you tell her she is putting on weight, and threatens to hire herself out as a laundress. We rise late and go to bed late too. The tables are heaped with Platos and mathematics; I am too lazy to sort through them. To go ski-running alone is somehow uninviting.

Unexpected, though elementary: on the unit sphere of Hilbert space the weak topology coincides with the strong:

It is in Plesner, p. 32. (2-2-1944) [Editor’s note:] ⟨Added later — 2 February 1944.⟩ The cross-reference is to A. I. Plesner’s survey “Spectral theory of linear operators” in Uspekhi matematicheskikh nauk (1941, issue 9, pp. 3–125). The date is the day of his own Mathematical Society talk on the representations of infinite groups — a second, later stratum of the manuscript, which the greyscale facsimile cannot otherwise show.

Proof: $x_n = \lambda_n x + \xi_n$, $(x, \xi_n) = 0$; $(x, x_n) = \lambda_n \to (x, x) = 1$.

Thus the introduction of the weak topology reduces to a topological extension of the surface of the sphere by interior points. The “complete sphere” in the weak topology is closed. Accordingly, the surface of the sphere is a $G_\delta$. The normalised positive-definite functions subordinate to a given representation are, in their bicompact topology, continuous images of this $G_\delta$ and consequently $A$-sets.

In the space $H$ an element $x$ is determined by the $\{c(h)\}$, with $\|x\| = 1$. The dependence of $\psi(g)$ on $\varphi(h)$ and $c(h)$ is continuous (in the bicompact topology).

The precise construction of a representation from the decomposition of a positive-definite function.

where $\Psi \subset \Phi$ is the set of normalised positive-definite functions ($\Psi$ is a $G_\delta$). On $\Psi$ the $x_\psi = \{c_\psi(h)\}$ are given as $\mu$-measurable functions, with

It is essential that $\|x_\psi\|$ too is $\mu$-measurable. In fact, this is so when $|\varphi(e)| = 1$!