Friday, October 20, 2017

Tasks to do now

‘Tasks to do now: 1) Finish small jobs as soon as possible (shooting, quality control, Lobachevsky). [. . .] 3) Maintain constant and steady work on big projects (analysis course, turbulence, spectra). Only later let mathematics join the variety of purely personal and general interests and hobbies that have flourished in the last two years.’ This is from a diary kept - albeit briefly - by one of most eminent of Soviet 20th century mathematicians - Andrey Nikolaevich Kolmogorov - who died 30 years ago today. There appear to be only a few, tantalising extracts of a diary he kept in his 40th year, and even fewer that have been translated into English.

Kolmogorov was born in Tambov, some 300 miles south of Moscow, in 1903, but his unmarried mother died in childbirth, and he was raised by two aunts on the estate of his aristocratic grandfather in Yaroslavl, 160 miles northeast of Moscow. In 1910, his aunt adopted him, and they moved to Moscow. There he graduated from high school in 1920 and went on to study both at the Moscow State University and the Mendeleev Moscow Institute of Chemistry and Technology. He attended seminars by the Russian historian S. V. Bachrushin, and he published his first research paper on medieval landholding practices in the Novgorod Republic. At the same time, he worked out and proved several results in set theory and in the theory of Fourier series.

Kolmogorov graduated from Moscow State University in 1925, by which time he had published ten papers, mostly on trigonometric series, and he continued publishing influential work until completing his doctorate in 1929. He was then elected a member of the university’s Institute of Mathematics and Mechanics, and a professor in 1931. That same year he published the influential work, About the Analytical Methods of Probability Theory. This was followed in 1933 by Foundations of the Theory of Probability, laying the modern axiomatic foundations of probability theory which established his international reputation. He was appointed director of the Mathematical Research Institute at the university, a position he held until 1939 (and then again in the early 1950s).

From 1938, Kolmogrov also headed the new department of probability and statistics at the Steklov Mathematical Institute. He was elected to the Academy of Sciences in 1939. He married Anna Dmitrievna Egorova in 1942. During WWII, he contributed to the Russian war effort by applying statistical theory to artillery fire, and by developing a scheme of stochastic distribution of barrage balloons intended to help protect Moscow from German bombers. After the war, he focused his research on turbulence, making a significant contribution to this scientific area, and becoming head of the Turbulence Laboratory at the Institute of Theoretical Geophysics in Moscow. In the mid-1950s, he began to work on problems of information theory; and, in the 1960s, he turned his attention to automata theory and theory of algorithms, and also to pedagogy, writing and rewriting school textbooks. He was much recognised in his lifetime with honours both at home and abroad. He died on 20 October 1987. Further information is available from Wikipedia, Encyclopaedia Britannica, Scholarpedia, or MacTutor.

According to an article in the Asia Pacific Mathematics Newsletter, Kolmogorov began keeping a diary at the age of 40, and wrote on the title page: ‘Dedicated to myself when I turn 80 with the wish of retaining enough sense by then, at least to be able to understand the notes of this 40-year-old self and to judge them sympathetically but strictly.’ The article also includes excerpts from the diary, translated by Fedor Duzhin, that were first published in Russian in 2003 on the 100th anniversary of Kolmogorov’s birth. Some extracts from this diary English also appear in A Biographical Sketch of His Life and Creative Paths written by A. N. Shiryaev and found in an edition of History of Mathematics called Kolmogorov in Perspective (Volume 20, American Mathematical Society and London Mathematical Society, 2006).

The following extracts are taken from Duzhin’s translation.

1 August 1943
‘New Moon. 6:30 am. It is a little misty and yet a sunny morning. Pusya and Oleg2 have gone swimming while I stay home being not very well (though my condition is improving). Anya has to work today, so she will not come. I ’m feeling annoyed and ill at ease because of that (for the second time our Sunday readings will be conducted without Anya).

Why begin this notebook now? There are two reasonable explanations: 1) I have long been attracted to the idea of a diary as a disciplining force. To write down what has been done and what changes are needed in one ’s life and to control their implementation is by no means a new idea, but it ’s equally relevant whether one is 16 or 40 years old. 2) Now that I’m 40, I feel more deeply as life flows and goes by since past experience has an independent significance as compared to what one expects at 16 or even 30, when everything is viewed as a preparation for a distant future. Hence the need to capture the present at the very moment it transits from the non-existence of something that has yet to happen to the non- existence of something that has already passed by.

Possibly, the third reason put forward is contentious. 3) The period of psychological research that began in February has been decided to be brought to an end. That caused a certain slackness in me and Pusya in July. So, this diary is being pursued to restore the discipline and at the same time to allow the passion for psychological research to be released in a more organised manner. Hopefully, there will not be too much of this research.

Eventually, this notebook might see some memories, thoughts, psychological analyses besides short current notes, but it will only happen after I have put my life in order.

Tasks to do now: 1) Finish small jobs as soon as possible (shooting, quality control, Lobachevsky). 2) Family matters (bring Vera and Varya, send Varya to Nadya, bring Anya from work and so on). 3) Maintain constant and steady work on big projects (analysis course, turbulence, spectra). Only later let mathematics join the variety of purely personal and general interests and hobbies that have flourished in the last two years.

Most important now: 1) Discipline in doing boring work. 2) Confident and consistent clearing [of tasks] to find possibilities for working calmly on big projects. 3) Fighting temptations (sweets, reading at the wrong time), including updating this notebook immoderately. (Agreement with Pusya to limit chatting!)

And where is love (Christian and non-Christian) I think a lot about and maybe talk too much about (for instance, to Oleg)? It seems that it is for the sake of love that I have to concentrate on disciplinary rules listed above!

Enough with reasoning! However, it ’s not prohibited to supplement records of labour deeds with short notes on moods and pleasures of life.’

7 August 1943
’It is a little misty, milk-sunny, warm day.
During the morning and after lunch I edited the first 15 pages of Gubler s work (had to
completely rewrite 7 pages). Satisfied with my work.

Pusya is listlessly writing on Lobachevsky, editing Yura ’s poetry, being upset about the
Kazan troubles. Marina was taken ill and Shurka drove her to a hospital in a horse cab accompanied by Spitsyn.

A letter came from Sergey Musatov telling us that he could come to Komarovka no sooner
than in a month. He also mentioned that he wanted to write more to me about certain questions .

21 November 1943
’Finally, on the way home from Dimetrusya I resolved my some rather naive puzzle on what distinguishes characters from positive-definite functions (and why characters are generally positive-definite yesterday I discovered that I had not understood that before!).

 Let G = {g} be represented by operators Ug (unitary) in E’. [ . . .] What remains now is to find out what representation is induced by x (g): for instance, is it always a representation in Er2? My definition of a character seems to work for all locally bicompact groups. However, Gelfand mentioned that, generally speaking, there was no analogue of characters as positive-definite functions. [. . . ]

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