Lev Semenovich Pontryagin, Soviet mathematician: biography, scientific career. Memoria. Lev Pontryagin

Lev Semyonovich Pontryagin (August 21 (September 3) 1908, Moscow - May 3, 1988, Moscow) - Soviet mathematician, academician of the USSR Academy of Sciences (1958; corresponding member 1939), Hero of Socialist Labor (1969).

At the age of 14, he lost his sight as a result of an accident. Graduated from Moscow University (1929). Since 1939, head of department at the Mathematical Institute. V. A. Steklov of the USSR Academy of Sciences, at the same time since 1935 a professor at Moscow State University.

In topology, he discovered the general law of duality and, in connection with this, constructed a theory of the characters of continuous groups; obtained a number of results in homotopy theory (Pontryagin classes).

In the theory of oscillations, the main results relate to the asymptotic behavior of relaxation oscillations. In control theory, he is the creator of the mathematical theory of optimal processes, which is based on the so-called. Pontryagin's maximum principle (see Optimal control); has fundamental results on differential games.

The work of Pontryagin's school had big influence on the development of control theory and calculus of variations throughout the world. His students are famous mathematicians D. V. Anosov, V. G. Boltyansky, R. V. Gamkrelidze, M. I. Zelikin, E. F. Mishchenko, M. M. Postnikov, N. Kh. Rozov, V. A Rokhlin.

Pontryagin wrote a detailed memoir, “The Biography of L. S. Pontryagin, a Mathematician, Compiled by Himself,” in which he assessed many scientists and the events of which he was a witness and participant, in particular, the campaign against N. N. Luzin.

— Honorary titles and awards
* Honorary Member of the London Mathematical Society (1953)
* Honorary member of the International Academy of Astronautics (1966)
* Vice-President of the International Mathematical Union (1970-1974)
* Honorary Member of the Hungarian Academy of Sciences (1972)
* Stalin Prize, second degree (1941)
* Lenin Prize (1962)
* USSR State Prize (1975) for the textbook “Ordinary differential equations", published 1974 (4th ed.)
* Hero of Socialist Labor (1969)
* Four Orders of Lenin (1953, 1967, 1969, 1978)
* Order of the October Revolution (1975)
* Order of the Red Banner of Labor (1945)
* Order of the Badge of Honor (1940)
* N. I. Lobachevsky Prize (1966)

— Proceedings
* Continuous groups. 3rd ed., rev. - M.: Nauka, 1973. - 519 p.
* Fundamentals of combinatorial topology. - M.-L.: Gostekhizdat, 1947. - 143 p.
* Ordinary differential equations: Textbook. for government univ. 3rd ed., stereotype. - M.: Nauka, 1970. - 331 p., fig.
* Mathematical theory of optimal processes. 2nd ed. - M.: Nauka, 1969. - 384 pp., figure, table. — Together with V. G. Boltyansky, R. V. Gamkrelidze and E. F. Mishchenko.
* Linear differential game of escape // Proceedings of the Mathematical Institute of the USSR Academy of Sciences. T. 112, pp. 30-63. - M.: Nauka, 1971.
* Selected scientific works. In 3 volumes - M.: Nauka, 1988.
* For an additional list of works, see Bibliography.
* Pontryagin’s articles in the journal Kvant (1992-1985).
* L. S. Pontryagin, “Generalizations of numbers.” - M., Nauka, 1986, 120 p.

Pontryagin Lev Semyonovich - Academician of the USSR Academy of Sciences.

Born on August 21 (September 3), 1908 in Moscow. At the age of 14, he lost his sight as a result of an accident. In 1925 he graduated from a unified ten-year labor school.

Entered the Moscow State University named after M.V. Lomonosov (MSU), from which he graduated in 1929. In the period from 1930 to 1932 - associate professor of the department of algebra and employee (graduate student) of the Research Institute of Mathematics and Mechanics at Moscow State University. Also in 1931, he became an employee of the oscillation laboratory of the Institute of Physics at Moscow State University. Since 1932, he served as an acting professor at Moscow State University.

Since 1934, he also worked at the V.A. Steklov Mathematical Institute of the USSR Academy of Sciences (now the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences). He successively held the positions of senior researcher (since 1934), head of the department of topology and geometry (since 1939), head of the department of differential equations (since 1980 - department of ordinary differential equations) (since 1959).

In 1935, L.S. Pontryagin was awarded the degree of Doctor of Physical and Mathematical Sciences without defending a dissertation, and he became a professor at Moscow State University.

In topology, L.S. Pontryagin discovered the general law of duality, and in connection with this he constructed a theory of the characters of continuous groups; obtained a number of results in homotopy theory (Pontryagin classes). In the theory of oscillations, his main results relate to the asymptotic behavior of relaxation oscillations. In control theory, he is the creator of the mathematical theory of optimal processes, which is based on the so-called Pontryagin maximum principle; has fundamental results on differential games. The works of L.S. Pontryagin’s school had a great influence on the development of control theory and calculus of variations throughout the world.

Later he was the head of the Department of Optimal Control at the Faculty of Computational Mathematics and Cybernetics of Moscow State University.

By Decree of the Presidium of the Supreme Soviet of the USSR of March 13, 1969, for great services in the development of Soviet science Pontryagin Lev Semenovich awarded the title of Hero of Socialist Labor with the Order of Lenin and the Hammer and Sickle gold medal.

From 1972 to 1988 - senior researcher at the Department of Mathematics of the All-Union Institute of Scientific and Technical Information of the State Committee for Science and Technology and the USSR Academy of Sciences.

He trained a galaxy of brilliant scientists. His students in different time were famous mathematicians D.V. Anosov, V.G. Boltyansky, R.V. Gamkrelidze, M.I. Zelikin, E.F. Mishchenko, M.M. Postnikov, N.H. Rozov, V.A. Rokhlin and others.

He devoted a lot of energy and time to social scientific activities. IN different years was a member of various organizations and held various positions:
- Member of the Academic Council of the Steklov Mathematical Institute of the USSR Academy of Sciences (from 1951 to 1988);
- Chairman of the Postgraduate Commission at the Steklov Mathematical Institute of the USSR Academy of Sciences (1954);
- member of the Expert Commission for awarding the N.I. Lobachevsky Prize (from 1957 to 1988);
- Chairman of the Expert Commission for awarding the P.L. Chebyshev Prize;
- member of the “Mathematics and Mechanics” section of the Committee for Lenin and State Prizes of the USSR in the field of science and technology under the Council of Ministers of the USSR (from 1959 to 1988);
- Member of the Bureau of the National Committee of Soviet Mathematicians (1961);
- Chairman of the Scientific Commission on the problem of “Ordinary Differential Equations” at the Department of Mathematics of the USSR Academy of Sciences (1962);
- Member of the Expert Commission on Mathematics of the Higher Attestation Commission (from 1963 to 1972);
- Member of the Executive Committee of the TS-7 Committee (on optimization) of the International Federation for Information Processes (from 1967 to 1985);
- Deputy Chairman of the National Committee of Soviet Mathematicians (from 1969 to 1983);
- Vice-President of the Executive Committee of the International Mathematical Union (from 1970 to 1974);
- Chairman of the group on mathematics at the Section (since 1987 - Section on Mathematics) of publications of the Main Editorial Board of Physical and Mathematical Literature of the Editorial and Publishing Council of the USSR Academy of Sciences (since 1970);
- Chairman of the Commission on Publishing Issues of the Mathematics Department of the USSR Academy of Sciences;
- Member of the Bureau of the Mathematics Department of the USSR Academy of Sciences (from 1971 to 1988);
- Member of the Executive Committee of the International Mathematical Union (from 1974 to 1978);
- Deputy Chairman of the Organizing Committee of the All-Union Scientific Conference on Non-Euclidean Geometry;
- Chairman of the Commission on School Mathematics Education of the Mathematics Department of the USSR Academy of Sciences (from 1982 to 1988).

Laureate of the Stalin Prize 2nd degree (1941), Lenin Prize (1962), State Prize USSR (1975), N.I. Lobachevsky Prize (1966).

Academician of the USSR Academy of Sciences (1958), corresponding member of the USSR Academy of Sciences (1939), honorary member of the London Mathematical Society (1953), honorary member of the International Academy of Astronautics (1966), vice-president of the International Mathematical Union (from 1970 to 1974) , honorary member of the Hungarian Academy of Sciences (1972), honorary doctor of sciences from the University of Salford (England) (1976), doctor of physical and mathematical sciences (1935), professor (1935).

He supervised the work of a number of scientific publications. Was editor-in-chief journals "Applied mathematics and optimization" (New York etc.) (from 1974 to 1988) and "Mathematical collection" (from 1975 to 1987), as well as a member of the editorial board of the journals "Mathematics" (VINITI), "Journal of optimization theory and applications" "(New York; London) (from 1967 to 1988), "Journal of differential equations" (New York; London) (from 1974 to 1980), "Izvestia of the USSR Academy of Sciences. Mathematical series" (from 1958 to 1975).

Lived in Moscow. Died May 3, 1988. Buried in Moscow on Novodevichy Cemetery(site 10).

Awarded four Orders of Lenin (1953, 1967, 1969, 1978), Orders of the October Revolution (1975), Red Banner of Labor (1945), “Badge of Honor” (1940), medals “For Valiant Labor in the Great Patriotic War” Patriotic War 1941-1945." (1946), “In memory of the 800th anniversary of Moscow” (1948), the anniversary medal “For Valiant Labor. In commemoration of the 100th anniversary of the birth of Vladimir Ilyich Lenin" (1970).

There is a bust on the wall of the house on Leninsky Prospekt in Moscow, where L.S. Pontryagin lived from 1938 to 1988.

Lev Semenovich Pontryagin
1908-1988

LOBBY

Of course, everyone has heard about the parallelogram of forces.

And even more so about the parallelogram.

Now imagine that you need to mentally depict this same parallelogram of forces, if you have never heard of such a thing before and geometric figure never seen anything like this. You haven't seen it because you are blind. Come on, do the section!

Well, God be with him, with a parallelogram and a section of a plane drawn through... mmm... points. But how to solve differential equations and all that other stuff, consisting of many incomprehensible icons that you have to at least just mentally imagine and about which even a sighted person begins to dazzle in the eyes?

How to do stereometry? Descriptive geometry? Topology?

How to do fundamental scientific discoveries in various branches of mathematical knowledge?

How can you simply LIVE?

"This is impossible!" - you say. Right. Impossible. Only Lev Semenovich Pontryagin was able to do this.

He SAW.

The outstanding Russian thinker V.V. Kozhinov told two amazing stories about him: “I came to visit a blind man, but soon I stopped noticing it. And I am convinced that such a victorious overcoming of a fatal loss was the fruit of a unique spiritual will and energy.

In general, we can rightfully say that Lev Semyonovich Pontryagin was perhaps the most sighted from his colleagues... To visually confirm his messages, Lev Semyonovich showed me the text of the “message” of a group of US mathematicians to the then President of the USSR Academy of Sciences A.P. Aleksandrov. This “message” made extremely stringent, even essentially arrogant demands, which indicated a completely abnormal situation in the relationship between the scientific circles of the two great powers of that time. I decided to ask Lev Semyonovich about how the American “message” ended up in his hands, and he said with ironic equanimity that he had stolen this document from the table in Alexandrov’s office... I admit that only later, remembering our conversation, I I thought: how could a person deprived of sight do this?! The riddle remains a mystery to me.

Lev Semyonovich reports, for example, about his impressions of a trip to a mathematical conference in San Remo in 1969: “In Italy, I was amazed at the density with which buildings are located on the coast of the Azure Sea, and the huge number of cars that completely ruin life with their noise and the stench." The second half of the sentence is clear, but how to understand the first? It remains to be believed that it is possible spiritual vision, in its own way not inferior to the sensual or even superior to it...” V. Kozhinov: ON THE PUBLICATION OF PONTRYAGIN’S “BIOGRAPHY...”

(http://ega-math.narod.ru/LSP/ch8.htm#b)

Now, for those who are not familiar, take a look at his brief track record.

Corresponding Member of the USSR Academy of Sciences (1939)

· Full member of the USSR Academy of Sciences (1958)

· Honorary Member of the London Mathematical Society (1953)

· Honorary member of the International Academy of Astronautics (1966)

· Vice-President of the International Mathematical Union (1970-1974)

· Honorary Member of the Hungarian Academy of Sciences (1972)

· Stalin Prize, second degree (1941)

· Lenin Prize (1962)

· USSR State Prize (1975) for the textbook “Ordinary Differential Equations”, published in 1974 (4th ed.)

· Hero of Socialist Labor (1969)

· Four Orders of Lenin (1953, 1967, 1969, 1978)

· Order of the October Revolution (1975)

· Order of the Red Banner of Labor (1945)

· Order of the Badge of Honor (1940)

· Prize named after. N.I.Lobachevsky (1966)

One of the streets in his native Moscow was named after him in 1996.

Sometimes, in order to be rightfully recognized as great, it is enough to have one single theorem named after you.

The following are named after Pontryagin:

· “Characteristic classes of Pontryagin”

· “Pontryagin surface”

· “Pontryagin’s maximum principle”

· “Pontryagin’s duality”

Based on our formal “working” definition, we can say that Pontryagin is at least FOUR TIMES GREAT.

It was a man gigantic strength will. His research on topology, the theory of continuous groups, differential equations, and the mathematical theory of optimal processes, in which he created an entire scientific school, became world classics.

This great Russian man repeatedly put aside his existing work and began research in a completely new area for him and others. Started everything from scratch.

He started for you and me.

“I took up applied branches of mathematics largely for ethical reasons, believing that my products should find application in solving vital problems. important issues society,” writes L.S. Pontryagin in his book “Biography of Lev Semenovich Pontryagin, mathematician, compiled by himself. Born 1908, Moscow" (http://ega-math.narod.ru/LSP/ch1.htm#a). Thus, Pontryagin’s maximum principle has found numerous applications, in particular in astronautics.

IN last years Throughout his life, he fought to change the existing methods of teaching mathematics at school, which he considered pure sabotage. How much work it took him, with all his authority, to publish an article on this topic in the magazine “Communist”!

... He was born and raised in a simple bourgeois family. His father was a shoemaker, his mother a dressmaker. My father had a sixth-grade education, he loved books and collected a library, which Lev Semenovich kept until his death. These were mainly Russian classics, which little Lev, named, by the way, in honor of Leo Tolstoy, re-read in childhood and adolescence. By the way, his origin almost cost him admission to the university: the new government put strict filters on Russian people. Thank you, a familiar face in the People's Commissariat for Education helped.

“During my school and university years,” wrote L.S. Pontryagin, “I often said and sincerely thought that mathematics is easier than other subjects, since it does not require memorization. After all, any formula and theorem can be deduced logically without remembering anything by heart. And other subjects, such as history or social studies, need to be learned by heart: memorize chronology, names, learn from memory, what decisions were made at various party congresses, and the like. It was always difficult for me to learn such cramming; it was difficult for me to learn foreign languages ​​and memorize foreign words, memorizing poetry. I have noticed that people who memorize poetry well usually know how to write them themselves. Apparently, there is some element of creativity in memorization.”

And further: “Despite the fact that much in mathematics was easy for me, the perception of mathematical knowledge, especially scientific work, was hard but joyful work for me. Scientific work, as a rule, required the utmost effort from me and was accompanied by heavy emotional stress. The latter arose because the path to success always went through many unsuccessful attempts; Having achieved the desired result, I was usually so exhausted that I no longer had the strength to rejoice. Joy came much later, and even it was sometimes darkened by the fear that what was done contained a mistake.”

Since my student years, I have worked diligently and with passion, although at the same time taking some breaks necessary for rest. But as I approach old age, I somehow forget more and more how to rest. Breaks from work have now become boring and painful for me. Laziness has never really bothered me. True, after a break it is usually difficult to resume work, and a reluctance to work arises. Laziness also occurs when you need to complete work by a certain, quite close deadline, for example, to prepare a lecture or report, so overcoming laziness is also work!” (http://ega-math.narod.ru/LSP/book.htm)

He had a will of steel and enormous personal and civic courage.

His colleague at the Institute of Mathematics, Academician I.R. Shafarevich, recalls: “It was the end of the 40s - the era of pogrom regulations on literature, music, biology. Only physicists were not touched; they were in a privileged, special position, some were even returned from the camps. I think after creation atomic bomb our rulers began to fear that scientists and technicians would get out of control. This is where, perhaps, the idea arose: to alarm the physicists, organize a pogrom among their neighbors - mathematicians. How a letter appeared out of the ground, signed by three little-known Leningrad “colleagues”, which demanded to “reconsider” the situation in Soviet mathematics, indicating hostile “decadent” trends in it. Today this is funny, but then an extended meeting of the Academic Council of the Mathematical Institute of the Academy of Sciences was convened to discuss the letter. After the announcement of the message from opponents of mathematical decadence, the chairman invited people to speak out. There was silence, and in these seconds, perhaps, the fate of our mathematics for entire years was decided. If someone starts calling for “correction of mistakes” then, one can imagine the consequences based on the precedents that have already taken place. Suddenly Pontryagin’s calm, seemingly bored voice was heard: “Why, exactly, are we discussing this letter at the Academic Council?” The chairman explained that this was a “letter from the workers” sent to us through the Central Committee.

— The Institute receives many letters from “mathematics reformers,” why are we discussing this at the Academic Council?

I don’t remember what answer was received, but the hypnotizing atmosphere of fear dissipated. At first timidly, then more boldly, the members of the council began to object to the authors, and the meeting ended with a resolution taking mathematics under protection, although with all the caution and reservations typical of that time.”I. R. SHAFAREVICH PONTRYAGIN ABOUT MYSELF AND MY THOUGHTS ABOUT HIM (“Tomorrow” No. 40, 1998)

And in 1937, Pontryagin wrote a letter to Stalin asking him to release his mathematician friend Efremovich from prison. The Jew, by the way, had previously betrayed him, Pontryagin. The friend was released, and he then lived for seven whole years in the apartment of Pontryagin, who had to work hard to evict the rescued man. In general, an old, old fairy tale about the fox and the hare and the ice and bast huts.

This is about the question of Lev Semenovich’s “anti-Semitism”.

It is characteristic of Pontryagin that he did not shy away from such a painful (in many respects) issue as the role of the Jewish intelligentsia in our life. Of course, he cannot be suspected of any initial racial or national antipathy, as evidenced by the names of his friends and colleagues mentioned in the “Biography” - especially where we are talking about the first half of his life. But gradually some impressions accumulated. Thus, Pontryagin writes about one of his graduate students: “She completely amazed me with one of her statements. She complained to me that very few Jews were accepted into graduate school this year, no more than a quarter of all those accepted. But before, she said, they always took at least half.”

By the way, the well-known “debunker of Stalinism” G. Kostyrchenko published documentary information about the “proportion” of Jews among graduates of the physics department of Moscow University in the late 1930s - early 1940s (they entered Moscow State University in 1933-1937): 1938 - 46% , 1940 - 58%, 1941 - 74%, 1942 - 98%, ... ! (See: G. Kostyrchenko. Captured by the Red Pharaoh. Political persecution of Jews in the USSR. Documentary research. - M.: 1994, p. 286.)

It was these “lads and girls” who joined the ranks of “jokers” and dissidents in the 60s. And here is another interesting and revealing episode: in 1932, Pontryagin received an invitation to go to the USA, but... “They didn’t let me in. The previously very easy trips abroad for Soviet mathematicians had by this time become more difficult.

Apparently, my friend at the university, student Victoria Rabinovich, and our philosophy teacher Sofya Aleksandrovna Yanovskaya had a hand in denying me the trip. In any case, one day Yanovskaya told me:

— Lev Semyonovich, would you agree to go to America with Vika Rabinovich, and not with your mother?

I answered Yanovskaya with a sharp refusal, saying: “What position do you want to put me in? Who is Vika Rabinovich to me? She’s not my wife.”

Such a joint trip to America for a year with Vika Rabinovich could have ended in marriage with her, which was not what I wanted at all. Yanovskaya at that time was an influential party figure, and I can imagine that a lot depended on her, in particular, if she invited me to go with Vika Rabinovich, then she probably had reason to think that she could organize this trip. But I didn't agree to this.

The trip to the United States planned for the 33rd year did not take place for a year" (http://ega-math.narod.ru/LSP/ch2.htm#a ).

In a word, young Lev Semenovich did not understand that Madame Yanovskaya wanted to arrange his personal life, give him a “start in life,” and at the same time have more than “promising personnel” at hand. Later he became simply an “anti-Semite.”

Well, let's talk about this slippery topic.

A direct “accusation” of “anti-Semitism” was openly brought against L.S. Pontryagin as the editor-in-chief of the “Mathematical Collection” in 1978. Someone “calculated” that mathematicians of Jewish origin who previously appeared on the pages of this publication accounted for 34% of all authors, and now they make up 9%. This was interpreted as "explicit discrimination against Jewish mathematicians." Lev Semenovich with with good reason defined such claims as “racist demands.”

However, his persecution began much earlier, and it was connected with Pontryagin’s fight against Zionism.

He himself wrote that long before the Moscow International Congress of Mathematicians (1966), “a new wave of Zionist aggression began to approach the world. The so-called six-day war of 1967, in which Israel defeated Egypt, sharply spurred it on and contributed to the incitement of Jewish nationalism... In 1978, L.S. Pontryagin was the head of the Soviet delegation at the International Congress of Mathematicians in Helsinki, where a large-circulation manuscript “The Situation in Soviet mathematics”, about which L.S. Pontryagin wrote the following: “A significant part of the information contained in it is obviously erroneous and, perhaps, deliberately false...”. At the same time, he asks the question: “Why are those leaving Soviet Union carry such information abroad? There are two reasons for this, I think. The first is that people leaving the Soviet Union are dissatisfied with something happening in our country, they are offended by someone. This dissatisfaction and resentment may not be related to nationality at all. But the easiest way is to attribute grievances and discontent to anti-Semitism. Secondly, emigrants from the Soviet Union are expected to provide anti-Soviet information. Such information is highly remunerated in both position and money. There is a great demand for it. And so, in order to pay for America’s dollar hospitality, some people give deliberately false information” (http://ega-math.narod.ru/LSP/ch2.htm#a).

In Helsinki, L.S. Pontryagin had a meeting with L. Bers, who, after a long farewell conversation, called Pontryagin an anti-Semite and expressed the hope of “meeting him again.” In the same 1978, the President of the USSR Academy of Sciences A.P. Aleksandrov removed Pontryagin from the post of Soviet representative in the International Union of Mathematicians. Work in the Executive Committee International Union mathematicians ended with his trip to the International Mathematical Congress as the head of the Soviet delegation. L.S. Pontryagin notes: “... as a member of the Executive Committee, I stubbornly resisted the pressure of international Zionism, seeking to strengthen its influence on the activities of the International Union of Mathematicians. And this caused the Zionists to become angry against themselves. I think that by removing me from work in this international organization, A.P. Aleksandrov consciously or unconsciously fulfilled the wishes of the Zionists.”

What else could you expect from a sophisticated courtier?

Descendants from the “tribe of Dan” did not leave Pontryagin alone even after his death. Thus, in 1998, an international conference dedicated to the 90th anniversary of the birth of the great Russian mathematician was successfully held in Moscow. And a few months earlier, a certain learned lady sent out a call throughout the world to boycott the conference, since it was “a gathering of fascists.”

Read, if you haven’t read, the book by L.S. Pontryagina, fellow comrades! This is a striking document of the era, written in large, energetic strokes, in precise and succinct language.

This is how he sums up his life path Russian genius: “Success in work constitutes the main joys of my life. These joys, however, lose their sharpness with age. Successes at work are often replaced by failures. Sometimes months of labor prove fruitless. Having realized this or discovered a mistake in the work done, I always feel a feeling of great misfortune that has befallen me.

Based on many years of experience, I have come to the belief that serious success in any field human activity requires extreme effort. At the same time, numerous failures are inevitable. You have to put up with the latter. And you should be tolerant of the failures of others. Despite numerous failures that led to alternating emotional ups and downs, I consider the overall emotional outcome of my professional activity positive.

Still, I don't think I was born destined to be a mathematician. In other words, my gene pool uniquely determined my profession.”

He was a believer, but he spoke very sparingly and casually about his religious feelings: “In my adolescence, I lost my religious feeling for some time.”

And finally, about his literary and artistic passions: “As a child, I was very fond of reading fiction. I borrowed books from my father's library. It seems to me that no one guided me in choosing books. I still remember how strong an impression A. K. Tolstoy’s trilogy “The Death of Ivan the Terrible”, “Tsar Fyodor Ioannovich” and “Tsar Boris” made on me. During my life I have re-read these masterpieces of Russian drama many times. Boris Godunov has become my favorite historical hero. I believed then (perhaps I still agree with this) that the image given by A.K. Tolstoy was much more correct than that given by Pushkin in his drama “Boris Godunov”. The image given by Pushkin seemed completely unconvincing to me, since I believed that such a political figure as Boris Godunov could not suffer from remorse over the murder of a baby. Reading fiction has always been and continues to be an essential part of my life. While still a schoolboy, I read Tolstoy’s War and Peace, Anna Karenina, as well as Dostoevsky’s main novels: The Brothers Karamazov, The Idiot, The Demons. I read these writers with great fascination. I.S. I never liked Turgenev. But N.S. Leskov liked and continues to like now.

I really like to reread Blok’s short poems, and among them there are even ones I haven’t read before. I really remember Blok’s short poems “ Railway", "Portrait", "Scythians", of the larger ones - "Nightingale Garden". Tyutchev's short poems are also the subject of my fascination. I love it very much and even once memorized “Gemini”, “Cicero” and others. I re-read the poems of A.K. Tolstoy, his ballads, especially “Vasily Shibanov”, “Ballad with a Tendency” and others, as well as lyrical works- “Alyosha Popovich” and much more.

There was a period when I was fascinated by Byron and Heine, but, of course, one cannot feel all their charm in translations. By Lermontov I mainly like short lyrical works of a love nature. Of the larger works, I only like “The Demon.” “Mtsyri,” for example, I don’t like, it’s boring. Of course, I really like “Merchant Kalashnikov” and “Valerik”. I never liked Mayakovsky.

I absolutely can’t read and don’t like Shakespeare’s major works. Shakespeare was spoiled for me by Lev Nikolaevich Tolstoy with his critical analysis of his works. I can’t get rid of this, but I think that even without Tolstoy’s influence I would not have loved Shakespeare - too many corpses, too much blood. I only like Shakespeare's sonnets, they are full of charm. With great enthusiasm I read and re-read “Quiet Don” by M. Sholokhov. Talk that the end of this novel was written by Sholokhov himself, and the beginning was stolen from someone, seems completely unconvincing to me, since the whole novel seems equally good to me. The few works of A. Solzhenitsyn published in the Soviet Union - “One Day in the Life of Ivan Denisovich”, “An Incident at Kochetovka Station”, “Matryonin’s Dvor” - seem to me to be very accomplished literary works, albeit with a strong tinge of gloom. I read larger things in Russian during my trips abroad. I really like “Cancer Ward” and “In the First Circle”. Solzhenitsyn is a major artist. My wife and I did not read The Gulag Archipelago. My strength was already running out..."

And about music: “I must say that I don’t like Shostakovich and Prokofiev, as well as I. Stravinsky, maybe I haven’t gotten used to them yet. I really appreciate the singing of E. V. Obraztsova.”

And of course, one of his favorite composers was the “sunny genius” - Mozart.

This is what Lev Semyonovich Pontryagin was like - the Genius of the Russian Land.
Everlasting memory!

"Rest in peace with the Saints!"

An entire era in the development of mathematics is associated with the name of Pontryagin. The works of Lev Semenovich Pontryagin had a decisive influence on the development of topology and topological algebra. He laid the foundations and proved the main theorems in optimal control and the theory of differential games. His ideas largely predetermined the development of mathematics in the 20th century... Great importance Lev Semyonovich Pontryagin always contributed to public life: his bright, emotional speeches at various meetings are memorable; for a number of years he represented the Soviet Union in the International Mathematical Union, supervised the publication of mathematical literature, and dealt with issues of school education.

"Small Soviet Encyclopedia"(1959) summed up the first half of L.S. Pontryagin’s life:

“... Soviet mathematician, academician (since 1958). At the age of 14, he lost his sight in an accident. The main works relate to topology, the theory of continuous groups and the theory of ordinary differential equations with their applications.”

The second half of L.S. Pontryagin’s life and his scientific achievements of this period are reflected in the “Encyclopedia for Children. Mathematics" (1998):

“...The design of long-range missiles stimulated the development of optimal control (L.S. Pontryagin, R. Bellman)... Let us mention the theory of optimal control of technical and production processes. The concept of convexity plays important role in the proof of one of the most important theorems of this theory - the maximum principle (“Pontryagin’s maximum principle” - V.B.), which was established in the mid-50s by Soviet mathematicians L.S. Pontryagin, V.G. Boltyansky and R.V. .Gamkrelidze (about Boltyansky, see below - V.B.)...". One of the creators (of a new direction called optimal control) was the “Russian mathematician Lev Semyonovich Pontryagin”...

Now about the personal. In the chapter “Slander” of L.S. Pontryagin’s book, we read:

“I want to understand why I became the object of such vicious attacks from the Zionists. For many years I was widely used by Jewish Soviet mathematicians and provided them with all kinds of assistance. In particular, I helped Rokhlin get out of Stalin's testing camp and get a job. I was even ready to put him in my apartment. Now they no longer remember about it. True, at the end of the 60s, when I realized that I was being used by the Jews in their purely nationalistic interests, I stopped helping them, but did not act against them at all. Thus, for a long time The Zionists considered me their reliable support. But at the end of the 60s they lost it. It is possible that this is why they had the feeling that I was, as it were, a traitor to their interests.”

“The outstanding algebraic geometer and topologist Solomon Aleksandrovich Levshits first appeared in my apartment, apparently in 1931. Shnirelman brought him to me.”
And further about Levshits: “At the beginning of our acquaintance, he invited my mother and me (remember, from the age of 14 L.S. Pontryagin was blind) to the USA for one year... I was not allowed. The previously very easy trips abroad for Soviet mathematicians had by this time become more difficult... Apparently, my friend at the university, student Victoria Rabinovich, and our philosophy teacher Sofya Aleksandrovna Yanovskaya had a hand in denying me the trip. In any case, one day Yanovskaya told me: “Lev Semyonovich, would you agree to go to America with Vitya Rabinovich, and not with your mother?” After L.S. Pontryagin’s refusal, “a trip to the United States planned for the 33rd year didn’t take place for a year.”

“Among the Muscovites newly attracted to the institute, six were named, who were considered then as young and talented. That included me. It is interesting to note that these six people were classified into three pairs according to their “quality.” In first place were A.O. Gelfond and L.G. Shnirelman, in second place were M.A. Lavrentiev and L.A. Lyusternik, and in third place were L.S. Pontryagin and A.I. Plesner...”

“Shnirelman died from mental incompetence when he was barely 30 years old. Gelfond flashed a brief brilliance in his early youth, solving the problem of the transcendence of certain numbers. Lyusternik did not reach significant heights at all, and Plesner was hardly any significant mathematician.
We can say that only Lavrentyev and Pontryagin stood the test of time... And Lavrentyev, in addition, turned out to be an outstanding organizer. He founded a new Russian research center in Novosibirsk - the Siberian Branch of the USSR Academy of Sciences."

Now more about Rokhlin:

“My pre-war student, the most diligent and capable listener of my lectures, Vladimir Abramovich Rokhlin, reappeared on my horizon. At the beginning of the war, he joined the militia and disappeared for many years. Only at the end of the war did we begin to hear rumors that he had been captured by the Germans, and then we learned that he had been released and was being checked in a Soviet camp. I wrote a letter to some authorities asking to release Rokhlin.”

“When Rokhlin defended his doctoral dissertation, he announced to me that he could no longer remain in the position of my assistant... In his place I took V.G. Boltyansky, who by that time had completed his graduate studies at Moscow University with me.”

“At the end of Academician Zeldovich’s book it is said: “I hope that the reader will receive pleasure and benefit from my book and will close it with pleasure.” I also close this book with great pleasure, but so that no one returns to it again.”

“I devoted a lot of space to describing the case with Zeldovich’s book. But this case is typical. It convinced me that even a small group of conscientious people can resist evil if they take on the task with perseverance and perseverance.”

Before the war, L.S. Pontryagin met “a very nice student Asya Gurevich” (later the wife of the mathematician Rokhlin).

“During our acquaintance, Asya Gurevich repeatedly turned to me with a request to help one of her friends in some sense. It was always Jews. This did not seem strange to me, since she herself was Jewish and, naturally, had the same environment. But after the war, she completely amazed me with one of her statements. She complained to me that very few Jews were accepted into graduate school this year, no more than a quarter of all those accepted. But before, she said, they always took at least half...”

After this phrase, V.V. Kozhinov (“On the publication of “Biography””) writes:

“In 1978, an “accusation” of this kind was brought directly against L.S. Pontryagin himself as the editor-in-chief of the Mathematical Collection. Someone “calculated” that mathematicians of Jewish origin who previously appeared on the pages of this publication accounted for 34% of all authors, and now 9%. This was interpreted as "explicit discrimination against Jewish mathematicians."
“Lev Semenovich rightly defined such claims as “racist demands.” Of course, those who put forward these demands were ready to consider a decrease in the “share” of Jews as an expression of “racism.”
However, with an elementary objective approach to the matter, one cannot help but come to the conclusion that the requirement according to which Jews, who then made up less than 1% of the population of the USSR, “must” make up 34% of the authors of a mathematical publication, is in the strict sense of the word racist. For it clearly implies that Jews are no less than 34 times more capable of discoveries in mathematics than people of other nationalities...
Recently, documentary information was published about the “share” of Jews among graduates of the Faculty of Physics of Moscow University in the late 1930s - early 1940s: 1938 - 46%, 1940 - 58%, 1941 - 74%, 1942 - 98%.”

“Isn’t the obvious “abnormality” of this state of affairs? It, of course, could not be some kind of accident. It is well known that after 1917, more or less educated Russian people - with the exception of those relatively few who most actively supported the new government - were subjected to real and global "discrimination." The situation of their children was especially deplorable, whose path to higher and special education was blocked in every possible way.”

“A new wave of Zionist aggression began to approach the world. The so-called six-day war of 1967, in which Israel defeated Egypt, sharply spurred it on and contributed to the incitement of Jewish nationalism... The Zionist wave of this period had a pronounced anti-Soviet character... I remember such a case. There was such a chemist - Levich - corresponding member of the USSR Academy of Sciences. He wanted to leave for Israel, but he was not given a visa for a long time... While waiting for his departure, the rector of Moscow University G.I. Petrovsky tried to assign Levich to the university... I could never understand why Levich wanted to leave his homeland, the country in which he was born, was brought up, became a scientist...”

“Levich is not such a significant scientist to organize an international conference in honor of his anniversary. In any case, this is not accepted in the Soviet Union. It is possible that the organizers of the conference had a humane goal to help Levich leave the Soviet Union. It's unlikely that this will help him. The glorification of Levich, which does not correspond to his scientific merits, can only inflame Jewish nationalism, i.e. increase national discord..."

“Why do those leaving the Soviet Union carry such information abroad? There are two reasons for this, I think. The first is that people leaving the Soviet Union are dissatisfied with something happening in our country, they are offended by someone. This dissatisfaction and resentment may not be related to nationality at all. But the easiest way is to attribute grievances and discontent to anti-Semitism. Secondly, emigrants from the Soviet Union are expected to provide anti-Soviet information. Such information is highly remunerated in both position and money. There is a great demand for it. And so, in order to pay for America’s dollar hospitality, some people give deliberately false information.”

“...as a member of the Executive Committee, I stubbornly resisted the pressure of international Zionism, seeking to increase its influence on the activities of the International Union of Mathematicians. And this caused the Zionists to become angry against themselves. I think that by removing me from work in this international organization, A.P. Alexandrov, consciously or unconsciously, fulfilled the wishes of the Zionists.”

“The fact is that in the works of Poincaré, long before Einstein, the main provisions of the theory of relativity were expressed... Meanwhile, Zionist circles persistently strive to present Einstein as the sole creator of the theory of relativity. It's not fair.

Boltyansky also played an active role in the persecution of his scientific supervisor, who, according to L.S. Pontryagin, “began to complain about me to the Jews, interpreting my actions as anti-Semitic. .."
Note that a similar story, only on a larger scale, with exclusion from a number of international academies, happened with academician Igor Rostislavovich Shafarevich after the publication of his book “Russophobia”. In July 1992, I.R. Shafarevich received an “Open Letter” from the President of the US National Academy of Sciences F.Press and the Secretary for foreign affairs J.B. Weingaarden, in which his work “Russophobia” was qualified as anti-Semitic, and for this reason he himself was offered at will leave the Academy. This letter was signed by 152 members of the Academy. Although it was classified as “personal and confidential,” a massive campaign was launched in the foreign press accusing I.R. Shafarevich of preparing public opinion for the start of events similar to Hitler’s. Here, for example, is what a group of French scientists led by the laureate wrote: Nobel Prize Georges Charpak:

“For a long time, science in your country has been poisoned by anti-Semitism. It is regrettable to note that such great mathematicians as Vinogradov and Pontryagin were subject to its harmful influence, and academician Shafarevich even wrote the book “Russophobia,” which, starting as a sociological study, ends with an expression of undisguised anti-Semitism. Academician Shafarevich fans the fire at a dangerous moment when, as in Germany after 1929, this fire can grow to the size of a real hell into which the whole country will be plunged.” Again, this is very similar to the following.” “Remember, by cheating on me, you are cheating on the whole country!” The authors continue: “We are most shocked that this is being done by a famous mathematician whose work is recognized throughout the world. True, he does not consider the Jewish people to be a “lower race” and does not call for pogroms, but his conclusions, pathological conclusions about a Jewish conspiracy whose goal is the collapse of Russia, will quickly find adherents. All the faster that a world-famous mathematician, a courageous opponent of the Brezhnev regime, declares this... We have great respect for the past of I. Shafarevich, but the position he currently takes is simply terrible. Does he really want history to go backwards? Auschwitz and Treblinka again?..”

“We really hope that, together, your society will find ways to counter all manifestations of racism and anti-Semitism.”

“There is only one nation whose concerns we hear about almost daily. Jewish national emotions are feverish both our country and the whole world: they influence disarmament negotiations, trade agreements and international relations of scientists, cause demonstrations and sit-ins, and come up in almost every conversation. The “Jewish question” acquired an incomprehensible power over the minds, overshadowing the problems of Ukrainians, Estonians, Armenians or Crimean Tatars. And the existence of the “Russian question” is apparently not recognized at all.”

“First of all, to the Zionists, since Zionism cannot exist without anti-Semitism, and if it does not exist, then it must be invented. In the United States, all this is used as supposedly existing public opinion needed to make anti-Soviet decisions at a high government level. Zionism and US government circles are quite unanimous on this.”

Excerpts from the book by V.I. Boyarintsev - "Russian and non-Russian scientists. Myths and reality."

Russian mathematician who worked on topology, the theory of optimal processes, and differential equations.

At the age of 14, he lost his sight from an exploding primus stove, but was able to successfully graduate from the Faculty of Physics and Mathematics of Moscow State University.

“When I graduated from high school in 1925, I already had an excellent command of the school mathematics course, which cannot be said about other subjects. So, for example, I didn’t know Russian grammar at all and couldn’t write correctly. However, I didn’t have to write. When I started writing after my first year at university, having acquired a typewriter, my illiteracy was completely revealed. I don’t remember now how I knew other subjects. Apparently, I knew chemistry and physics quite well, as well as literature and history. I knew practically no foreign languages. I only knew a little German, which was taught in our school, but very little. My knowledge of mathematics at that time went significantly beyond school curriculum. I think that I knew mathematics at the level of a technical university. He knew the basics of analytical geometry, differential and integral calculus, and a little bit of differential equations, but without any bias towards the theory of functions of a real variable and set theory. Not only did I not know the theory of limits, but I did not even suspect its existence. The issue of continuity of functions also did not interest me at all. If someone asked me what a real number is, I would react to this question with bewilderment, since this question seemed completely clear to me. Knowledge of higher mathematics I acquired it on my own by reading popular books, textbooks, and individual articles that I came across by chance...”

Pontryagin L.S., Biography of Lev Semenovich Pontryagin, mathematics, compiled by himself, born 1908, Moscow, M., “Komkniga”, 2006, p. 41.

“We can say that my professional work turned out happily. I have never faced emptiness - what to do next. There was always something that needed to be done."

Pontryagin L.S., Biography of Lev Semenovich Pontryagin, mathematics, compiled by himself, born 1908, Moscow, M., “Komkniga”, 2006, p. 173.

Scientific supervisor at the university: P.S. Alexandrov.

Mathematics students: D.V. Anosov, V.G. Boltyansky, R.V. Gamkrelidze, M.I. Zelikin, E.F. Mishchenko, M.M. Postnikov, N.Kh. Rozov and V.A. Rokhlin.

“- It is clear that there are some scientific ideas, which are passed on from teacher to student, but human qualities are no less important. What did you like about Pontryagin?
D.V. Anosov: Restraint. For example, there are scientists who publish a huge number of articles. The same academician Kolmogorov. The personality in science is certainly bright and famous. He published more 500 works But only a dozen or two defined his contribution to mathematics, well, you can also add a dozen or three articles that clarified and developed the main ideas. And the rest of the publications are from incontinence. No, these were quite decent articles, not hack work, but they added little to the level of a scientist. Pontryagin was demanding and therefore restrained. And I learned this from him.”

Gubarev V.S., Academician Dmitry Anosov: “Will the fire of hope go out?” (interview) / Dream of the Universe, M., ICC “Academic”, 2002, p. 360.

"Mathematics has amazing property suck the whole person, take all the strength. To practice it, neither complex laboratories nor expeditions are needed; everything depends on the person himself. In addition, operating with very abstract concepts, it does not require life experience; in principle, mathematical creativity is accessible to a teenager.
Thanks to this, an unusual intensity of feelings is created, captivating the person entirely, sometimes with great intensity. early age. The intensity can be so great that it leaves no strength for other aspects of life - and even among the most outstanding mathematicians. By devoting themselves entirely to science, they sacrifice a lot, including some aspects of their personality becoming pale.
And here, as in many other respects, L.S. Pontryagin was an exception: his strikingly bright individuality not only caught the eye, but powerfully influenced the entire life of the mathematical community and far beyond its borders. Lev Semyonovich described to me more than once the psychological impulse that drove him. “I’ve been afraid all my life,” Lev Semyonovich said more than once, and, knowing him, I took it for a joke or even coquetry. Until he paid attention to what he was afraid of.
He really was always afraid of the failure of his business. The fact that the begun mathematical research will not succeed and the enormous efforts expended will be in vain, that the published work will turn out to be incorrect, that an important undertaking will encounter opposition...
And this fear made him completely forget about what “ordinary” people are afraid of: overwork, damaged relationships, displeasure from superiors, harassment. It was precisely this fearlessness that Lev Semyonovich became famous for, first among mathematicians, and then much more widely. […]
I remember one phone conversation. The interlocutor refused to do what Lev Semyonovich insisted on, saying it was impossible. “So do the impossible!” - Pontryagin exclaimed.
Then it seemed to me - “a catchphrase”, a rhetorical turn of phrase. But later I realized that he was simply talking about an approach to life that was usual for him!
Lev Semyonovich all the time did what others would consider impossible. The struggle with the terrible misfortune that befell him in his youth may have forged his character.
Pontryagin found his way - he refused to acknowledge this misfortune, declared war on it and won.
He never used devices for the blind - books with a special font, for example. He did not write down lectures at the university, but memorized everything and then at night, lying in bed, he smoked and thought through them. He preferred to walk alone, without the help of others, often fell, hurt himself, and constantly had scars and abrasions. And, what is most difficult, he managed to completely avoid the psychology of a somewhat inferior person.
No one ever thought of him as blind. This was also indicated by such a subtle barometer as his attitude towards women and their attitude towards him.
Why did Lev Semyonovich manage to do so much? I think because he never asked himself whether he had the strength to do anything. He got down to business, and found the strength himself. He constantly pushed the boundaries of what was possible."

Shafarevich I.R. , So do the impossible! (To the 80th anniversary of L.S. Pontryagin) - afterword in the book: Pontryagin L.S., Biography of Lev Semenovich Pontryagin, mathematics, compiled by himself, born 1908, Moscow, M., “Komkniga”, 2006. , pp. 292 and 296.