Ivan Georgievich Petrovsky

Born: 18 January 1901 in Sevsk, Orlov guberniya, Russia
Died: 15 January 1973 in Moscow, USSR

Ivan Georgievich Petrovsky's name is often written as Petrovskii. He was born in Sevsk, a small town near Brynsk, in western Russia. His grandfather was a highly respected merchant in Sevsk who had made a major contribution to the building of the school his home town which had been funded entirely by the local inhabitants. Ivan Georgievich attended this school and his favourite subject was chemistry [30]:-

He had a small laboratory at home, in a corridor, and performed various experiments there. His father encouraged his scientific interests and supplied him with equipment. Ivan Georgievich loved his father very much, and they were close friends ...

His school record was outstanding but at first sight it is surprising that his performance in mathematics, although very good, was weaker than his other subjects. The reason, as happens so often, was due to the quality of his teachers. The chemistry teacher was outstanding while the mathematics teacher, who had trained as an engineer, confessed that he did not really understand the theory. This was bad enough but he received advice which could easily have prevented him from ever following an academic career. He was advised not to study at a university since this could only lead to a career as a school teacher. Ivan Georgievich, however, decided to study science at university. His grandfather was very upset by this decision since he wanted his grandson to become a merchant but he did not put pressure on him. After graduating from the Sevsk high school in 1917, Petrovsky entered Moscow University with the intention of studying biology and chemistry. Events, however, prevented him even beginning his course for the Russian Revolution began and fighting broke out in Moscow in October 1917.

Petrovsky returned to Sevsk and then in 1918 the whole family moved to Yelizavetgrad in the Ukraine (the city was renamed Zinovyevsk in 1924, Kirovo in 1936, and Kirovograd in 1939). Petrovsky worked for a while as a clerk and then entered the technical school for machine construction. He was keen to do well and happened to find Nikolai Egorovich Zhukovsky's book on theoretical mechanics which he tried to read. He quickly realised, however, that his knowledge of mathematics was insufficient to let him understand Zhukovsky's book so he looked for some books from which he could learn mathematics. The first text he found was Dirichlet's book on the theory of numbers [30]:-

This book, as Ivan Georgievich related, made a great impression on him by the beauty of facts and reasoning and turned his interest forever towards mathematics.

With the ending of the Russian Civil War in November 1920 and stability returning, Petrovsky returned to Moscow University in 1922 but by now his interests were so firmly in mathematics that he did not take up the course he had been intending to follow five years earlier, but read for a degree in mathematics. However, he had to find some means of support [30]:-

As a student Ivan Georgievich had to earn his own living. When in 1922 he came to Moscow, he had no accommodation and no means of living. His first nights were spent at the railway station. Then by chance he saw an announcement that orphanage No. 4 needs a dvornik (a person who takes care of the yard and the pavement in front of the house) and a stoker. They promised accommodation and food. Arriving at the given address, Ivan Georgievich learned that the position of stoker was already taken by another student. It remained only to work as dvornik. But he really had to work for two. It was hard work: he had to carry wood to high floors, stoke ovens, and carry heavy flour sacks and other food for the orphanage. His health at that time was considerably weakened by serious illnesses he had gone through: malaria and pneumonia. The children from the orphanage loved him very much and called him Vaniusha. He made toys for them, sharpened pencils, helped them to arrange a Christmas tree.

Working at the orphanage had one very positive result, however, for while there he met Olga Afanasyevna Kornilaeva who, like Petrovsky, was a student at Moscow University; they later married. From the beginning of his second year of study he earned money teaching mathematics to students in art courses run by the Ministry of Education. He also taught mathematics at a Moscow school. He did not find attending lectures as useful a way of learning mathematics as reading books so he bought many texts. Charles de la Vallée-Poussin's text based on his course on mathematical analysis was one of Petrovsky's favourite. From this time he began to build up his collection of books, described by P S Aleksandrov and O A Oleinik in [10]:-

From his student days onwards, he was always buying books. His personal library contained over thirty thousand books ... It is remarkable that Petrovsky did not have a catalogue but knew his way round the library very well and was able to find his favourite books quickly.

He completed the usual five year undergraduate course in 1927 but in the previous year, even before beginning his graduate studies, he had written his first mathematics paper on the Dirichlet Problem. Kolmogorov writes [24]:-

Even in his student years, Petrovskii was passionately concerned with community action - he was elected a students' representative on the mathematical syllabus commission and threw himself into this task with all the seriousness that was one of his characteristics. I recall how in 1927, as a modest young man in a blue blouse with close-cropped hair, he was entrusted with the duty of greeting the First Conference of Soviet Mathematicians in the name of the students of the University of Moscow.

Petrovsky spent three years undertaking research (1927-30) supervised by Dimitri Fedorovich Egorov [24]:-

It seems no accident that [Petrovsky] chose as his supervisor D F Egorov, a profound and subtle scholar, but a somewhat stern man, an unwearying toiler, avoiding all ostentation.

He also attended the seminars of Aleksandr Yakovlevich Khinchin and Andrei Nikolaevich Kolmogorov on probability theory. During his years as a research student his first published papers appeared: Einige Bemerkungen zu den Arbeiten von Herren 0 Perron und L A Lyusternik über das Dirichlet'scbe Problem (1928) and Sur les fonctions primitives par rapport à une fonction continue arbitraire (1929). The 1928 paper deals with the Dirichlet problem for Laplace's equation and in the 1929 paper he solved a problem originally posed by Lebesgue.

Petrovsky taught at Moscow University beginning in 1929 and, in 1933, he was appointed as a professor. He was awarded his doctorate (a much higher degree in Russia) in 1935. It was in 1933 that his third paper appeared in print, Sur la topologie des courbes réelles et algébriques and in the following year five of his papers appeared. In addition to his roles at Moscow University, from 1931 to 1941 he was also Head of the Mathematics Department at the Institute of Mechanical Engineering, where he taught evening courses. From 1940 to 1944, Petrovsky was the Dean of Mechanics and Mathematics Faculty of Moscow University [24]:-

His time as Dean included the difficult war years, when the main body of the University operated in Ashkhabad and later in Sverdlovsk. The whole Faculty recall Petrovskii's constant concern about material resources and his unswerving efforts to maintain a high potential of academic and scientific work.

From 1943 he also taught at the Steklov Institute. Despite holding these major roles, he had to live and work under difficult conditions [30]:-

Together with his wife Olga Afanasyevna he had two small rooms in a communal flat (flat shared with other families) on 2nd Tverskaya-Yamskaya street. They lived there up to the autumn of 1949. One room served as I G Petrovskiy's study. This was a basement room, and electrical light had to be on even in daytime. Neighbors always had the radio on, and this hindered work considerably. Ivan Georgievich worked at home. Usually he read and reflected lying on a sofa. He used the desk only to write down the calculations and to finish the work. Ivan Georgievich remembered that this made one of the neighbors say: "A strange family it is: the wife goes to work every day, and the husband is always at home lying on a sofa."

He became rector of Moscow University in 1951 having been Vice-Director of the Steklov Institute from 1947 to 1949. His approach to the role of rector is described in detail in [4] and [5] but we give a quotation from [30]:-

Ivan Georgievich had no special reception hours. He tried to speak to everyone coming to him. He was always rector: every moment and under any circumstances he had in mind the necessities and interests of Moscow University. Imagine him speaking with a scientist that came to him. After having discussed the problem the visitor came with comes the avalanche of questions on the visitor's specialty. It seems that I G Petrovsky specially prepared himself for this conversation. He asks about the people working in his domain and having obtained interesting results, about the articles the visitor has recently read, and about the interesting books in the visitor's domain. He also asks: "What do you think about the level of former Moscow University students working in your domain? What has to be done to raise this level?" This last question was very important to I G Petrovsky; he was constantly thinking about the improvement of teaching standards in Moscow University. He did his best to assure a good education for undergraduate and postgraduate students, and he wanted all talented young people to have the possibility to develop their talents; he wanted the best scientist to teach in Moscow University, and he wanted the best young students to be admitted.

P S Aleksandrov and O A Oleinik write in [10] about his achievements as rector:-

It can be said without exaggeration that among the Rectors of Russian Universities two have a special and prominent place: [Lobachevsky and Petrovsky]. Both of them lived the life of the universities of which they were head, took part in all aspects of this life, and tried to steer it along the best possible path.

Also in 1951 he was appointed as Head of the Department of Differential Equations at the University.

Petrovsky's main mathematical work was on the theory of partial differential equations, the topology of algebraic curves and surfaces, and probability. Petrovsky also worked on the boundary value problem for the heat equation and this was applied to both probability theory and work of Kolmogorov. Garding [32] spoke about three of Petrovsky's papers on partial differential equations:-

... the 1937 paper on the Cauchy problem for hyperbolic systems, the 1939 paper on the analyticity of solutions of elliptic systems, and the 1945 paper on lacunae for solutions of hyperbolic systems. In all three cases the work contained new definitive results; it took 20 years to understand and re-prove them. The head-on attacks on these problems undertaken by Petrovskii have now been replaced by more humane approaches. To tell the truth, the original proofs of Petrovskii were extraordinarily difficult to understand, although each detail seemed to be plain. Somehow the author managed to hide the magic of his mighty intuition, allowing him to combine "ice and flames"; in this case the Fourier transform and non-linearity. Apparently, Petrovskii was the first to use the Fourier transform to study higher-order equations with variable coefficients.

He published a number of important textbooks: Lectures on the Theory of Ordinary Differential Equations (1939) (based on courses of lectures he gave at the universities of Moscow and Saratov); Lektsii po teorii integralnykh uravneny (1948), translated into German as Vorlesungen über die Theorie der Integralgleichungen (1953) (based on courses of lectures he gave at the universities of Moscow); Lektsii ob uravneniakh s chastnymi proizvodnymi (1948), translated into English as Lectures in Partial Differential Equations (1954) and into German as Vorlesungen über partielle Differential gleichungen (1955) (based on courses of lectures he gave at the universities of Moscow); and Lectures on Partial Differential Equations (1950) (based on courses of lectures he gave at the universities of Moscow).

P S Aleksandrov and O A Oleinik sum up his career in [10]:-

Petrovsky is one of the few mathematicians whose work shapes the face of modern mathematics. However, he regarded his rectorship as the most important thing in his life, even more important than his mathematical research.

In the same work the breadth of his contributions is emphasised:-

Petrovsky's knowledge was encyclopaedic. He had a thorough understanding of modern science and all its interconnections, was perspicacious and far-sighted, was able to discern long-term trends, and always emphasised them. He also showed a wide general culture, knowledge of diverse branches of science, a deep understanding of state problems in many outstanding public and state activities.

As to his interests outside mathematics, these are described in [8] (written in the present tense since he was sixty years old at the time):-

Petrovskii is a profoundly versatile cultured man with a very wide circle of interests. He passionately loves books on all branches of knowledge. In his home library, comprising many thousand books, all natural and humanitarian sciences are represented in detail, art and fiction (excluding detective stories) in many languages, and he remembers each book he has. Petrovskii is interested not only in the contents of the book, but also in the personality of the writers, about which he owns numerous biographies and memoirs. Petrovskii is intensely fond of nature, especially the beauty of the Mid-Russian belt at all seasons of the year; his favourite form of rest is long walks, during which he often thinks over the next mathematical investigation. In art, as in science, he values depth, simplicity and clarity; in painting he likes Rembrandt, Serov, Nesterov, in music, Bach, Vivaldi, in architecture, simple and severe forms.

He received many honours to mark his achievements. He was awarded the title of Hero of Socialist Labour, won the Order of Lenin five times, the Order of the Red Banner of Labour three times, and also many medals. He was elected to the Academy of Sciences of the USSR and made an Honorary Member of the Moscow Mathematical Society. He was awarded an Honorary Doctorate from the University of Bucharest, the University of Prague and from Lund University, Sweden. He was elected an Honorary Member of the Romanian Academy of Sciences. One of the main streets in Moscow is named after Petrovsky.

Article by: J J O'Connor and E F Robertson

November 2010

MacTutor History of Mathematics