On 24 March 2015 Russian newspaper Troitskiy Variant published my article about my father. Here is my English translation of it.
Arkadii Viktorovich Kryazhimskiy, mathematician and member of the Russian Academy of Sciences, passed away on November 3, 2014. This was my father. He was an exceptional scientist, a talented painter, a poet, and a writer. He was a true artist, a man with boundless imagination and a charge of warm optimism. As for me, he was my principal teacher, my point or reference, and my major supporter.
Now, after he is gone, it is impossible to fully reconstruct his personality or recreate his thoughts, feelings, goals. One can only hope to put together a coarse vastly incomplete portrait from disarrayed snippets of memory. Nevertheless, I will attempt to capture his image here for us and for our descendants.
Arkadii Kryazhimskiy was born in 1949 in the town of Qingdao, China, into a family of Russian emigrants. His father, my grandfather, was a successful architect; my grandmother was a teacher of English language and stenography. Driven by patriotism, the Kryazhimskiy family with their two small sons, Arkadii and Fyodor, repatriated to USSR in 1954. The motherland’s welcome was harsh – the junior architect was sent straight to tselina. But after one year in Kazakhstan, they managed to move to Sverdlovsk where Arkadii and Fyodor grew up and spent most of their lives.
The childhood of Kryazhimskiy brothers in the fifties and sixties was hard but happy. My father used to recall this period quite often. They lived in Vtorchermet, a residential district that was then rapidly developing around the recently constructed iron works. He told us how he and his brother chased each other around Vtorcherment, put nails under passing trains to make daggers, and climbed into construction sites. In short, they led lives of normal Soviet boys. But already at an early age both brothers discovered remarkable creative abilities. They drew comics, wrote poetry and short stories. When my father was about 16, our relative, aunt Katya, invited both of them to see a theater play. She was studying how teenagers perceived theater and decided to use the brothers as her subjects. After the play she asked them to write down their thoughts and feelings with the intention of using these as raw material for further analysis. After a few days, Arkadii turned in his essay. According to the family legend, the teenager analyzed the play and his own attitude to it so deeply and comprehensively that aunt Katya had to present this work to her advisor without edits.
Career choice for my father was difficult. He spent several years in high school mastering the art of drawing. As a result, he seriously considered pursuing a career of an artist. At the same time, science attracted him a lot. First, he was attracted by physics and later by math because it was more rigorous and precise. At the end, science prevailed, and my dad matriculated at the Department of Mathematics at the Ural State University. Yet, his interest in the arts has never vanished. He dreamed of returning to drawing after retirement. But this dream was never meant to come true – many of his ideas will remain pencil sketches.
Being an artist at heart, my dad was a master of interpretation: in art galleries he gladly assumed the role of a guide and gave us fascinating tours. He told us, his captivated audience, not so much about the historical context of paintings but his vision of what the artist had presented. With his boundless imagination, my dad extracted enthralling multi-layered stories from the most abstract seemingly incomprehensible paintings. The richest and most interesting interpretations became themselves pieces of art. For example, my dad described in his poems and songs several paintings by Bruegel, Petrov-Vodkin, Malevich. The ability to find new non-trivial interpretations for art works, mathematical results or even simple life events was my dad’s hallmark.
During his college years, my dad became interested in the problems of optimal control. In these problems one has to find a control function of a dynamical system that would optimize certain criteria of the system’s behavior. For example, how should the driver push the gas pedal in order to reach point B from point A with the minimal gas consumption? The optimal control theory began developing in the 1950s in the school of Lev Pontryagin in Moscow. In Sverdlovsk, these problems were actively investigated by Nikolai Krasovsky and his students at the Institute for Mathematics and Mechanics (IMM).
In 1971 my father entered the PhD program at Ural State University. Three years later he defended his Candidate of Sciences dissertation (equivalent to PhD) on differential games with delay, under the supervision of Yuri Osipov, Krasovsky’s student. While still being a PhD student he became a staff member of the nascent laboratory of differential equations at IMM that Osipov created. My dad continued to work there after his defense. He started studying the behavior of differential games in systems with non-Lipschitz right-hand side. The Lipschitz condition is a standard “natural” condition on the right-hand sides of differential equations. Properties of such “typical” differential games were previously characterized by Krasovsky and Subbotin. But in some applied problems the Lipschitz condition was violated, and it was necessary to understand how much one can relax this condition while preserving the key features of the behavior of the system. A characterization of this “preservation domain” became the basis of my father’s Doctor of Sciences dissertation which he defended in 1981. Many of his colleagues, including Krasovsky, regarded this result very highly.
Many year later, being a PhD student myself, I asked my dad about this period of his scientific career. How did he, a novice researcher with little experience, not succumb to the feeling of powerlessness in comparison with such giants as Krasovsky and Subbotin? Wouldn’t they, with their great talent, solve problems in minutes on which you would spend months? My dad’s answer was surprising to me. ‘Yes,’ he said, ‘they might be much more talented than you are. But even their time and approaches are limited. Even giants cannot solve all scientific problems, there are just too many unsolved ones. And they wouldn’t necessarily find solutions to all those problems that they try to solve, because the solutions may be simply beyond their view. So, look for new problems and look for new original solutions.’
Together with success at work, changes happened in Arkadii’s private life. In 1973 he met his future wife and dedicated life companion Galina Nosova (later Kryazhimskaya) who also worked at IMM at that time. In 1981 their son Sergey was born and in 1986 they had their daughter Alexandra. Despite the general economic stagnation in the country, 1970s and the early 80s were probably the happiest days of my dad’s life. Even though he was quite young, he already had substantial research experience. Not only did he earn respect of his colleagues, he became friends with many of them; some of these friendly-professional relationships lasted for decades. During working days they did what they loved at the Institute, and during weekends and holidays they went out of town for hiking and camping, played soccer, discussed art and literature. In those years, my parents, as many ordinary Soviet citizens, went for annual vacations to various parts of USSR and Eastern Europe. My dad recalled these years, his youth, as the most carefree period of his life.
At that time, my father got perhaps some of his most important scientific results. He solved the problem of the stable inversion of a controlled system in real time. His approach infers the parameters of a system (its speed, control criteria, and noise) from an observation time series, and allows to dynamically use these parameters in the future control process. Gradually he worked out his own unique research style and his research philosophy. He penetrated deeply into the heart of the problem and looked for new original solutions. He used to say that he doesn’t like to walk well-trodden paths, but instead prefers to walk ‘perpendicularly’, to ‘take side-tracks’. And he succeeded in finding such side-tracks that eventually led him to the initially posed goal. And yet, such creative approach to problems never came at the expense of clarity of exposition and utmost rigor of the proof. Here is what his friend and colleague, a corresponding member of the Russian Academy of Sciences, Aleksandr Chentsov says about my father’s work.
‘AVK’s research spanned a wide spectrum of directions in modern mathematics, and he mastered all of the necessary tools in these apparently disparate sub-disciplines. He managed to make a lot of important and useful progress in many of these areas. Using the sports language, he was a ‘multi-athlete’ in mathematics. He often saw such constructions that other investigators simply did not see. His methods were both exquisite and powerful. One could say without any stretch at all that theory and applications were truly united in his research. His work was poetry of sorts in science, as opposed to important but rather mundane prose, which is what many other people do.’
The decay of the Soviet Unition in 1991 caught my father’s scientific career at its peak and took him by surprise. The ideal and precise world of mathematics suddenly hit insurmountable practical obstacles. Overnight Sverdlovsk turned into Ekaterinburg, store shelves emptied out, the salary stopped, and inflation burned the savings. And that, while there were two kids at home. Many of my father’s colleagues were forced to leave the institute and go into business in order to feed their families. It is hard for me to imagine what my father would do if he were forced to leave academia. Luckily he didn’t have to make this difficult decision. Through a fortunate turn of events, he was able to secure a position at the International Institute for Applied Systems Analysis (IIASA) in Laxenburg, near Vienna, and in 1993 our family moved to Austria.
And so, at the age of 44 Arkadii Kryazhimskiy started a new life. In Vienna, he did not have to worry about feeding the family. But the new job presented a new collection of difficulties instead of the old one. IIASA’s aim was to carry out research and formulate strategic recommendations on solutions to global problems. My father became the leader of the “Dynamical Systems” (DYN) project whose goal was to develop new methods of mathematical modeling of complex social, economic and ecological systems, so that other projects at IIASA could apply these methods. Nobody else worked in his project permanently at the time – his colleagues came to visit for a few months a year. This post required him not just to do math. He was supposed to develop the project practically from scratch. He had to build relationships with the leaders of other projects. He had to understand what sorts of models they would potentially be interested in. And he had to initiate productive collaborations with them. Besides the fact that managerial tasks were new to him, IIASA, being an international institute, turned out to be a highly political organization. The atmosphere there in the beginning of the 90’s was dominated by stiff competition for financial resources. Some colleagues at IIASA were very suspicious, if not openly unfriendly, towards a newcomer from a recently formed Russia, a country that barely paid its dues to IIASA.
But after a while, my dad organically incorporated himself into the institute community (in part thanks to his perfect English). He gained new friends and allies. My father won people over no only with his massive scientific potential, but also with his irreproachable professional ethics and kind attitude to people. He has always been very considerate towards his colleagues. His door was literally open all the time. And he did everything in his power to help people even if it wasn’t easy for him. At the same time, he was tough on himself: all promises had to be fulfilled precisely and on time.
Soon enough new results appeared. Together with his colleagues Alexander Mikhailovich Tarasiev and Sergei Mironovich Aseev, my father formulated and solved several important applied problems that emerged from their interactions with their colleagues-economists. Among them was the problem of how a technologically lagging country should optimally distribute its work force in order to minimize its lag. Aside from the practical interest, this problem turned out to be interesting from the mathematical perspective because it fell into an understudied class of optimal control theory problems with infinite horizon for which standard Pontryagin’s results failed. My dad arrived at the formulation of this problem in part by thinking about the future of Russia. It was clear to him that Russia is lagging behind the West in its technological development. Solving this problem was his attempt to help his homeland.
My dad was a true patriot in the classical sense of this word, i.e., in actions, not words. When his contract with IIASA expired in 1996, he decided to return to Russia, even though a possibility to extend the contract existed. I was 15 at that time, and I had to decide where to go to college. My father was absolutely certain that I should get my higher education in Russia. He thought that with its strengthening democracy Russia would soon recover from its serious intellectual losses that happened in the early 90’s, and that Russian science would again be at the forefront. Just as his own father 40 years ago, he firmly believed in the bright future of his country.
When we came back to Russia, my dad got a position at the Steklov Mathematical Institute in Moscow and also started teaching at the Chair of Optimal Control at the Department of Computational Mathematics and Cybernetics (CMC) in Moscow State University (MSU). In 1997 he was elected to be a corresponding member of the Russian Academy of Sciences. Although math has always been my dad’s true passion, with age (and with the experience acquired at IIASA) he started feeling the need to contribute to society more directly. His work on applied problems was partially motivated by this desire because such problems could, at least in theory, have a direct impact on society in solving practical questions in economics, environment, demography. Aside from that, my dad was trying to help his students and colleagues at MSU as much as he could by organizing seminars on new topics, tapping new funding sources, facilitating summer school positions for students at IIASA. His pivotal role was to connect together different groups of researchers and students. Among other things, he initiated several joint projects between IIASA in Vienna, IMM in Ekaterinburg, MSU in Moscow, and other institutions. My dad saw IIASA as one of the few functional instruments for integrating Russian science into the global network. He believed that without such integration Russian science would not survive.
My dad always cared deeply for the fate of junior scientists in Russia. He saw with his own eyes that graduate students at MSU were forced to earn money elsewhere and do research on the side. This was very different from the time when he was a graduate student. Many of the current students failed to meet the strict standards for defense that were established in the Soviet times and were forced to leave academia. And even those who successfully defended had very uncertain prospects in Russia, at least in academia. One thing was very clear to my dad: it was important to create demand for science. But how? He thought that scientists should self-organize and develop a strategy to generate demand for science from the government and business. It was obvious to him that it is exactly those countries and companies that are at the forefront of scientific and technological innovation that would have the long-term competitive advantage. One would just have to make this simple fact clear to the government and business leaders. My dad spent several years trying to organize Russian scientists to form an initiative that would work out a game strategy for generating demand for science. But these attempts failed. He was unable to garner enough support even among his closest colleagues. Most people were not prepared to go against the already established system.
After becoming a permanent member of the Russian Academy of Sciences in 2006, my dad returned to IIASA for four years as the leader of the DYN program. Following his own philosophy of “moving across, not along”, my dad expanded the scope of his research beyond his traditional topics of differential games and control theory. He started working on problems in applied probability theory and statistics. Together with his colleagues and students at IIASA he developed a method of forecasting catastrophic changes in the dynamics of a system, based on an observed time series. The primary motivation for this problem was the financial crisis in Russia in 1998 when the Russian stock market collapsed. Was it possible to predict or even prevent this catastrophe? An analysis of fluctuations of some financial indicators showed that the collapse was preceded by a series of microscopic yet detectable warning signals. The results of this analysis turned out to be applicable to a broad range of systems in economics and ecology.
In the last years of his life, my dad became deeply interested in the fundamental problem of how to obtain an integrated understanding of complex systems, such as the climate of our planet. In contrast to “simple” systems, such as the mechanical pendulum, it is impossible to describe complex systems with a single equation or even with a system of equations. An adequate description of such systems consists of multiple layers that are often described with mathematical models of different types. My dad started with a seemingly elementary question. Suppose we make a measurement of a certain parameter of a system with two different methods. Situations like this one are quite common in science. The problem is that these two measurements are never in perfect agreement with each other. So, how does one estimate the true value of the parameter from these partially contradictory sets of data? My father developed a method of “integration” of random variables that constructively answers this question.
At the end of 2012 my dad left the post of the leader of the DYN program. He said that he didn’t want to occupy this post for too long and that it was important to give way to the next generation. So, Elena Aleksandrovna Rovenskaya, my father’s student, took over his position. In the mean time, my dad went back to Moscow where he devoted himself to the organization of science. He initiated the Summer Academy on Economic Growth and Governance of Natural Resources, based at the CMC Department in MSU. Organizing such events in Russia is a rather difficult task. Not only is it hard to get funding, but even when funding is available, beaurocratic obstacles are countless. My dad has never really learned how to use his high RAS-member status to overcome these kinds of hurdles – he despised playing political games. Instead he surmounted the obstacles with his hard work. On several occasions he had to invest his own money into the organization of the summer school. However, the ultimate goal of the event – the integration of junior Russian researchers into the global scientific environment – was too important for him to put the school in jeopardy.
After work, my dad devoted himself to art. He continued to write poetry. He joined several societies of amateur poets, e.g., the literary club “Russian poetry in Russia”, the art organization “Art pro & contra”, both in Vienna; later he also joined the project “Library of modern poetry” in Moscow. In 2013 some of his poems were published for the first time. My dad was very proud of this achievement. Aside from poetry, my dad acquired a new hobby. He started writing plays in the style of fantastic realism. He put his vivid multidimensional characters into tragic situations inspired by Soviet history. One the characters is an air force pilot Osipovich who does not know yet that in a few hours he will fire the missile that will shoot down the Southern Korean passenger jet…
In July 2013 Russian Parliament (Duma) passed the law dissolving the old Russian Academy of Sciences and forming the new one. Catastrophic consequences of this decision for the science in Russia were immediately clear to my dad. My father openly opposed this decision, revealing his internal toughness which he rarely demonstrated in ordinary life. Together with a few of his like-minded colleagues he wrote an open letter to the leadership of the country repudiating the law. They carried out a survey of what researchers think about the problems in academia and possible solutions. They organized an emergency meeting for scientists to discuss the reform. It is likely because of these activities the most devastating consequences of the new law were avoided, but the law itself remained in power. In the end, my father was deeply disappointed by the collective passiveness of scientist. He thought that a major battle for the future of Russian science was lost.
In August 2014 my parents visited me in the United State for the first time in 10 years. With the whole family we were driving across vast open spaces of the “Wild West”. We argued, laughed, talked about life, dreamed about the future. At some point, the car ran out of gas, and we had to stop off the highway. I was fussing around anxiously waiting for help. But my dad was calm and unperturbed, as if he did not take part in these events. He took his video camera and started filming: mountains, slowly setting sun, trucks roaring by, and us, waiting anxiously near the car. Trifles. At the airport, we were saying “Good-bye” for a few months, until the New Year, as usual. But on November 3 my father was gone.
The author sincerely thanks G.S.Kryazhimskaya, A.A.Kryazhimskaya, E.A.Rovenskaya, A.G.Chentsov, S.M.Aseev, A.M.Tarasiev, V.I.Maksimov, A.P.Kuleshov, and B.Fath for help.