
This article is cited in 1 scientific paper (total in 1 paper)
Nikolai Nikolaevich Konstantinov (obituary)
V. L. Arlazarov^{}, A. Ya. Belov^{}, V. O. Bugaenko^{}, V. A. Vassiliev^{}, A. L. Gorodentsev^{}, S. A. Dorichenko^{}, Yu. S. Ilyashenko^{}, V. M. Imaykin^{}, S. I. Komarov^{}, A. G. Kushnirenko^{}, Yu. P. Lysov^{}, A. L. Semenov^{}, V. M. Tikhomirov^{}, A. K. Tolpygo^{}, A. G. Khovanskii^{}, P. A. Yakushkin^{}, I. V. Yaschenko^{}
The life of Nikolai Nikolaevich Konstantinov, an outstanding figure of our time in the field of mathematical education, came to an end on July 3, 2021.
The Moscow mathematical school has a tradition of working with school children and with students, going back to the midthirties. Konstantinov belonged to this tradition, and his promotion of the subject made of mathematics the favourite intellectual activity of thousands of children, and made entry to a mathematical school the ambition of a great many Moscow families. His ideas spread throughout the country and have had a significant influence all around the world on the education of lovers of mathematics.
Developing his own system for the teaching and learning of mathematics and its applications to the natural sciences, he inspired many young people, students as well as teachers, to join in his work. He created new kinds of mathematical competitions, across dozens of countries. Thousands of alumni of this system, outside Russia as well as inside, form an intellectual community enthusiastically working for the benefit of science.
1. Short biography Nikolai Nikolaevich Konstantinov was born on January 2, 1932 in Moscow. His father, also Nikolai Nikolaevich, was an engineer, and a hereditary honorary citizen of the Russian Empire. His mother, Irina (Inna) Konstantinovna—née Avaliani—came from a noble Georgian family. Some details of his biography can be found in [1]. Nikolai Konstantinov attended school no. 436 in Moscow, and graduated from there in 1949 with a gold medal. During the years 1941 to 1943 he was evacuated to Yelabuga. Already as a schoolboy, Nikolai organized his first mathematical Olympiad, for students of his school. During his school years, Nikolai Nikolaevich became interested in biology. He says: “…in the ninth grade I joined a club for school children at the biological faculty. $\langle{\dots}\rangle$ Classes at the club were both theoretical and practical (on flies). Experiments were carried out on crossbreeding: we examined chromosomes under the microscope, and so on” [2]. “…but summer of 1948 marked the catastrophic appearance of Lysenko and his theories. After that there was no sense in going to the biology faculty” [3]. He continues [2]: “Every time I did anything stupid, mathematics, which I had enjoyed since the 7th grade, seemed to draw my attention to my foolishness. $\langle\dots\rangle$ It was as if it enhanced my mental faculties, and I decided ‘you need to put your mind to mathematics’. $\langle\dots\rangle$ Later, becoming a professional in that subject led me into pedagogical activity, which my friends and students consider to be my main occupation. $\langle\dots\rangle$ In the 10th grade, physics came into my field of vision. One of the organizers (Mika Bongard) of a physics olympiad encouraged me to prepare for it, and a result of this was that I ended up going to the physics department.” In 1949 Konstantinov enrolled in Moscow State University. Straight away he started to run study groups for schoolchildren in physics and mathematics. In 1950 he became deputy chairman of the Moscow Physics Olympiad. During the academic year 1953/54, himself a fifthyear student, he began to organize a seminar on real analysis for students of mathematics at the university. In 1954 Konstantinov graduated with honours. From 1954 to 1959 he worked as an assistant at the Department of Mathematics, in the Faculty of Physics at Moscow State University. Konstantinov writes: “In 1959 I went to graduate school, and chose to work with A. A. Lyapunov. $\langle{\dots}\rangle$ I was interested in the problem of pattern recognition. Bongard considered this to be a mathematical and a logical problem; otherwise, it just cannot be posed. After this though, it can also be seen as physiological. $\langle{\dots}\rangle$ One day I found an article by L. V. Krushinskii about the extrapolation reflex, published by A. A. Lyapunov^{1}^{[x]}^{1}Who was the editor of the journal. – Translator’s note. in the journal Problemy Kibernetiki. It made a big impression on me, and I went to Lyapunov to tell him about my ideas. He received my account very well and soon he agreed to be my scientific advisor” [2]. So Konstantinov became a Ph.D. student at the Department of Mathematical Logic (nowadays – the Department of Mathematical Logic and the Theory of Algorithms) in the Faculty of Mechanics and Mathematics (Mekhmat) of Moscow State University. In 1961 Lyapunov introduced him to N. V. TimofeevRessovsky. This was partly responsible for the ‘biological thread’ in Konstantinov’s destiny, later finding expression in the fact that, on his initiative and with his assistance, ‘biological classes’ were opened in all schools with which he worked. His memoirs contain a lot of autobiographical and philosophical material about TimofeevRessovsky [2]. After the departure of Lyapunov to Novosibirsk, Nikolai moved to work with A. S. Kronrod at the Institute of Theoretical and Experimental Physics (ITEP). One of the last students of N. N. Luzin, Kronrod was an outstanding mathematician, and later an outstanding programmer, who occupies an important place among the founders of computer science in the USSR. In 1965 Konstantinov defended his Ph.D. dissertation, with the title “Some problems in the settheoretic geometry of plane curves”. D. V. Anosov and E. V. Zhuzhoma later wrote of it in [4]: “… the noteworthy work [5], in which, on a bounded piece of the Euclidean plane, there is constructed a nontrivially recurrent semi infinite curve without selfintersections and with bounded curvature”. Konstantinov wrote in [6]: “The term ‘selfcoiling’ was proposed by A. Lelek (Wroclaw). $\langle\dots\rangle$ A. Lelek proposed the following problem: prove that the complement to the closure of a selfcoiling smooth curve with bounded curvature consists of at least four components. The present note is devoted to a proof of this theorem”. Konstantntinov was a wonderful ‘mathematical composer’, inventing (or discovering) beautiful and instructive mathematical problems. He was deservedly proud [3] of the fact that at the very beginning of his textbook [7] V. I. Arnold writes “Let us consider an example where the mere introduction of the phase space makes it possible to solve a difficult problem: Problem 1 (N. N. Konstantinov). Two nonintersecting roads lead from city $A$ to city $B$. It is known that two cars traveling from $A$ to $B$ over two different roads and joined by a cord of length less than $2l$ were able to travel from $A$ to $B$ without breaking the cord. Is it possible for two circular wagons of radius $l$ to pass without touching?” In 1968, together with V. V. Minakhin and V. Yu. Ponomarenko, Kostantinoc created a computer program to model the movement of a cat by means of differential equations [8]–[10], producing the animation [11] as a result. In 1963 he started work as a senior researcher in the Mathematics Laboratory at ITEP, led by Kronrod. In 1968 the laboratory was closed after its leader and a number of employees signed a letter in defense of the mathematician and dissident A. S. YeseninVolpin, who had been forcibly placed in a psychiatric hospital [12]. This letter also created problems for A. I. Alikhanov, the director of the institute. After losing his position at ITEP, Konstantinov first found a job for a couple of years as a senior engineer at the power company Mosenergostroy, before he moved on to run the Department of Computer Technology (working with the “Razdan” computer), in the role of Deputy Head of the Information and Computing Center in the Central Research Institute of Patent Information. Already during the ITEP period, the team of Kronrod had started cooperating with economists, and Konstantinov continued this activity by working in parallel also at the Institute of Economics of the Academy of Sciences of the USSR, where from 1969 until 1989 he had the position of senior researcher. This time is represented by several of his works (coauthored with colleagues), concerned with the application of mathematical methods and of computers to economics. Reputable economists, V. D. Belkin and V. V. Ivanter, included Konstantinov as coauthor in the series of works [13]–[16]. The article [15] is one of the three papers of 1975 that are included in the list of top articles published in the journal Èkonomika i Matematicheskie Metody. At that time, the model they constructed was the only numerical model of the country’s economy. Belkin called it the ‘income–goods’ model. The last work of Konstantinov on the development of the model [17] was published in 1988. The academician Ivanter wrote in 2015 : “We worked with a team of firstclass mathematicians from… the Institute of Theoretical and Experimental Physics. The participation in our studies of mathematicians of the highest level, among whom were A. S. Kronrod, N. N. Konstantinov, and Yu. P. Orevkov, became one of the important factors of our work. $\langle\dots\rangle$ Financial modelling with the ‘income–goods’ model is still in use today. It is a real combination of planned and marketled methods… $\langle\ldots\rangle$ … designed to improve balance in the economy… This accounts for its exceptional success” [18]. In the years to follow, Konstantinov’s places of work were associated with the education of schoolchildren: from 1989, coordinating the scientific and methodological council Zodiac (a nonstate organization established by the Centre for Experimental Scientific Activity, Research, and Social Initiatives); from 1998, working at the Moscow Institute for the Professional Development of Teachers, reorganized in 2001 into the Moscow Institute for Open Education (MIOE). In 2002 school no. 179 was included in the MIOE, but Konstantinov and his students began to restore mathematics classes there even before that, and he continued to work at school no. 179 after 2017, when it was withdrawn from the MIOE. Although it leaves out some significant moments—for example, his parttime work at the Institute of New Technologies, this concludes the formal curriculum vitae of Konstantinov according to his ‘work record’. Next we look at the main directions of his activities in education.
2. Mathclasses. Results of incorporating special mathematical education into schools Professional mathematicans started the ‘mathclass’ system for children (including their own children) at the beginning of the 1960s, as a unique educational project, encouraged to some extent by the powers that be, who were interested in the technological progress of the country and in finding personnel to achieve this progress. In 1962 Konstantinov joined his supervisor Kronrod, working with children in one of the first two mathclasses set up in school no. 7 in Moscow, where, amongst other radical changes, classes in programming and in radio installation were introduced as technology subjects. The first classes for mathematicians and programmers were started in school no. 444 (which emerged on the basis of school no. 425), and shortly afterwards school no. 2 in Moscow was established in coordination with no. 7. In Leningrad in 1961, mathclasses were organized in schools no. 30 and no. 239. Around 1963, physics and mathematics boarding schools were opened at four universities. It is, however, directly as a result of the activities of Konstantinov and his students, that a ‘replicable’ System was created, and this, in addition to its openness, distinguishes it from many other excellent pedagogical systems. For example, Konstantinov’s System interacts naturally with the Advanced Educational Scientific Centers (boarding schools) attached to universities. Participants in the Konstantinov System acquire a mastery of mathematics through searching for solutions to problems and through discussing the successes and failures of their searches with a mathematicianmentor. Each task has some significant element of novelty. Often a task turns out to be a proof of some theorem previously unknown to the student, or a step in this proof. Whatever form it takes, it is always to some degree a discovery. Tasks form lists, cycles; socalled ‘listki’ (or ‘listochki’), meaning leaves or sheets [19], [20]. The student is expect to solve a required minimum of tasks from the worksheet, but there are also extra, additional ones. This models the work of a mathematician: an adult or maybe a student—a relative novice, whose supervisor has set them research tasks. This research model of teaching requires analysis and discussion with the teacher of all of the student’s solutions. Evaluation fades into the background. Thus, an error in a solution does not mean a verdict and cessation of work on a task, but leads to the need for refinement, of continuation and development of discussion. All this is different from the traditional school mathematics ‘honed’ for the quick and errorfree solution of tasks that, for the most part, have a ‘known method of solution’. In those schools which run mathclasses, in order to meet the rules for entry to university, study of the ‘school curriculum’ and of ‘school mathematics’ continues as usual, and ‘special mathematics’ classes are an additional extra. Implementing the Konstantinov System in a class requires several teachers with whom students can discuss their solutions. One teacher cannot do it alone, and needs to be able to summon helpers such as university students, in many cases themselves graduates of the System, working almost for free. The return as teachers of graduates of the school is important for operation of the System. However, influence of the System is not limited to this: its graduates and teachers have formed in our country a community of people with a shared understanding of how one can create and how one can study mathematics. These people have extended their ideas to other scientific fields, as well as, for example, to the teaching of mathematics in elementary school [21]. Many graduates of the Konstantinov System emphasize that it had a powerful effect on their development. It forms a worldview where people—teachers and students—are equal, where correctness is determined by absolute (mathematical) truth, to be comprehended by independent research, by critical analysis of information, and by a logical drawing of conclusions. Konstantinov set up mathclasses in schools no. 7, 57, 91, 179. For a while, those classes existed simultaneously, forming a single organism. Often, however, they faced difficulties for their survival. Beginning in 2001, with the support of L. P. Kezina—at that time head of the Moscow Department of Education—what amounts effectively to a ‘pure experiment’^{2}^{[x]}^{2}Measuring the success of the Konstantinov System. – Translator’s note. took place over the course of the next few years. Konstantinov had been forced out of school no. 179 in the early 1980s by the school administration. By the end of the 1990s, as a result of dramatic movements of people away from the city centre, school no. 179, located as it is in the very heart of Moscow, found itself with almost no students. It was included in the MIOE, led at that time by A. L. Semenov, and explicitly labelled a ‘Konstantinov school’, and Konstantinov was called back to work there. At first there lacked still a principal able to understand the meaning and value of Konstantinov’s System, but in due course a suitable director was found, in the person of P. A. Yakushkin, a previous participant in Konstantinov’s study groups. Rebuilding the System in the school gave impressive results: despite being one of the smallest in the city, school no.179 now regularly ranks first in ratings, based on the absolute number (as opposed to the relative number) of competition winners, on marks in state matriculation exams, and so on. For the last ten years of his life, Kostantinov himself worked as scientific director of the school. The three school profiles at no. 179—mathematical, biological and engineering—represent his main scientific interests. An account of the history and context of the emergence of the Konstantinov System, together with a description of its possible development, can be found in [22]. The Konstantinov System is implemented in the tradition of summer conferences “Tournament of Towns” that gather strong students from different regions together with professional mathematicians who are ready to work on research projects with schoolchildren, individually or in groups. The result of this work is that participants work on some area of mathematics in the form of solving a problem, finding results, new at least for themselves, and sometimes even really previously unknown. Despite its name, there are no winners at the conference. The common victory of everyone is participation in the project and in the tasks it solves. Konstantinov also organized summer educational events of a different kind: starting in 1967, a summer construction team at the White Sea Biological Research Station of Moscow State University; starting in 1973, mathematics summer camps in Estonia (as a place where work culture was highly developed), combining mathematics with physical work. As with his other undertakings, student activities like these continued to function, even without his direct involvement.
3. Mathematics study groups School mathematical study groups appeared in the USSR before World War II, they continued the most effective traditions of the universities. Kostantinov fit organically into this tradition and became a central figure in the study groups community. Kronrod invited Konstantinov to participate in the mathclasses he was setting up precisely because of his already successful involvement in such activities, and mathclasses were essentially an extenson of the study groups ideology to schools. For a student, a mathematics study group served as a ‘soft route’ to entering a mathclass. While staying in a normal school, a student could try the different model of teaching practised in a study group. The supervisors of the group would invite those who adapted well to join a mathclass. In many cases, a mathclass was formed by the supervisors of a study group and consisted mostly of schoolchildren who were already participating in the work of the group. The main element for class recruitment was not ‘strength in mathematics’, but a readiness and desire to study in the proposed model; in the ‘study group style’. Today the tradition of Konstantinov’s study groups is continued by Mekhmat Minor at Moscow State University, where thousands of children study, and more than 1000 students from other schools come to study in the math study groups of school no. 179.
4. Competitions In order to identify and support students who are focused on learning mathematics, along with mathclasses and circles, it is important to organize olympiads and other similar competitions. Konstantinov did a lot for this sphere, in Moscow as well as at the country level, significantly expanding it in the following important directions. In 1979 he organized the multisubject Lomonosov Tournament for schoolchildren from the 7th grade and older, and he was its permanent chairman. The purpose of the Tournament is to support the versatility of interests of schoolchildren. It is for the creation of this Tournament, that in 2008 Konstantinov was awarded the Prize of the Government of the Russian Federation (as it is usually the case, this award also reflected his other services to Russian education). In 1980, together with A. K. Tolpygo (Kyiv) and A. V. Andzhans (Riga), Konstantinov organized the International Mathematical Tournament of Towns and became its permanent president. Participants in this tournament come from more than 100 cities, with a total population of about 100 million people in 20 countries of the world. Annually, about 10 thousand schoolchildren participate, and each year about 1000 of them receive an award. Approximately two thirds of the towns and the participants are from Russia [23], [24]. Konstantinov was a member of international associations for mathematical competitions and, despite having limited foreign language skills, he took part in the organization and conduct of many such competitions.
5. The Independent University of Moscow (IUM) Despite the undisputable success of mathclasses, their graduates often faced difficulties in continuing their education and gaining admission to a university where research mathematicians are trained. This was the case for Mekhmat during the 1970s1980s. Not all capable graduates of mathematical classes managed to enter there: for a number of years there was an informal but very effective barrier to the admission of Jews, and there was clearly a degree of discrimination against graduates of leading mathematical schools. On the other hand, a talented graduate of a mathclass might often fail to match the style of work required to pass the entrance exams for Mekhmat. All this led to a need for the creation of an alternative university programme, and its institutionalization in the form of a nonstate university. Konstantinov undertook this task, collecting a group of mathematicians of various generations. The Program began in September 1991 and became possible due not only to the need, but also to the presence of strong mathematicians and physicists (some of whom were unable to find a place at Moscow State University, while some other were faculty members there) who were eager to participate in the Program. Funding was received from individual scientists and patrons, and later from foreign scientific structures. With the low wages of that time, a small program where students mastered mathematics and physics for free at international level could become a reality. At the ‘university’—known as the Independent University of Moscow (IUM) —two ‘colleges’ were launched: Mathematical Physics (dean O. I. Zavyalov), in the building of the Steklov Mathematical Institute, and Mathematics (dean A. N. Rudakov), first at the Lycée for Information Technologies (Moscow school no. 1533), and then at school no. 2. Subsequently, the local government of Moscow allocated a building in the city center for the nonstate Moscow Center of Continuous Mathematical Education (MCCME), and the university could use it. Classes were held in the evenings, and many students studied there in parallel with their studies at other universities, although several wellknown mathematicians have a diploma only from IUM. Over the years, IUM has transformed. It now formally consists of a single Mathematics college. Its publishing house has developed into the MCCME publishing house. One can reasonably claim that the Scientific and Educational Center of the Steklov Mathematical Institute has inherited important elements of the IUM program. Principally transmitted through people, the Konstantinov System has had an influence on the teaching of mathematics at the Moscow Insitute of Physics and Technology, and in various cases both at Mekhmat and, in the period of 2013–2016, at Moscow State Pedagogical University. The Faculty of Mathematics at the Higher School of Economics (HSE University) was established, in its current form, by teachers and graduates of IUM, and they have naturally continued the same style and traditions.
6. “I want to do only what I can” [25] The system created by N. N. Konstantinov constantly came into conflict with the state ideology and politics in the field of education, with programs and standards, with principles of organization and financing, with personnel policy. A number of similar conflicts would also arise in other countries and in other educational systems. Conflicts often led to crises, as a result of which work of the System in some particular school was stopped. How then did this System continue to exist and develop as a whole, even independently from Konstantinov’s personality? With an obvious and clear difference between the Konstantinov System and the state, it is embedded in the state, uses school infrastructure and, even more importantly, student resources—their time and their motivation—so that the teaching of children in the System is legitimized for parents and for the whole of society. Its very relation with the state education system led in Moscow to а reinforcing of the Konstantinov schools. Around its core—the working of Konstantinov’s system in any particular school—the concentration of strong pupils, the best teachers of various subjects, influential and wellresourced families was growing up, and the attention of the authorities was increasingly drawn to academic successes and competition results. In the end this provided versatile support for the director and helped to bring about a ‘symbiosis’ with the state, which turned a blind eye to deviations. The following observations seem to be significant. In Konstantinov we find a truly historically great teacher. However, he did not present himself as anything special. His communication with people of all ages and social statuses took place on an equal level: to call him by the familar ‘ты’ or the polite ‘Вы’, ‘Nikolai Nikolaevich’, or simply ‘Kolya’, was up to his interlocutor (who might be forty years younger than him). If something in the affairs or views of a person appeared to Konstantinov to be mistaken, his first reaction was of concern for how such a fallacy might affect the person themselves. In an effort to convey something important to somebody, he tried to understand them, the system of their premises, to pose a question, tell a story, a parable, often paradoxical or funny. His students and friends (these are almost the same group) created websites dedicated to him, including konstnn.ru.
7. Awards and honours N. N. Konstantinov received the Paul Erdős award “for his significant contribution in developing the ‘Tournament of Towns’ Contest in Russia”, and a Certificate of Appreciation in 2002 from the Moscow City Duma “for services to the urban community”. In 2004 he was awarded the Moscow Prize in the Field of Sciences and Technologies for Contributions to Education, and in 2008 was winner of the Prize for Education of the Government of the Russian Federation. He also received a prize for teachers from the International Soros Education Program.



Bibliography



1. 
S. A. Dorichenko, “Biography of Nikolai Nikolaevich Konstantinov”, Mat. Obrazovanie, 2007, (40), 3–4 (Russian) 
2. 
N. N. Konstantinov, “Reflections on N. V. TmofeevRessovsky”, Nikolai Valdimirovich TimofeevRessovsky: essays, recollections, materials, Nauka, Moscow, 1993, 239–251 http://elib.biblioatom.ru/text/timofeevresovskiy_1993/go,240/ (Russian) 
3. 
S. Dorichenko, “Interview with N. N. Konstantinov”, Kvant, 2010, no. 1, 19–23 (Russian) 
4. 
D. V. Anosov and E. V. Zhuzhoma, “Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings”, Tr. Mat. Inst. Steklov., 249, Nauka, MAIK ‘Nauka/Interperiodika’, Moscow, 2005, 3–239 ; English transl. in Proc. Steklov Inst. Math., 249 (2005), 1–221 
5. 
N. N. Konstantinov, “Nonselfintersecting curves in the plane”, Mat. Sb., 54(96):3 (1961), 253–294 (Russian) 
6. 
N. N. Konstantinov, “Complement of a selfcoiling plane curve”, Fund. Math., 57:2 (1965), 147–171 (Russian) 
7. 
V. I. Arnol'd, Ordinary differential equations, 3d revized and augmented ed., Nauka, Moscow, 1984, 272 pp. ; English transl. Springer Textbook, SpringerVerlag, Berlin, 1992, 334 pp. 
8. 
N. N. Konstantinov, V. V. Minakin, and V. Yu. Ponomarenko, “A program modelling a mekhanisn and making an animation film about it”, Problemy Kibernetiki, 1974, no. 28, 193–209 (Russian) 
9. 
“Cat: a contribution to computer animation”, Mat. Obrazovanie, 2007, 5–8 (Russian) 
10. 
N. Konstantinow, Ankunft einer Katze: Geschichte und Theorie der ersten Computersimulation eines Lebewesens, Ciconia Ciconia, 23, eds. M. Warnke and W. Velminski, Ciconia Ciconia Verlag, Berlin, 2019, 152 pp. 
11. 
Pussy cat (a cartoon) https://www.youtube.com/watch?v=JWiWYqvP0BU&t=2s (Russian) 
12. 
Letter of the 99 https://ru.wikipedia.org/wiki/Письмо_девяноста_девяти (Russian) 
13. 
V. Belkin, V. Ivanter, and N. Konstantinov, “Planned production model and the realization of social and national product”, Voprosy Èkonomiki, 1968, no. 5, 58–69 (Russian) 
14. 
V. D. Belkin, V. V. Ivanter, and N. N. Konstantinov, Computerassisted drawing up a state budget: the method and calculation algorithm, Institute for Electronic Control Mashines, Moscow, 1969, 47 pp. (Russian) 
15. 
V. D. Belkin, V. V. Ivanter, and N. N. Konstantinov, “Dynamical ‘income–goods’ model for planning and prognostic calculations”, Èkonomika i Mat. Metody, 11:2 (1975), 211–226 (Russian) 
16. 
V. D. Belkin, V. V. Ivanter, N. N. Konstantinov, and V. Ya. Pan, “Modification of the ‘icome–goods’ balanve model into an equilibrium one”, Èkonomika i Mat. Metody, XI:6 (1975), 1037–1048 (Russian) 
17. 
N. N. Konstantinov, “Developing the ‘income–goods’ model and planning the acivement of a balance”, Balance and efficacy, Nauka, Moscow, 1988, 254–275 (Russian) 
18. 
V. V. Ivanter, “The ‘income–goods’ model”: V. D. Belkin, Selected papers, v. 2, A parallel rouble and systemic balance of economy, Central Economics and Mathematics Institute of the Russian Academy of Sciences, Moscow, 2015, 9–11 (Russian) 
19. 
M. L. Gerver, N. N. Konstantinov, and A. G. Kushnirenko, “Problems in algebra and analysis proposed to high school students (grades 9 and 10)”, Teaching in mathematical schools, Problemy Mat. Shkoly, Prosveshchenie, Moscow, 1965, 41–86 https://www.mathedu.ru/text/obuchenie_v_matematicheskih_shkolah_1965/p41/ (Russian) 
20. 
N. N. Konstantinov, Calculus for high school students, Konstantinovskii Sb., no. 2(06), Fond Matemaicheskogo Obrazovaniya i Prosveshcheniya, Moscow, 2021, 121 pp. https://matob.ru/files/nn_sbornik_06_final.pdf (Russian) 
21. 
N. A. Soprunova, A. L. Semenov, M. A. Posetsel'skaya, S. E. Positsel'skii, T. A. Rudchenko, T. V. Mikhaikova, and I. A. Khovanskaya, Mathematics and informatics, Moscow Center for Continuous Mathematical Education, Center of Teaching Excellence, Institute of New Technologies, Moscow, 2012–2019 (Russian) 
22. 
N. N. Konstantinov and A. L. Semenov, “Effective education in mathematical school”, Chebyshevskii Sb., 22:1 (2021), 413–446 (Russian) 
23. 
N. N. Konstantinov, J. B. Tabov, and P. J. Taylor, “Birth of the Tournament of Towns”, Math. Competitions, 4:2 (1991), 28–41 
24. 
N. Konstantinov and S. Dorichenko, “International mathematical tournament of towns”, Competitions for young mathematicians. Perspectives from five continents, Springer, Cham, 2017, 205–241 
25. 
N. Demina, “The Konstantinov manifold”, Troitskii Variant, 2017, no. 227, 8–9 https://elementy.ru/nauchnopopulyarnaya_biblioteka/433594/Mnogoobrazie_Konstantinova (Russian) 
Citation:
V. L. Arlazarov, A. Ya. Belov, V. O. Bugaenko, V. A. Vassiliev, A. L. Gorodentsev, S. A. Dorichenko, Yu. S. Ilyashenko, V. M. Imaykin, S. I. Komarov, A. G. Kushnirenko, Yu. P. Lysov, A. L. Semenov, V. M. Tikhomirov, A. K. Tolpygo, A. G. Khovanskii, P. A. Yakushkin, I. V. Yaschenko, “Nikolai Nikolaevich Konstantinov (obituary)”, Uspekhi Mat. Nauk, 77:3(465) (2022), 161–170; Russian Math. Surveys, 77:3 (2022), 531–541
Linking options:
https://www.mathnet.ru/eng/rm10052https://doi.org/10.1070/RM10052 https://www.mathnet.ru/eng/rm/v77/i3/p161

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