A jury meeting of the competition for the N. I. Lobachevsky Medal and Prize "For Outstanding Work in Fundamental and Applied Mathematics" was held at Kazan Federal University. The winner was Academician of the Russian Academy of Sciences Yuri Leonidovich Ershov. Below is a translation of Alexey Nadtochy’s 2010 article “Hierarchy,” dedicated to the laureate’s work and containing information from his biography.

"Yuri Leonidovich Ershov is one of the ten best mathematicians in the world"
Alexander Leonidovich Aseev, Academician of the Russian Academy of Sciences,
in 2008-2017 - its vice-president and
chairman of the Siberian Branch (SB) of the Russian Academy of Sciences.

To try to present in accessible language the results of half a century of scientific activity of the current director (as of 2010) of the Institute of Mathematics of the SB RAS named after S. L. Sobolev, the leader of the Siberian school of mathematical logic and algebra, academician Yuri Leonidovich Ershov - is a waste of time: the average reader will not understand anything anyway. Therefore, let us take the word of the mathematicians themselves first of all, as well as those scientists whose work is closely connected with this precise and remarkable science: in our Akademgorodok lives and creates with the help of numbers and formulas a person of the rarest talent, who combines exceptional mathematical abilities, the broadest scientific erudition and - perhaps most importantly - enormous creative will and imagination, without which no sphere of scientific activity is conceivable.

On the paradoxes of science

Strictly speaking, the "Ershov Hierarchy" is just a scientific term, one of many that Yuri Leonidovich brought to world mathematical science, and it expresses one of the theories of the structural alignment of mathematical concepts as you ascend the mathematical "Fujiyama" - the higher up the "mountain", the deeper into logic and the theory of algorithms.

"The higher - the deeper" is not the only paradox of modern mathematics and science in general. The level of its current development has differentiated specialists in various fields of knowledge so much that not only mathematicians, but also physicists, chemists, biologists, etc. do not always understand each other, not to mention ordinary people.

And, for example, one of Yuri Leonidovich's senior colleagues, a recognized scientific authority, academician Sergei Konstantinovich Godunov, when meeting with the author of these lines, expressed himself as follows:

— As far as I can judge, since Yuri Leonidovich and I work in different specializations, his contribution to science is very significant. The restructuring of the paradigm of domestic education and science, which began in the 1940s and was hastily adapted for the needs of creating a nuclear shield (I am, of course, simplifying), was further developed in subsequent years. But not only for the purposes of defending the country — in general, new technologies needed a new mathematical apparatus that would allow the development of machine programming. This work was continued by Academician Maltsev, and from him the baton of developing mathematical logic and algebra was picked up by Ershov.

But in these notes, we would like to put a broader meaning into the concept of "Ershov's Hierarchy": hierarchy — as steps of depth (or height) not only of scientific knowledge, but also of the construction of principles of attitude to life. After all, any scientist, even such an outstanding one as Ershov, remains first and foremost a human being: with his joys and pains, some of which easily pour out onto the world and those around him, extroverts by nature (they say that one of the "fathers" of the Siberian Branch, Academician S. L. Sobolev, was like that), while others, like Ershov, are not so open, reserved, but still somewhere there, inside, very stormy, sometimes painful (otherwise where do illnesses come from?). Science and we, society, should be grateful to both of them for their life's feat. Because the life of a real scientist is precisely a feat, a dedication, which, unfortunately, most often can only be truly appreciated, alas, by themselves.

A characteristic touch: when Mikhail Fradkov, who held the post of Prime Minister at the time, presented Ershov with the State Prize of the Russian Federation for the monograph “Multiple Normalized Fields”, he quietly asked the scientist, who showed up at the ceremony in the “White House” without a tie: “Is it true that your work has great practical significance?” To which the somewhat embarrassed academician muttered something affirmative. And for the fact that he showed up without a tie, he paid a funny price: the “non-protocol” photo was never sent to him, someone rejected it...

And in this also peculiar paradox, one of the dramas of modern reality is seen: life, on the one hand, requires behaving according to “protocol”, in accordance with generally accepted rules, on the other hand, people who think in a standard way are always no more than good performers. And science is moved forward by non-standard individuals...

About “milestones” and “bumps”

Judging by external signs, you will not see a person behind the list of milestones in the biography of the academician celebrating his anniversary. He was born into a prosperous and hardworking family of railway engineers (so prosperous and hardworking that his brother Valery also became an academician). School with a silver medal, university, Lenin scholarship. Just a few months after defending his diploma - a candidate's dissertation based on ready-made publications in a mathematical journal. At 25, already a doctor of science. At 30 - a corresponding member of the Academy of Sciences of the then USSR (full member since 1991). Head of the Department of Mathematical Logic of the Institute of Mathematics, head of the department, dean, rector of NSU, director of the Institute of Discrete Mathematics and Informatics, which was in the Department of Education. And a new stage - director of one of the most famous and oldest in the Siberian branch of the Institute of Mathematics named after S. L. Soboleva, Chairman of the United Academic Council on Mathematics and Computer Science, Editor-in-Chief of the journal "Algebra and Logic", Chairman of the Charitable Public Foundation, etc., etc. - several pages of text listing his positions, titles, awards, scientific works, etc.

It is important to highlight the "root" in this entire huge list: he was born in Novosibirsk, graduated from Novosibirsk school No. 30, then Novosibirsk State University with a preliminary "entry" into TSU, from where he persistently sought a transfer for more than one year, grew up on his native "soil" of the Siberian mathematical school to a world-class scientist and today its leader. By general recognition, Yuri Leonidovich is one of the "pillars" of Siberian science as a whole, on which, in fact, the authority of our city and Akademgorodok is based. His works on mathematical logic and algebra, topology and philosophy formed the basis of new research areas, and the results obtained by Yu. Ershov form the basis of these studies.

Ershov is constantly invited to give reports at the most prestigious international mathematical congresses and symposia; in 1996 he was co-chairman of the UNESCO Congress "Education and Informatics". His works, written personally and in collaboration, are translated, cited, and several of his books are reference books for mathematicians.

Take a look at the Internet: in the post-Soviet space alone, several textbooks on Ershov's theorems have been published in Russian, including one on the hierarchy named after him. But there is also English, which the scientist is fluent in, and one of the most famous books in the mathematical world - the fundamental two-volume "Handbook of Recursive Mathematics", co-authored with the Americans A. Neroad and J. Remmel and his student Sergei Goncharov.

But when I asked Yuri Leonidovich about the place of Siberian mathematicians in world science, he thoughtfully said:

— You see, some of our institute’s employees are members of the American Mathematical Society, the largest professional association of scientists. Many of our compatriots who now work in the United States and other countries are also members. But people from all over the world willingly come to our scientific events, like the Maltsev Readings. The world of mathematics, as well as all science, is now essentially indivisible. In addition, communications allow it. We have a lot of joint projects, we do not just actively correspond electronically — we work together. Therefore, either the American or the London Mathematical Society — these names most likely indicate the location of the “headquarters”. Indian, Japanese, German, Russian — the color of the skin and the composition of the blood are not important, what is important is what you do in science. Which, however, does not diminish the responsibility and pride for Akademgorodok, for the fate of Russian science. And the state of our affairs in many respects is very alarming, much has already been said about this.

How the complex, invisible process of turning a talented young man into a great scientist happens is largely a mystery to science itself. But it is clear that without the most purposeful work there will be no ascent up the "hierarchical ladder". Recognition, fame, material wealth come to talented people later: first, obsession with work. Sometimes literally according to the principle: they beat him, but he climbs!

Funny everyday details: when a very young applicant was seen off to study in Tomsk by his future wife and only friend in life Nadezhda Semyonovna, formerly Nadya-Nadyusha, she asked with tears in her eyes: "Yurka, do you at least love me?" To which the young man answered solemnly: "After mathematics." A cracker, and nothing more. At home, Nadya sobbed, her mother consoled her: "Stop crying! There are better guys!" It is unlikely that anyone could seriously believe then that Yuri Ershov would become a major scientist and organizer of science and education, and his Nadya would remain by his side for the rest of her life, with three children together, four grandchildren and... mathematics.

He was beaten enough. It is difficult to judge by his outward eternal restraint, but what was, was. With excellent mathematical abilities, having read the newspapers, he first went to enroll in the Moscow Phystech. The capital's public from the admissions committee and examiners treated him indulgently, if not snobbishly: well, come on, little Siberian! Ershov passed the written exams in mathematics and physics with excellent grades. During the oral exam, two of them "cut" the rest as they saw fit. Ershov held out for about four hours. Then, in order to finally "put to sleep" the "Siberian", they gave him a problem that he basically could not solve, because he did not have enough knowledge. He remembered the quiet triumph on the examiners’ faces for the rest of his life, and later, when recruiting at NSU, he always tried first of all to understand how much a person was not just prepared, but also capable of mathematical thinking.

Or take 2002, when he, a long-known scientist, who had many years of heading a department at his native institute and eight years of heading a university, began to run for the post of director of the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, but it was not to be: he did not overcome all the stages of a truly democratic election the first time. It took time for his colleagues to recognize his right to lead a team with an outstanding history, numbering in its ranks several other academicians and corresponding members, dozens of doctors and candidates of science, rightfully proud of its "iconostasis" of bas-reliefs of great mathematicians on the facade of the building. From the outside, no one will ever understand what passions sometimes rage in the souls of "dry mathematicians", how complex the picture of a clash of scientific views and positions can be. And if we consider that all of these people also have an incredible imagination, then we can understand why Ershov had to prove for a year that he could bring this scientific ship, which was moving forward on the waves of a not so calm sea, into balance. He found and applied the wonderful word "consensus" in time. To preserve and increase the authority of the institute, to provide everyone with the best opportunities to realize their abilities, to unite everyone around an enduring idea - temporarily everything except science - this became the program of his activities in his new position.

The world of the Academy in the broad sense of the word, although infinitely diverse, is dominated by the same principles: the head of a scientific institution relies on the authority of his team, his colleagues, but his personal merits to science are a kind of guarantor of the stability of the "ship". And everything ultimately depends on how successful this "alloy" is: the level of scientific activity, the authority of the institute in the scientific world and society, budget financing, grants, business trips, contracts, and finally, salaries.

NSU is also a school

His experience of running a university came in very handy in his new post. Corresponding Member of the Russian Academy of Sciences (now a full member of the Russian Academy of Sciences, editor's note), his student Sergei Goncharov, showed me on the computer the historical-hierarchical ladder of who is who in mathematics (Goncharov is Ershov's student, Ershov is Maltsev's student, Maltsev is Kolmogorov's student, etc. up to the classics of mathematics Karl Theodor Weierstrass and Carl Friedrich Gauss), when I asked what kind of rector Yuri Leonidovich was, he said:

— A very good one. He knew what the university needed and consistently achieved it.

— And what did NSU need?

— 1986-1994: the peak of perestroika and the destruction of everything that was. Ershov managed to keep the staff, under his leadership, part-time workers at the university received more than the salary at that time in the absolutely impoverished institutes of the Siberian Branch of the Russian Academy of Sciences. It is almost unbelievable, but it was in those years that he began to actively build and strengthen the material base. I know how difficult it was for him to resolve organizational issues in the conditions of raging democracy, the "Shvonders" pressed him, but he endured, and I do not remember him raising his voice even once, and stubbornly led NSU forward.

Take at least this fact: during this period, they began to call up students for the army, there was a riot, it came to a strike. Ershov flew specially to Moscow, met with high-ranking officials, the conflict was peacefully resolved. And those guys who had to serve, every single one of them returned to NSU. Yu. L. Ershov achieved the creation of the Specialized Educational and Scientific Center named after M. A. Lavrentyev on the basis of the Physics and Mathematics School, which became part of NSU; based on the reorganization and inclusion of the Polytechnic School into NSU, the Higher College of Informatics of NSU with a technical faculty was created, which began to train specialists in the field of informatics, the demand for which has been growing all these years. A program was also implemented to begin the construction of a new sports center at NSU.

Well, and an important detail that speaks about the atmosphere of those years at the university: our KVN team was one of the strongest in Russia!

I dare say that Rector Ershov was loved by students and respected by teachers. He is a very modern, erudite, widely read in both specialized and fiction type of leader. But, I emphasize, the main thing in a scientific director is that he himself is a scientist. And here Yuri Leonidovich is at his best.

Ershov's colleagues note: despite all his correctness, he is very firm and straightforward in his judgments when it comes to obvious mistakes in someone's work. For example, he once wrote a statement and left the department at NSU when, in his opinion, the then rector began to pursue an incorrect policy that devalued the quality of training specialists. So he laid it all out on paper...

About his position

Yuri Leonidovich was almost never involved in any public activity in the ordinary sense of the word. When, while still a student, he, a newly elected member of the NSU Komsomol committee, was heaped with reproaches for inaction (and at that time he was completely immersed in mathematical logic), he, confused, asked his scientific supervisor Anatoly Ivanovich Maltsev for advice. He scratched his huge bald head:

— Tell them that your public assignment is to pull up those who are lagging behind in mathematics!

That is, however, how it was...

This may seem incredible, another would, as they say, be proud all his life that he was a delegate to the last, historical XXVIII Party Congress (the author of these lines remembers well the young rector of NSU in the delegation of the Novosibirsk Region), but for Ershov it was somehow “off the mark”: “Well, probably it was necessary, the rector - so they elected him...”

But the social activity of the scientist is not so much participation in various congresses and meetings, as his clearly expressed civic position. And here one cannot help but pay tribute to Ershov's strict consistency, when it comes primarily to protecting the interests of science and education. The author of these notes has had the opportunity to see and hear Academician Ershov's statements on this matter for many years.

His articles, interviews in magazines and newspapers are always problematic. He never tires of repeating: the reform of science and education is only legitimate when it is carried out for the benefit of the cause, and not to satisfy the vanity of officials. "Will the integral be negative?", "Where are the high goals?", "For NSU, the 'comb doesn't fit'" - these are just a few of the titles of his publications on this topic. He directly, by name, names those people - from the ministry to the SB RAS and NSU - who do not act in accordance with the needs of the development of science and society, but in favor of short-term interests. As a scientist and citizen, he is outraged by the incompetence, sometimes even the denseness of some "leaders of science", and is worried about the danger of the commercialization of science and education, which has nothing in common with real innovative activity.

In this sense, his short speech at the celebration of the 50th anniversary of the S. L. Sobolev Institute of Mathematics is especially indicative. Discussing the difficult fate of science and education in today's Russia, Academician Ershov proposed introducing, as he put it, the term "intellectual security of society, the country" into circulation. In order to reduce, as much as possible, the unforeseen risks that are opening up before humanity today. He is deeply convinced that it is only possible to solve more and more new problems that the development of civilization itself presents to us on the basis of highly developed science and education. It is difficult to add anything significant...

Quite recently, the author of this essay asked the Chairman of the Siberian Branch of the Russian Academy of Sciences, Academician Alexander Aseev:

— Alexander Leonidovich, how do you personally assess the significance of the work of Yuri Leonidovich Ershov?

— You see, mathematics was originally the "secret weapon" of the Siberian Branch. This is our "hobbyhorse", the basis, the foundation of the work of all scientific institutions. And the current Director of the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Yuri Leonidovich Ershov, according to experts, is one of the ten best mathematicians in the world. So judge for yourself...