### Quick Info

Born
1 January 1931
Kushchi, Dashkesan District, Azerbaijan Soviet Republic
Died
5 May 2020
Moscow, Russia

Summary
Sergei Ivanovich Adian was an Armenian mathematician who worked in group theory and is known for his work on the Burnside problem.

### Biography

Sergei Ivanovich Adian was born in Kushchi, a mountain village forty kilometres from the city of Kirovabad (now Gjanja). His father, Ivan Arakelovich Adiyan, was born the son of a shepherd in 1908. Not having the opportunity to finish secondary school, Ivan became a carpenter and worked on local building sites. In 1930 he married Lusik, the 17-year-old daughter of a local farmer, Konstantin Truziyan. Two years later Sergei's parents moved to Kirovabad, where Ivan worked as a carpenter. Initially they rented a room, and it was only at the end of the 1930s that the father bought a plot of land in the centre of the city and built a small house with one room, a porch, and a little cellar. Being a builder, Ivan planned to add a second floor to the house, but this plan was disrupted by the war. By that time there were already four children in the family. The mother did not work, but the parents completed their secondary education studies at an Armenian evening school for labourers. Although at the time Sergei, like his parents, did not speak Russian, he was sent in 1938 to study at the Russian secondary school no. 11 in Kirovabad. His father insisted on that, since he believed that after finishing the school it would be easier for his son to get a higher education. And so from his very first year in school young Sergei had to develop persistence and diligence. His problems with Russian were overcome by the end of this first year.

I should admit that at that time I was extremely lucky: I was not able to go to MSU. As fate willed, I went to the Moscow State Pedagogical Institute (MSPI), where I met Petr Sergeevich Novikov, and he introduced me to his wife Lyudmila Vsevolodovna ...
If ever there was an encounter that could be called fortunate, it was the meeting of Adian and his future teacher, mentor, and friend (in spite of the difference in age) Petr Sergeevich Novikov. Adian started his research work at MSPI, with Novikov as his advisor, in the field of the descriptive theory of functions. In his first work as a student in 1950, he proved that the graph of a function $f (x)$ of a real variable satisfying the functional equation $f (x + y) = f (x) + f (y)$ and having discontinuities is dense in the plane. (Clearly, all continuous solutions of the equation are linear functions.) This result was not published at the time. It is curious that about 25 years later the American mathematician Edwin Hewitt from Seattle gave preprints of some of his papers to Adian during a visit to MSU, one of which was devoted to exactly the same result, which was published by Hewitt much later.

In his graduate work in 1953 relating to the theory of discontinuous functions, Adian constructed examples of semicontinuous functions on the interval [0, 1] that, for any partition of the interval into a countable number of subsets $E_{i}$, have discontinuities on at least one of the subsets upon restriction to this subset. This contribution also was not published right away. In 1958, following a proposal of Adian, the work was published in the Scientific Notes of MSPI as joint work with Novikov.

After completing his graduate studies, Adian worked for several years (in close cooperation with Novikov) as an assistant professor in the Mathematical Analysis Department of MSPI. And in 1957 an event happened which completely changed life for both him and his teacher, the Department of Mathematical Logic was created in the Steklov Mathematical Institute (MIAN), and Novikov was invited to lead it. Adian became one of the first members of this new department, and his subsequent research career was closely connected with it. Furthermore, the collaboration between Novikov and Adian on the Burnside problem started (about 1960) already within the precincts of MIAN. In 1960, at the insistence of Novikov and his wife Lyudmila Keldysh, Adian settled down to work on the Burnside problem. Completing the project took intensive efforts from both collaborators in the course of eight years, and in 1968 their famous paper Infinite periodic groups appeared, containing a negative solution of the problem for all odd periods $n > 4381$, and hence for all multiples of those odd integers as well. Adian published the classic monograph The Burnside problem and identities in groups (Russian) in 1975 (an English translation was published four years later).

In 1965, at the invitation of A A Markov, Adian also took a second position, in the Department of Mathematical Logic at MSU. His work there continues to ensure a close and fruitful collaboration of the department with the Department of Mathematical Logic at MIAN. In 1973, because of a serious illness of Novikov and at Novikov's personal request supported by Vinogradov, the director of MIAN, Adian was appointed head of the department. This appointment happened despite the fact that neither Adian nor Novikov were members of the Communist Party. The Department of Mathematical Logic in the Faculty of Mechanics and Mathematics at MSU went through a similar period of turbulence, for similar reasons, when the head of the department, A A Markov, fell sick at the end of the 1970s. In many respects due to the energy, integrity, and diplomatic skills of Adian, this situation was also resolved favourably for the department.

Adian has always devoted much attention to strengthening the Department of Mathematical Logic at MIAN, to training researchers in the Department of Mathematical Logic at MSU, and to developing new connections between these two related groups. He has had great success in this direction. Under his guidance more than thirty Ph.D. and D.Sc. dissertations have been written. His students are prominent researchers in algebra, mathematical logic, and computational complexity theory. After finishing at MSU, the strongest of them transferred to positions in the Department of Mathematical Logic at MIAN, which under his leadership became one of the most prominent and respected research centres in logic.

For many years Adian was the head of the Specialized Scientific Council of Vysshaya Attestatsionnaya Komissiya (VAK, the Higher Certification Commission) concerned with defence of D.Sc. dissertations in mathematical logic, algebra, number theory, geometry, and topology, first as the vice-chairman and later, after the death of Vinogradov, as the chairman. In 1991 he asked to be relieved of the chairman position in view of his 60th birthday. However, when the directorate of MIAN proposed for this post a person who manifestly was not suitable, Adian could not reconcile himself with this and declared that he was prepared to remain in the position until a more appropriate successor was proposed. Finally, a candidate was chosen who was unanimously supported by the heads and the Division of Mathematics, and he was confirmed by VAK. Of course, such stands in life brought much trouble to Adian (the lateness in his being elected a member of the Academy was mostly due to his having such a 'high profile') and led to him making many enemies. However, the same strains of character have allowed him to acquire true friends among people of like mind who are impressed by his directness and open temperament. Adian did not wish to recognise government restrictions on human relations as necessary even at a time when this was fraught with various risks.

Even the people closest to Adian would probably not be so bold as to call him an easy person to work with. Everybody who has ever dealt with him knows his adherence to principles and his uncompromising nature with respect to quite diverse questions, as well as his careful attention to details. However, those who have been in closer contact with him (and the authors of the present note belong to this list) well know another aspect. In the end it almost always happens, in some incomprehensible way, that Adian has in fact been right from the very beginning. And his arguments have been at least worth considering always, without exception.

Adian has three adult children, two daughters and one son. His son Ivan graduated from the Faculty of Mechanics and Mathematics at MSU. The older daughter Vera graduated with honours from the Faculty of Philology of MSU and in recent years has taught Russian on contract in London. The younger daughter Lena graduated from the S G Stroganov Moscow State University of Arts and Industrial Design (Ceramics Department). She does painting and ceramic arts and has displayed her works often at the Central House of Artists and at exhibitions of young Russian artists; very recently she was elected a member of the Union of Artists of the Russian Federation.

### References (show)

1. B Chandler and W Magnus, The history of combinatorial group theory. A case study in the history of ideas (Springer-Verlag, New York, 1982).
2. L D Beklemishev, I G Lysenok, A A Mal'tsev, S P Novikov, M R Pentus, A A Razborov, A L Semenov and V A Uspenskii, Sergei Ivanovich Adyan (on the occasion of his 75th birthday) (Russian), Uspekhi Mat. Nauk 61 (3)(369) (2006), 179-191.
3. L D Beklemishev, I G Lysenok, A A Mal'tsev, S P Novikov, M R Pentus, A A Razborov, A L Semenov and V A Uspenskii, Sergei Ivanovich Adyan (on the occasion of his 75th birthday), Russian Math. Surveys 61 (3) (2006), 575-588.