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

- Two years later Sergei's parents moved to Kirovabad, where Ivan worked as a carpenter.
- 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.
- And so from his very first year in school young Sergei had to develop persistence and diligence.
- There were good and, more importantly, exacting teachers in the school Sergei attended.
- While everybody else was still working hard on the first problem, Sergei had already solved several of them.
- As a result, Sergei solved 40 problems in one lesson.
- The teacher asked everyone to solve only a couple of problems from each section, and he was immensely surprised when one of the students, Sergei Adian, handed him a thick notebook with complete solutions, drawings included, of all the problems from Rybkin's book! It is not surprising that the Education Department of Kirovabad submitted to Baku, the capital of the Azerbaijan Republic, a petition to send Sergei Adian to Moscow State University (MSU) to continue his education after completing his secondary school studies.
- Following his headmaster's recommendation, Sergei then went to Erevan intending to enter Erevan University.
- Finally, in 1948 Adian had to enter the Russian Pedagogical Institute of Erevan.
- As a consequence, Adian was refused admission to MSU, so again for technical reasons, another attempt to enter there failed.
- 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.
- 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 the autumn of 1954, Novikov suggested to Adian (then in his third year of graduate study) that he work on the word problem for finitely presented groups, noting that though Adian's results already obtained in the theory of functions were certainly enough for a Ph.D. thesis, this new problem was more interesting, was mentioned in Kurosh's monograph, and was a difficult problem that had resisted solution by Novikov's methods.
- In suggesting it, Novikov considered the fact that Adian had already mastered thoroughly the methods of Novikov's proof, not yet published, of the unsolvability of the word problem.
- By the beginning of 1955 Adian had managed to prove the undecidability of practically all non-trivial invariant group properties, including the undecidability of being isomorphic to a fixed group G, for any group G.
- This is one of the most remarkable, beautiful, and general results in algorithmic group theory and is now known as the Adian-Rabin theorem (Michael O Rabin published a simpler proof of the result some years later).
- However, what distinguishes the first published work by Adian even in this brilliant company is its completeness.
- For this work Adian was awarded the Moscow Mathematical Society Prize in 1956 and the Chebyshev Prize of the Soviet Academy of Sciences in 1963.
- It should be noted that A S Esenin-Volpin, one of the official opponents of Adian's Ph.D. thesis, after reading and verifying the thesis, made a special trip to Novikov's dacha in the summer of 1955 to convince him that such work merited a D.Sc. degree.
- Novikov answered that there was nothing to be concerned about: he did not doubt that Adian would write another work for his D.Sc. dissertation.
- 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.
- 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.
- 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.
- 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.
- 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.
- In the Department of Mathematical Logic at MSU Adian has for many years led a seminar on algorithmic problems of algebra and logic, in addition to sharing leadership of the department's main seminar with V A Uspenskii.
- Adian is in essence the creator and leader of a whole research school in mathematical logic and algorithmic problems of algebra.
- Besides his productive research and teaching activities, Adian is active in editorial and organizational work.
- As long ago as the end of 1950s, S M Nikol'skii invited Adian, at the suggestion of Novikov, to edit the section on mathematical logic in Referativnyi Zhurnal: Matematika, the Russian mathematical review journal, because there was then a huge backlog of articles to be reviewed.
- In the shortest possible time Adian rectified the situation there with respect to logic by mobilizing almost all his colleagues for the thankless task of writing reviews (for only a paltry fee).
- Adian told him that this was simply unacceptable and began to help in revising and editing the book.
- 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.
- 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.
- 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.
- 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.
- In the end it almost always happens, in some incomprehensible way, that Adian has in fact been right from the very beginning.

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

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Algebra, Group Theory, Origin Azerbaijan, Puzzles And Problems

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive