Sergei Adian

Sergei Ivanovich Adian, also Adyan (Armenian: Սերգեյ Իվանովիչ Ադյան; Russian: Серге́й Ива́нович Адя́н, born 1 January 1931), is a Soviet and Russian mathematician. He is a professor at the Moscow State University and is known for his work in group theory, especially on the Burnside problem.

Adian was born near Elizavetpol. He grew up there in an Armenian family. He studied at Yerevan and Moscow pedagogical institutes. His advisor was Pyotr Novikov. He has been working at Moscow State University since 1965. Alexander Razborov was one of his students.

In his first work as a student in 1950, Adian 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.

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. These results made up his Ph.D. thesis and his first published work. This is one of the most remarkable, beautiful, and general results in algorithmic group theory and is now known as the Adian–Rabin theorem. What distinguishes the first published work by Adian, is its completeness. In spite of numerous attempts, nobody has added anything fundamentally new to the results during the past 50 years. Adian’s result was immediately used by A. A. Markov in his proof of the algorithmic unsolvability of the classical problem of deciding when topological manifolds are homeomorphic.

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