Gennady (or Gennadii or Gennadiy) Semenovich Makanin (1938–2017) was a Russian mathematician, awarded the 2010 I. M. Vinogradov Prize for a series of papers on the problem of algorithmically recognizing the solvability of arbitrary equations in free groups and semigroups.

Education and career

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

he received his undergraduate degree and in 1967 his Russian

Candidate of Sciences Candidate of Sciences (russian: кандидат наук, translit=kandidat nauk) is the first of two doctoral level scientific degrees in Russia and the Commonwealth of Independent States. It is formally classified as UNESCO's ISCED level 8, "do ...

degree (PhD). His dissertation К проблеме тождества в конечно-определённых группах и полугруппах (On the identity problem in finitely-presented groups and semigroups) was supervised by

Andrey Markov Jr. Andrey Andreyevich Markov (russian: Андре́й Андре́евич Ма́рков; Saint Petersburg, St. Petersburg, September 22, 1903 – Moscow, October 11, 1979) was a Soviet Union, Soviet mathematician, the son of the Russian mathem ...

and

Sergei Adian Sergei Ivanovich Adian, also Adyan ( hy, Սերգեյ Իվանովիչ Ադյան; russian: Серге́й Ива́нович Адя́н; 1 January 1931 – 5 May 2020), 4381, and hence for all multiples of those odd integers as well. The solutio ...

. Makanin spent his career (since 1966) working at the Steklov Institute of Mathematics (since 2013 as a freelance employee). From the Steklov Institute of Mathematics he received in 1977 his Russian

Doctor of Sciences Doctor of Sciences ( rus, доктор наук, p=ˈdoktər nɐˈuk, abbreviated д-р наук or д. н.; uk, доктор наук; bg, доктор на науките; be, доктар навук) is a higher doctoral degree in the Russi ...

degree (similar to

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

) with dissertation Проблема разрешимости уравнений в свободной полугруппе (The problem of solvability of equations in a free semigroup). On the basis of his 1977 dissertation he was an invited speaker at the 1978

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in Helsinki. He gained international recognition for his research on combinatorial group theory and algorithmic problems in the theory of semigroups. Zlil Sela,

Eliyahu Rips Eliyahu Rips ( he, אליהו ריפס; russian: Илья Рипс; lv, Iļja Ripss; born 12 December 1948) is an Israeli mathematician of Latvian origin known for his research in geometric group theory. He became known to the general public fo ...

, and others have made important applications of Makanin-Razborov diagrams to

geometric group theory Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such group (mathematics), groups and topology, topological and geometry, geometric pro ...

. In 1982 Makanin published a complete solution (an algorithm with proof of validity) to the problem of recognizing the solvability of equations in a free group. An English translation was published in 1983. In 1984 (followed by English translation in 1985) he published a proof, using techniques similar to those in his 1982 paper, of the decidability, for any free group, of two different formal theories generated by that free group.

Remarks on Makanin's research

Martin Davis and

Julia Robinson Julia Hall Bowman Robinson (December 8, 1919July 30, 1985) was an American mathematician noted for her contributions to the fields of computability theory and computational complexity theory—most notably in decision problems. Her work on Hilbe ...

worked unsuccessfully on the problem which was eventually solved in 1977 by Makanin:

Yuri Matiyasevich Yuri Vladimirovich Matiyasevich, (russian: Ю́рий Влади́мирович Матиясе́вич; born 2 March 1947 in Leningrad) is a Russian mathematician and computer scientist. He is best known for his negative solution of Hilbert's t ...

published a generalization of what he called the "celebrated theorem of G. S. Makanin about decidability of word equations".

Selected publications

* * * * * * * * *

References

External links

Маканин Геннадий Семёнович (Russian full list of publications)

Makanin, Gennadiy Semenovich (English full list of publications)
* http://www.mathnet.ru/person/13873 {{DEFAULTSORT:Makanin, Genady Semenovich 1938 births 2017 deaths Mathematical logicians Soviet logicians Russian logicians Russian philosophers Soviet mathematicians 20th-century Russian mathematicians 21st-century Russian mathematicians Moscow State University alumni