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 Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

he received his undergraduate degree and in 1967 his Russian

Candidate of Sciences A Candidate of Sciences is a Doctor of Philosophy, PhD-equivalent academic research degree in all the post-Soviet countries with the exception of Ukraine, and until the 1990s it was also awarded in Central and Eastern European countries. It is ...

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. and

Sergei Adian Sergei Ivanovich Adian, also Adyan (; ; 1 January 1931 – 5 May 2020), 4381, and hence for all multiples of those odd integers as well. The solution of the Burnside problem was certainly one of the most outstanding and deep mathematical results ...

. 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 A Doctor of Sciences, abbreviated д-р наук or д. н.; ; ; ; is a higher doctoral degree in the Russian Empire, Soviet Union and many Commonwealth of Independent States countries. One of the prerequisites of receiving a Doctor of Sciences ...

degree (similar to

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

) 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 IMU Abacus Medal (known before ...

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

Zlil Sela Zlil Sela () is an Israeli mathematician working in the area of geometric group theory. He is a Professor of Mathematics at the Hebrew University of Jerusalem. Sela is known for the solution of the isomorphism problem for torsion-free word-hype ...

Eliyahu Rips Eliyahu Rips (; ; ; 12 December 1948 – 19 July 2024) was an Israeli mathematician of Latvian origin known for his research in geometric group theory. He became known to the general public following his co-authoring a paper on what is popularl ...

, 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 groups and topological and geometric properties of spaces on which these group ...

. 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 Hilber ...

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

Yuri Matiyasevich Yuri Vladimirovich Matiyasevich (; born 2 March 1947 in Leningrad Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is ...

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 1938 births 2017 deaths Mathematical logicians Soviet logicians Russian logicians 20th-century Russian philosophers 21st-century Russian philosophers Soviet mathematicians 20th-century Russian mathematicians 21st-century Russian mathematicians Moscow State University alumni