Pyotr Sergeyevich Novikov (; 15 August 1901,

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

– 9 January 1975, Moscow) was a Soviet

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

known for his work in

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

. His son, Sergei Novikov, was also a mathematician.

Early life and education

Pyotr Sergeyevich Novikov was born on 15 August 1901 in

Russia Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...

to Sergei Novikov, a merchant, and Alexandra Novikov. He served in the Red Army during the

Russian Civil War The Russian Civil War () was a multi-party civil war in the former Russian Empire sparked by the 1917 overthrowing of the Russian Provisional Government in the October Revolution, as many factions vied to determine Russia's political future. I ...

from 1920 to July 1922. He studied at Moscow University from 1919 to 1920 and again from 1922 until he graduated in 1925. He studied under Nikolai Luzin until he finished his graduate studies in 1929.

Career

Novikov worked at the Moscow D. Mendeleev Institute of Chemical Technology from 1929 until 1934, when he joined the Department of Real Function Theory at the

Steklov Institute of Mathematics Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Stek ...

. He was awarded his doctorate in 1935 and promoted to full professor in 1939. Novikov became head of the Department of Analysis at the Moscow State Teachers Training Institute in 1944. In 1957, he became the first head of the Department of Mathematical Logic at the Steklov Institute. He jointly held both positions until he retired in 1972 and 1973 respectively. Sergei Adian and Albert Muchnik were among his students.

Research

Novikov is known for his work on combinatorial problems in

: the

word problem for groups A word is a basic element of language that carries meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no consensus among linguists on its ...

, and his progress in the Burnside problem. In 1955, he proved the Novikov–Boone theorem: that there is a finite

presentation of a group In mathematics, a presentation is one method of specifying a group. A presentation of a group ''G'' comprises a set ''S'' of generators—so that every element of the group can be written as a product of powers of some of these generators—and ...

for which there is no algorithm which, given two words ''u'', ''v'', decides whether ''u'' and ''v'' describe the same element in the group.

Awards and honors

Novikov was elected a corresponding member and then a full member of the Academy of Sciences of the Soviet Union in 1953 and 1960, respectively. He was awarded the Lenin Prize in 1957 for proving the undecidability of the word problem in groups.S. I. Adian, ''Mathematical logic, the theory of algorithms and the theory of sets'', AMS Bookstore, 1977, , p. 26. (being Novikov's Festschrift on the occasion of his seventieth birthday) He received the Order of Lenin in 1961 and again in 1971. He was awarded the Order of the Red Banner of Labour. The State Prize of the Russian Federation was awarded to Novikov posthumously in 1999.

Personal life

He was married to mathematician Lyudmila Keldysh (1904–1976). Their son Sergei Novikov (1938–2024) became the first Soviet mathematician to receive the Fields Medal. He died on 9 January 1975 in Moscow.

Notes

References

1901 births 1975 deaths 20th-century Russian mathematicians Mathematicians from Moscow Academic staff of the D. Mendeleev University of Chemical Technology of Russia Academic staff of Moscow State Pedagogical University Full Members of the USSR Academy of Sciences Moscow State University alumni Recipients of the Lenin Prize Recipients of the Order of Lenin Recipients of the Order of the Red Banner of Labour State Prize of the Russian Federation laureates Group theorists Soviet mathematicians {{Russia-mathematician-stub Burials at Novodevichy Cemetery Russian scientists