Pyotr Sergeevich Novikov

Pyotr Sergejewitsch Novikow ( Russian Пётр Сергеевич Новиков ; born August 15, 1901 in Moscow , Russian Empire ; † January 9, 1975 ibid., Soviet Union ) was a Soviet mathematician who dealt with mathematical logic, set theory , mathematical physics and group theory.

Live and act

Pyotr Sergejewitsch Novikow was the son of a Moscow businessman and studied from 1919 at the Lomonossow University in Moscow, interrupting his service in the Red Army in the civil war from 1920 to 1922. In 1925 he graduated and did research under Nikolai Nikolayewitsch Lusin . He taught at the Institute of Chemical Technology in Moscow and became a member of the Steklov Institute in 1934 . In 1935 he made his doctorate (candidate) and became a professor in 1939. In 1973 he retired. From 1944 to 1972 he was also head of the analysis department at the Moscow State Teachers' College.

In 1953 he became a corresponding and in 1960 full member of the Academy of Sciences of the USSR .

Since 1934 he had been married to the mathematician Lyudmila Vsevolodovna Keldysch , who was also a student of Lusin and a professor at the Steklov Institute, and the family had five children, including the Fields Medal laureate Sergei Petrovich Novikov and the physicist Leonid Weniaminowitsch Keldysch (der Pyotr Novikov's stepson).

Novikov proved in 1943 the consistency of arithmetic with recursive definitions. In 1952 he showed the unsolvability of the word problem for groups (an effective procedure to find whether a “word” (product of group elements) corresponds to the identity of a group with a finite number of generators and relations). For this he received the Lenin Prize in 1957 . He also made important contributions to solving the Burnside problem in group theory (is every finitely generated periodic group finite?) In the special case of the same finite exponent for every group element. His first proof from 1959, which showed the existence of infinite such groups depending on the number of generators and the order of the periodicity of the elements (that is, for all group elements ), was not entirely correct, but with Sergei Adjan he gave an existence proof for 1968 with Sergei Adjan , in her book The Burnside Problem and Identities in Groups from 1979 to improved. He also showed the finiteness for . ${\displaystyle d}$ ${\displaystyle n}$ ${\displaystyle x^{n}=1}$ ${\displaystyle x}$ ${\displaystyle n>4380}$ ${\displaystyle n>664}$ ${\displaystyle n=2}$

He should not be confused with the Soviet general Pyotr Georgievich Novikov (1906-1944).

Works

• Elements of Mathematical Logic (1959)

literature

• NI Kondakow: Dictionary of Logic ; VEB Bibliographisches Institut Leipzig 1978

Web links

• John J. O'Connor, Edmund F. Robertson :  Pjotr ​​Sergejewitsch Novikow. In: MacTutor History of Mathematics archive .
• Mathematics Genealogy Project

Remarks

1. ↑ independently proven by William Boone