Andrei Andrejewitsch Markow (mathematician, 1903)

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Andrey Markov junior, Russian Андрей Андреевич Марков , (born September 9 . Jul / 22. September  1903 greg. In St. Petersburg ; † 11. October 1979 in Moscow ) was a Soviet mathematician who is particularly concerned with the foundations of mathematics, formal Logic , algorithm theory and constructive mathematics , but also with differential equations (dynamic systems) and topology.

Life

Markov was the son of the famous mathematician Andrei Andreevich Markov . He received his doctorate in 1921 at the University of Petrograd , in 1935 he qualified as a doctor of science and was professor in Leningrad from 1936 (head of the geometry department) and from 1959 at the Lomonosov University in Moscow , where he founded a school of constructive mathematics and headed the Department of Mathematical Logic was. In 1979 he retired. He was also at the Steklow Institute from 1939 to 1972 . In 1950 he was the founder of the Mathematical Logic Laboratory at the Computing Center of the Academy of Sciences of the USSR and headed it for twenty years.

In 1947, independently and simultaneously with Emil Post , he proved the first undecidable result of a problem in classical mathematics. In 1958 he showed that the classification problem for manifolds (except for homeomorphism ) in four and more dimensions is undecidable.

He is known for concepts such as the Markov principle (and associated Markow's rule ) and the Markov algorithm in theoretical computer science.

In 1953 he became a corresponding member of the Academy of Sciences of the USSR.

He also published a few essays on applied mathematics, including an essay on the principles of variation in plasticity theory. (Another essay was on wave mechanics in 1927). One of his first essays (1929) was on the three-body problem in celestial mechanics. He also published on the theory of braids in topology and topological groups.

Fonts

  • The theory of algorithms, American Mathematical Society Translations 1960, new edition with NM Nagorny, Kluwer 1988 (Russian first Trudy Mat. Inst. Steklov., Volume 42 1954, pp. 3–375)
  • On the Logic of Constructive Mathematics (Russian), Moscow 1972
  • On constructive Mathematics, AMS Translations, Series 2, Volume 98, 1971, pp. 1-9 (Russian in: Trudy Mat. Inst. Steklow, Volume 67, 1962, pp. 8-14)
  • On constructive functions, AMS Translations, Series 2, Volume 29, 1963, pp. 163-195 (Russian in: Trudy Mat. Inst. Steklow, Volume 52, 1958, pp. 315-348)
  • On the non-independence of axiom B 6 from the other axioms of the Bernays-Gödel system (Russian), Izv. Akad. Nauka USSR, Vol. 12, 1947, pp. 569-570

literature

  • Boris A. Kushner: The constructive mathematics of AA Markov, Amer. Math. Monthly, Vol. 113, No. 6, 2006, pp. 559-566.
  • S. Artemov (Editor): Papers presented at the Second St. Petersburg Days of Logic and Computability Conference on the occasion of the centennial of Andrey Andreevich Markov, Jr., August 24 to 26, 2003, in St. Petersburg, Russia, North Holland 2006.
  • Maurice Margenstern, L'école constructive de Markov Revue d'histoire des mathématiques, Volume 1, 1995, pp. 271-305 numdam

Web links

References and comments

  1. ^ Andrei Andreevich Markov in the Mathematics Genealogy Project (English) .Template: MathGenealogyProject / Maintenance / id used Template: MathGenealogyProject / Maintenance / name used
  2. ↑ Markow, Doklady Akad. Nauka USSR, 55, 1947, 583-586.
  3. ^ Based on Martin Davis, The Undecidable, Raven Press 1965, p. 292.
  4. ↑ Markov, On principles of variation in the theory of plasticity (Russian), Prikl. Mat. & Mech., Vol. 11, 1947, pp. 335-350
  5. ↑ Markov, On a Minimal Property of Schrödinger Wave Groups, Z. f. Physik, Volume 42, 1927, pp. 637-640
personal data
SURNAME Markow, Andrei Andrejewitsch
BRIEF DESCRIPTION Soviet mathematician and logician
DATE OF BIRTH September 22, 1903
PLACE OF BIRTH St. Petersburg
DATE OF DEATH October 11, 1979
Place of death Moscow