Lev Semyonovich Pontryagin

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Lev Pontryagin (left) 1970

Lev Pontryagin ( Russian Лев Семёнович Понтрягин ; English transcription Lev Pontryagin, born August 21 . Jul / 3. September  1908 greg. In Moscow, † 3. May 1988 ) was a Russian mathematician . Pontryagin was one of the most influential mathematicians in Moscow during the Soviet era and the founder of his own maths school.

Live and act

He lost his eyesight in a gas furnace explosion at the age of 14. Thanks to his mother Tatiana Andreevna, who read mathematical books to him, he was able to become a mathematician despite his blindness . He made important discoveries in numerous areas of mathematics, particularly with regard to geometrical aspects of topology .

Pontryagin finished his studies at Lomonosov University in 1929 and received his doctorate (Russian doctor, equivalent to habilitation ) in 1935 with Pavel Alexandrov . In the same year he became a professor. From 1934 he was at the Mathematical Institute of the Soviet Academy of Sciences ( Steklow Institute ), where from 1935 he headed his own department for topology and functional analysis.

When he was still a student, he obtained important results on the duality of homology groups in algebraic topology: he proved the Alexander duality in its general form. In the 1930s he laid the foundations for an abstract theory of the Fourier transform by developing a theory of characters for commutative topological groups ( Pontryagin duality ). At the same time he solved Hilbert's fifth problem , which investigates the question of whether locally Euclidean groups are manifolds (Lie groups), for the Abelian (commutative) case (1934). In 1938 his classic book on topological groups was published.

In the topology he posed the problem of the cocycle theory. Around 1940, this led to the introduction of characteristic classes in the topology, which are now called Pontryagin classes . The Pontryagin- Thom construction forms one of the foundations of the Kobordism theory. The Pontryagin room was named after him, a special case of the Krein room .

Later he worked on the theory of optimal controls . The Pontryagin maximum principle, sometimes also called the minimum principle, was formulated as a thesis by Pontryagin and is still fundamental to the modern theory of optimal controls. It was proven in the mid-1950s by Pontryagin and his students Vladimir Boltjanski and Rewas Gamqrelidze . Earlier versions come independently from Magnus Hestenes (1950) and Rufus Isaacs as well as from Constantin Caratheodory (1935). In mechanics, he partly worked with Alexander Alexandrovich Andronow .

In the 1970s and 1980s, Pontryagin played an important role in Soviet science policy. He represented his country in the International Mathematical Union, was head of the editorial board that decided on the publication of all specialist books and editor-in-chief of the important journal Matematitscheskii sbornik . At the time, he was accused of anti-Semitic behavior, for example in a heated debate in the 1970s with Nathan Jacobson , who, together with Pontryagin, was Vice-President of the IMU at the time and who advocated improved travel options for Jewish scientists from the Soviet Union. Pontryagin defended himself against this in an article in Science 1979. In 1979, Der Spiegel described him as "the head [of the] small but [...] influential clique of functionaries who brought racism back into Soviet research policy" and reported that Pontryagin had become involved Praised in private circles that Matematitscheski sbornik is now "Jew-free". (“In the past, about a third of the hundred or so articles that the journal publishes annually came from Jewish scholars. In 1975, when Pontrjagin took over the management, their number fell to twelve, in 1976 to eight. In the first volume of 1977 there were four Article by Jewish authors, in the second volume there was only one, in the third volume none. ”) Like many other well-known Russian mathematicians of the next generation at the time, he played a role in the Lusin affair in the 1930s .

In 1970 he gave a plenary lecture at the ICM in Nice (Les Jeux Differentiels Lineaires, The linear differential games) and also in Edinburgh in 1958 (Optimal Regulation Processes ). In 1962 he gave a lecture at the International Congress of Mathematicians in Stockholm ( A statistical problem in the theory of optimal control ). In 1939 he became a corresponding and in 1959 full member of the Russian Academy of Sciences . In 1941 he was one of the first recipients of the Stalin Prize .

The asteroid (4166) Pontryagin is named after him.

literature

  • with Wladimir Boltjanski , RV Gamkrelidze , EF Mishchenko: Mathematical theory of optimal processes. Oldenbourg 1967 (English translation: The Mathematical Theory of Optimal Processes. Wiley / Interscience, 1962).
  • Learning higher mathematics. Springer 1984.
  • Generalizations of the numbers. German, Frankfurt am Main 1995.
  • Basic features of combinatorial topology (= university books for mathematics . Vol. 29). German Science Publishing House, Berlin 1956.
  • Ordinary differential equations. Deutscher Verlag der Wissenschaften, Berlin 1965 (English translation Ordinary Differential Equations , Addison-Wesley 1962).
  • Topological groups. 2 volumes. Teubner, 1957, 1958 (English translation Topological Groups , Princeton University Press 1952).

Web links

Individual evidence

  1. ↑ Maria Georgiadou Constantin Caratheodory , Springer 2004, p. 216, with reference to Pesch, Burlisch The maximum principle, Bellman's equation and Caratheodorys Work , Journal of optimization theory and applications, Volume 80, 1994, p. 199, Online, pdf
  2. ↑ [1] Spiegel 3/1979
  3. ^ Dictionary of Minor Planet Names, Volume 1 in the Google Book Search
personal data
SURNAME Pontryagin, Lev Semjonowitsch
ALTERNATIVE NAMES Понтрягин, Лев Семёнович (Russian); Pontryagin, Lev Semënovič; Pontryagin, Lev
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH September 3, 1908
PLACE OF BIRTH Moscow
DATE OF DEATH May 3, 1988