Lev Pontryagin
Lev Pontryagin  

Lev Semenovich Pontryagin (left)
 
Born 

3 September 1908
Died  3 May 1988 
(aged 79)
Nationality  Soviet Union 
Known for 
Pontryagin duality Pontryagin class Pontryagin cohomology operation Pontryagin's minimum principle Andronov–Pontryagin criterion 
Scientific career  
Fields  Mathematics 
Doctoral advisor  Pavel Alexandrov 
Doctoral students 
Dmitri Anosov Vladimir Boltyansky Revaz Gamkrelidze Evgenii Mishchenko Mikhail Postnikov Mikhail Zelikin 
Lev Semyonovich Pontryagin (Russian: Лев Семёнович Понтрягин, also written Pontriagin or Pontrjagin) (3 September 1908 – 3 May 1988) was a Soviet mathematician. He was born in Moscow and lost his eyesight due to a primus stove explosion when he was 14. Despite his blindness he was able to become one of the greatest mathematicians of the 20th century, partially with the help of his mother Tatyana Andreevna who read mathematical books and papers (notably those of Heinz Hopf, J. H. C. Whitehead, and Hassler Whitney) to him. He made major discoveries in a number of fields of mathematics, including algebraic topology and differential topology.
Contents
Work
Pontryagin worked on duality theory for homology while still a student. He went on to lay foundations for the abstract theory of the Fourier transform, now called Pontryagin duality. With René Thom, he is regarded as one of the cofounders of cobordism theory, and codiscoverers of the central idea of this theory, that framed cobordism and stable homotopy are equivalent.^{[1]} This led to the introduction around 1940 of a theory of certain characteristic classes, now called Pontryagin classes, designed to vanish on a manifold that is a boundary. In 1942 he introduced the cohomology operations now called Pontryagin squares. Moreover, in operator theory there are specific instances of Krein spaces called Pontryagin spaces.
Later in his career he worked in optimal control theory. His maximum principle is fundamental to the modern theory of optimization. He also introduced there the idea of a bangbang principle, to describe situations where either the maximum 'steer' should be applied to a system, or none.^{[citation needed]}
Pontryagin authored several influential monographs as well as popular textbooks in mathematics.
Pontryagin's students include Dmitri Anosov, Vladimir Boltyansky, Revaz Gamkrelidze, Evgeni Mishchenko, Mikhail Postnikov, Vladimir Rokhlin, and Mikhail Zelikin.
Controversy and antisemitism allegations
Pontryagin was accused of antiSemitism on several occasions. For example, he attacked Nathan Jacobson for being a "mediocre scientist" representing the "Zionism movement", while both men were vicepresidents of the International Mathematical Union.^{[2]}^{[3]} He rejected charges of antiSemitism in an article published in Science in 1979,^{[4]} claiming that he struggled with Zionism, which he considered a form of racism.^{[3]} When a prominent Soviet Jewish mathematician, Grigory Margulis, was selected by the IMU to receive the Fields Medal at the upcoming 1978 ICM, Pontryagin, who was a member of the Executive Committee of the IMU at the time, vigorously objected.^{[5]} Although the IMU stood by its decision to award Margulis the Fields Medal, Margulis was denied a Soviet exit visa by the Soviet authorities and was unable to attend the 1978 ICM in person.^{[5]} Pontryagin also participated in a few notorious political campaigns in the Soviet Union, most notably, in the Luzin affair.
Publications
 Pontrjagin, L. (1939), Topological Groups, Princeton Mathematical Series, 2, Princeton: Princeton University Press, MR 0000265
 1962  Ordinary Differential Equations
 1962  The Mathematical Theory of Optimal Processes
 1963  Foundations of Combinatorial Topology
See also
 Andronov–Pontryagin criterion
 Kuratowski's theorem, also called the Pontryagin–Kuratowski theorem
 Pontryagin class
 Pontryagin duality
 Pontryagin's minimum principle
Notes
 ^ Mackenzie, Dana (2010), What's Happening in the Mathematical Sciences, Volume 8, American Mathematical Society, p. 126, ISBN 9780821849996.
 ^ O'Connor, John J; Edmund F. Robertson "Nathan Jacobson". MacTutor History of Mathematics archive.
 ^ ^{a} ^{b} Memoirs, by Lev Pontryagin, Narod Publications, Moscow, 1998 (in Russian).
 ^ Pontryagin, LS (September 14, 1979). "Soviet AntiSemitism: Reply by Pontryagin". Science. 205 (4411): 1083–1084. doi:10.1126/science.205.4411.1083. PMID 17735029.
 ^ ^{a} ^{b} Olli Lehto. Mathematics without borders: a history of the International Mathematical Union. SpringerVerlag, 1998. ISBN 0387983589; pp. 205206
External links
 Lev Pontryagin at the Mathematics Genealogy Project
 O'Connor, John J.; Robertson, Edmund F., "Lev Pontryagin", MacTutor History of Mathematics archive, University of St Andrews.
 Autobiography of Pontryagin (in Russian)