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Lev Semyonovich Pontryagin (, also written Pontriagin or Pontrjagin, first name sometimes anglicized as Leon) (3 September 1908 – 3 May 1988) was a Soviet Union mathematician. Completely blind from the age of 14, he made major discoveries in a number of fields of mathematics, including algebraic topology, differential topology and optimal control.
In 1925 he entered Moscow State University, where he was strongly influenced by the lectures of Pavel Alexandrov who would become his doctoral thesis advisor. After graduating in 1929, he obtained a position at Moscow State University. In 1934 he joined the Steklov Institute in Moscow. In 1970 he became vice president of the International Mathematical Union.
In 1935, he was able to compute the homology groups of the classical compact Lie group, which he would later call his greatest achievement.
With René Thom, he is regarded as one of the co-founders of Cobordism, and co-discoverers of the central idea of this theory, that framed cobordism and stable homotopy are equivalent.. This led to the introduction around 1940 of a theory of certain characteristic classes, now called , 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.
Starting in 1952, he worked in optimal control theory. His maximum principle is fundamental to the modern theory of optimization. He also introduced the idea of a bang–bang principle, to describe situations where the applied control at each moment is either the maximum positive 'steer', or the maximum negative 'steer'.
Pontryagin authored several influential monographs as well as popular textbooks in mathematics.
Pontryagin's students include Dmitri Anosov, Vladimir Boltyansky, Revaz Gamkrelidze, Yevgeny Mishchenko, Mikhail Postnikov, Vladimir Rokhlin, and Mikhail Zelikin.
Pontryagin was accused of anti-Semitism on several occasions. For example, he attacked Nathan Jacobson for being a "mediocre scientist" representing the "Zionism", while both men were vice-presidents of the International Mathematical Union.O'Connor, John J; Edmund F. Robertson " Nathan Jacobson". MacTutor History of Mathematics archive. Memoirs, by Lev Pontryagin, Narod Publications, Moscow, 1998 (in Russian language). 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.Olli Lehto. Mathematics without borders: a history of the International Mathematical Union. Springer-Verlag, 1998. ; pp. 205-206 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.
Pontryagin rejected charges of antisemitism in an article published in Science in 1979. In his memoirs Pontryagin claims that he struggled with Zionism, which he considered a form of racism.
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