Lev Pontryagin | |
|---|---|
 Lev Semyonovich Pontryagin (left) | |
| Born | (1908-09-03)3 September 1908 |
| Died | 3 May 1988(1988-05-03) (aged 79) Moscow,Soviet Union |
| Known for | Pontryagin duality Pontryagin class Pontryagin cohomology operation Pontryagin's maximum principle Andronov–Pontryagin criterion |
| Scientific career | |
| Fields | Mathematics |
| Doctoral advisor | Pavel Alexandrov |
| Doctoral students | Dmitri Anosov Vladimir Boltyansky Revaz Gamkrelidze Mikhail Postnikov Mikhail Zelikin |
Lev Semyonovich Pontryagin (Russian:Лев Семёнович Понтрягин, also writtenPontriagin orPontrjagin, first name sometimes anglicized asLeon) (3 September 1908 – 3 May 1988) was aSovietmathematician. Completely blind from the age of 14, he made major discoveries in a number of fields of mathematics, includingalgebraic topology,differential topology andoptimal control.
Pontryagin was born inMoscow and lost his eyesight completely due to an unsuccessfuleye surgery after aprimus stove explosion when he was 14. His mother Tatyana Andreyevna, who did not know mathematical symbols, read mathematical books and papers (notably those ofHeinz Hopf,J. H. C. Whitehead, andHassler Whitney) to him, and later worked as his secretary. His mother used alternative names for math symbols, such as "tails up" for the set-union symbol.[1]
In 1925 he enteredMoscow State University, where he was strongly influenced by the lectures ofPavel Alexandrov who would become his doctoral thesis advisor. After graduating in 1929, he obtained a position atMoscow State University. In 1934 he joined theSteklov Institute in Moscow. In 1970 he became vice president of theInternational Mathematical Union.
Pontryagin worked onduality theory forhomology while still a student. He went on to lay foundations for the abstract theory of theFourier transform, now calledPontryagin duality. Using these tools, he was able to solve the case ofHilbert's fifth problem for abelian groups in 1934.
In 1935, he was able to compute the homology groups of the classical compactLie groups, which he would later call his greatest achievement.[2]
WithRené Thom, he is regarded as one of the co-founders ofcobordism theory, and co-discoverers of the central idea of this theory, that framed cobordism andstable homotopy are equivalent.[3] This led to the introduction around 1940 of a theory of certaincharacteristic classes, now calledPontryagin classes, designed to vanish on amanifold that is aboundary.
In 1942 he introduced the cohomology operations now calledPontryagin squares. Moreover, inoperator theory there are specific instances ofKrein spaces calledPontryagin spaces.
Starting in 1952, he worked inoptimal control theory. Hismaximum principle is fundamental to the modern theory of optimization. He also introduced the idea of abang–bang principle, to describe situations where the applied control at each moment is either the maximum positive 'steer', or the maximum negative 'steer'.[citation needed]
Pontryagin authored several influential monographs as well as popular textbooks in mathematics.
Pontryagin's students includeDmitri Anosov,Vladimir Boltyansky,Revaz Gamkrelidze, Yevgeny Mishchenko,Mikhail Postnikov,Vladimir Rokhlin, andMikhail Zelikin.
Pontryagin participated in a few notorious political campaigns in the Soviet Union. In 1930, he and several other young members of theMoscow Mathematical Society publicly denounced as counter-revolutionary the Society's headDmitri Egorov, who openly supported the Russian Orthodox Church and had recently been arrested. They then proceeded to follow their plan of reorganizing the Society.[2]
Pontryagin was accused of anti-Semitism on several occasions.[2] For example, he attackedNathan Jacobson for being a "mediocre scientist" representing the "Zionism movement", while both men were vice-presidents of theInternational Mathematical Union.[4][5] When a prominent Soviet Jewish mathematician,Grigory Margulis, was selected by theIMU to receive theFields Medal at the upcoming 1978ICM, Pontryagin, who was a member of the executive committee of the IMU at the time, vigorously objected.[6] 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.[6]
Pontryagin rejected charges of antisemitism in an article published inScience in 1979.[7] In his memoirs Pontryagin claims that he struggled withZionism, which he considered a form ofracism.[5]
