Lev Pontryagin

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Lev Semenovich Pontryagin.

Lev Semenovich Pontryagin (Russian: Лев Семёнович Понтрягин) (3 September 1908 – 3 May 1988) was a Soviet Russian mathematician. He was born in Moscow and lost his eyesight in a primus stove explosion when he was 14. Despite his blindness he was able to become a mathematician due to the help of his mother Tatyana Andreevna who read mathematical books to him. He made major discoveries in a number of fields of mathematics, including the geometric parts of topology.

[edit] Work

He 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. In topology he posed the basic problem of cobordism theory. This led to the introduction around 1940 of a theory of characteristic classes, now called Pontryagin classes, designed to vanish on a manifold that is a boundary. 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 bang-bang principle, to describe situations where either the maximum 'steer' should be applied to a system, or none.

Pontryagin was a controversial personality. Although he had many Jews among his friends and supported them in his green years, he was accused of anti-Semitism in his mature years. For example he attacked Nathan Jacobson while both men were vice-presidents of the International Mathematical Union^[1]. He rejected those charges in an article published in Science in 1979. He also participated in a few notorious political campaigns in the Soviet Union, in particular, in the so-called Luzin affair.