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 more geometric parts of topology.

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.

Later in his career he worked in optimal control theory. His minimum principle is fundamental to modern theory on the subject. 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.

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