**Lev Semenovich Pontryagin** was a blind Russian mathematician who produced important work in algebra and topology.

- At the age of 14 years Pontryagin suffered an accident and an explosion left him blind.
- For many years she worked, in effect, as Pontryagin's secretary, reading scientific works aloud to him, writing in the formulas in his manuscripts, correcting his work and so on.
- Tat'yana Andreevna helped Pontryagin in all other respects, seeing to his needs and taking very great care of him.
- It is not unreasonable to pause for a moment and think about how Tat'yana Andreevna, with no mathematical training or knowledge, made by her determination and extreme efforts a major contribution to mathematics by allowing Pontryagin to become a mathematician against all the odds.
- Even more remarkable was the fact that Pontryagin could 'see' (if you will excuse the bad pun) far more clearly than any of his fellow students the depth of meaning in the topics presented to him.
- Of the advanced courses he took, Pontryagin felt less happy with Khinchin's analysis course but he took a special liking to Aleksandrov's courses.
- Pontryagin was strongly influenced by Aleksandrov and the direction of Aleksandrov's research was to determine the area of Pontryagin's work for many years.
- By 1927, although he was still only 19 years old, Pontryagin had begun to produce important results on the Alexander duality theorem.
- Pontryagin graduated from the University of Moscow in 1929 and was appointed to the Mechanics and Mathematics Faculty.
- Pontryagin worked on problems in topology and algebra.
- In 1934 Pontryagin was able to prove Hilbert's Fifth Problem for abelian groups using the theory of characters on locally compact abelian groups which he had introduced.
- Among Pontryagin's most important books on the above topics is topological groups (1938).
- Pontryagin attended Cartan's lecture which was in French but Pontryagin did not understand French so he listened to a whispered translation by Nina Bari who sat beside him.
- Cartan had some ideas how this might be achieved and he explained these in the lecture but, the following year, Pontryagin was able to solve the problem completely using a totally different approach to the one suggested by Cartan.
- Pontryagin used ideas introduced by Morse on equipotential surfaces.
- Pontryagin's name is attached to many mathematical concepts.
- The essential tool of cobordism theory is the Pontryagin-Thom construction.
- A fundamental theorem concerning characteristic classes of a manifold deals with special classes called the Pontryagin characteristic class of the manifold.
- In 1952 Pontryagin changed the direction of his research completely.
- From the 1930s Pontryagin had been friendly with the physicist A A Andronov and had regularly discussed with him problems in the theory of oscillations and the theory of automatic control on which Andronov was working.
- He published a paper with Andronov on dynamical systems in 1932 but the big shift in Pontryagin's work in 1952 occurred around the time of Andronov's death.
- The following year an English translation appeared and, also in 1962, Pontryagin received the Lenin prize for his book.
- Another book by Pontryagin Ordinary differential equations appeared in English translation, also in 1962.
- Pontryagin received many honours for his work.

Born 3 September 1908, Moscow, Russia. Died 3 May 1988, Moscow, Russia.

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Origin Russia, Topology

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive