Wednesday, September 03, 2008

Lev Pontryagin: 100th anniversary

Lev Semenovich Pontryagin was born in Moscow exactly 100 years ago, on September 3rd, 1908.

If you think that something is wrong about his eyes, you're right. He became blind at the age of 14, when a primus stove exploded. That didn't prevent him from becoming a famous mathematician.

His mother, Tat'yana Andreevna Pontryagina, was a remarkable woman who should be partially credited for this miracle. (Her sewing skills were important for the family finances, too.)

Now, imagine that you are blind since your childhood and you attend schools that suck, as Pontryagin's schools. How the hell can you invent the Andronov-Pontryagin criterion, Pontryagin classes (related to Chern classes), Pontryagin spaces, Pontryagin duality, and study cobordism theory?

Well, it can be done. Your mother must be creative during reading. Of course, she has no idea about the mathematical symbols but that can't stop the two of you. For example, the intersection sign are "tails down" while the union sign are "tails up". You should now be able to guess that "A tails right B" means "A is a subset of B".

In 1925, when he entered the college, it was clear to everyone that he was an exceptional student. He could remember very complicated manipulations with symbols and "see" their meaning far more clearly than his classmates. Pavel Aleksandrov influenced Pontryagin with his charm and other things.




When Pontryagin was 19, his dad died while he began to produce results on the Alexander duality theorem. He could even become the chairman of a department (of topology and functional analysis). He always worked on the problems where algebra and topology come together, using his words. For example, he proved Hilbert's Fifth Problem for Abelian groups (after von Neumann did it for compact groups). He also co-authored books on topology.

In order to show you that what kind of obstacles could have been overcome, let me tell you another story. In 1934, Élie Joseph Cartan gave a talk in Moscow. Now, Pontryagin was not only blind but he also spoke no French. That was not a problem. Nina Karlovna Bari was sitting behind Pontryagin and she was whispering the translation to him. Cartan was making some first steps to calculate the homology groups of the classical compact Lie groups. Needless to say, Pontryagin solved the problem completely in the following year, using tools rooted in Morse theory.

In cobordism theory, he gave his name to the Pontryagin-Thom construction. But he also founded optimal control theory.

Pontryagin had also some provocative political opinions. Even though many of his friends were Jews, he was accused of anti-Semitism. He rejected those accusations in 1978 (in Science) and I have no reason not to believe him. On the other hand, he was almost certainly an active commie. In 1936, he participated in the Luzin affair - a witch hunt directed against "counter-revolutionaries" among the Russian mathematicians. Nikolai Luzin was the main person who was attacked - both by the Stalinist attack dogs as well as by some of his students (including Pavel Aleksandrov who could have convinced Pontryagin to join them) - but fortunately almost nothing happened to him.

These are bizarre things. However, what Pontryagin achieved given his initial conditions is nothing short of impressive.

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