CTK Insights

05 Jun

Naming Infinity - the book

My father was used to tell me a story of how in the late 1940s the famous Russian mathematician A. N. Kolmogorov slapped in the face another famous Russian mathematician N. N. Luzin. The occasion was a balloting at the Russian Academy of Sciences where Luzin blocked the candidacy of the third Russian mathematical luminary P. S. Alexandrov. The reason he explained was that Luzin had presented Alexandrov's long stays in Western Europe as an anti-Soviet activity. According to the book Naming Infinity by Loren Graham and Jean-Michel Kantor my father was wrong, and that on several accounts. In all likelihood, Graham and Kantor's version of the events is more trustworthy; I am satisfied to have learned at least a part of it, I am not sure I wanted to know all the details. Graham and Kantor write

Readers may wonder why we include such personal details in this discussion of an important chapter in the history of mathematics.

And subsequently the authors respond

We are not eager to denigrate anyone's accomplishments, and we have an immense respect for science, the most powerful means of knowing developed by human beings. But we think that our understanding of these episodes and, ultimately, our respect for the actors in them will be all the greater if we include the entire story and not just parts of it.

So, according to Graham and Kantor, Luzin - on being approached by Kolmogorov after the vote had been taken - rudely hinted at the alleged homosexual relationship between Kolmogorov and Alexandrov. I would not miss knowing the truth in that matter, but the other part of the story - not mentioned by my father, and which is probably neither gossip nor outright slander - presented the whole episode in entirely different light. In 1936, at the time of great purges, Kolmogorov and Alexandrov both denounced Luzin, their former teacher, to the Soviet authorities, which, if it were not for an intervention by Leonid Kapitsa, would have led to Luzin's imprisonment and likely execution. Understandably, Luzin carried a grudge against both Kolmogorov and Alexandrov.

Luzin was a religious person and vulnerable just for that reason. So were his teacher Dimitri Egorov and friend Pavel Florensky both of whom perished in the 1930s. It was a ghastly period in the Russian history, and, if nothing else, the book gives a broad picture of that time, with many terrible and beautiful details, lifting the curtain on human misery, ugliness, and bravery. Nikolai Chebotaryov resigned his professorship after learning that it was previously occupied by the fired Egorov; for this he was exiled to Kazan, where his doctor wife clandestinely cared for the dying Egorov who arrived there a few years later. Lev Shnirelman, who made a signficant contribution to solving the Goldbach conjecture, committed suicide at the age of 32, after an interrogation by the secret police, where he was apparently made to sign a fabricated confession that incriminated several of his friends.

It was a horrible time especially compared to the atmosphere of camaraderie that existed in the Moscow Mathematical School set up by Egorov and Luzin yet before the WWI. During the wartime and after the revolution, at the time of incredible deprivation, the school met on a regular basis at the Moscow University. The book tells us that at winter times students poured water in the corridors and, when it freezed, skated there.

The full title of the book is Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity; the above may give you an idea of why it really reads like a true story. This is a story in which mathematicians - mostly French and Russian - and not mathematics who play a central role. The (mathematical thread of the) story begins at the end of the nineteenth century with the turmoil that followed Cantor's introduction of hierarchy of infinities. The book describes what Hermann Weyl later called the foundational crisis in mathematics and its effects on the rational French school (Émile Borel, René Baire, and Henri Lebesgue) and ony the nascent Russian school (Dmitri Egorov, Nikolai Luzin and their associate Pavel Florensky - a student of mathematics and an ordained Russian Orthodox priest) with the characteristic tendency to interwine their work with societal, philosophical and ideological trends. The authors bring up many more names and illuminate many more lives, but these six are their main protagonists.

The Russian trio have been greatly influenced by the Name Worshiping sect in the Russian orthodoxy that evolved at about the same time. The adherents of the sect perceived the beginning of Genesis "And God said, Let there be light; and there was light" as affirming the existence of the word ("light" in this case) prior to the existence of the object or phenomenon that the word named. And so they worshiped the name of God as if it were God itself. Since God name is a linguistic idiosyncrasy, the sect's practice appeared to conflict with the established beliefs in the unity of orthodox God. The history of the sect, including the 1913 assault by tsarist marines on a Russian monastery on a Greek peninsula, was not a part of school curriculum, even in Russia. I was fascinated with the account.

This is an unusual book that eludes categorization. It's an outline of fundamental mathematical ideas cultivated by human beings, of mathematics as a human endeavor in the most candid sense of the word. It's a collection of biographical sketches - and not only of mathematicians - on a historic background, spread from the Dreyfus affair in France, and over the failed Russian revolution of 1905, the WWI, the October revolution, the Stalinists purges, the WWII, and post-Stalinist experimentations.

The book is a tangle of documented evidence and, likely, anecdotal testimony. It's warm, humane and makes an absorbing reading.

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