This page is a sub-page of our page on What is Mathematics?
/////// Related KMR-pages:
• Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity, by Loren Graham and Jean-Michel Kantor, The Belknap Press of Harvard University Press, 2009, ISBN 976-0-674-03293-4.
/////// Quoting “Naming Infinity” (page 101)
The Legendary Lusitania
Shortly before World War I, Nikolai Luzin and Dmitri Egorov began to offer together an undergraduate mathematics seminar at Moscow University that was the embryo of what became known as the Moscow School of Mathematics
The origin of this term is not clear, despite much discussion on the topic. Among later Moscow mathematicians, the most common explanation was that the student circle took its name from the British ocean liner Lusitania that was torpedoed by the German submarine U-20 on May 7, 1915. This event caused a great international outcry and was one factor influencing the entry, almost two years later, of the United States into World War I. The problem with this explanation is that, according to several participants in the seminar, the term “Lusitania” was used in the mathematics seminar /before/ the sinking of the ocean liner. Perhaps that event gave the name extra meaning.
Another explanation for the name, perhaps the most logical one, is that it involved a play on the word “Luzin,” and was actually, in its first form, “Luzitania.” However, this idea is also disputed, especially by those who note that Egorov was, at least in the early years, the senior professor of the seminar. Luzin was quoted by the students as saying that “Egorov is the chief of our society” and “our discoveries belong to Egorov.” It seems unlikely that Luzin would have agreed to the naming of the seminar after himself as long as Egorov was present, as he was throughout its history. Here again, though, the name gained extra strength through the resemblance of “Luzin” and “Lusitania,” especially after Luzin emerged as the intellectual leader of the group.
A sense of the place of religion in the concerns of the Lusitanians (before the impositions on religion that followed from the Soviet takeover) can be seen in early descriptions of the group. According to one of them, the early Lusitanians acknowledged two leaders: “God-the-father” Egorov and “God-the-son” Luzin. Students in the society were given the monstic titles of “novices.”
The intense camaraderie among the Lusitanians was facilitated by Luzin, who was described as extroverted and theatrical, and who inspired real devotion among students and colleagues. Egorov, the senior member, on the other hand, was more reticent and formal.
Lusitania put Moscow on the mathematical map of the world. Before World War I there was only one mathematician at Moscow University whose name was well known to mathematicians in western Europe: Dmitri Egorov. By the end of the 1920s, there was a constellation of such mathematicians. And by 1930 Moscow had become one of the two or three most concentrated focal points of mathematical talent anywhere on the globe.
A remarkable characteristic of Lusitania was the youth of the students who belonged to the group. When Lev Shnirelman, who eventually made significant contributions to number theory and the calculus of variations, joined Lusitania he was just 15 years old. Andrey Kolmogorov, one of the great mathematicians of the twentieth century, was 17 or 18 when he first came to the attention of Egorov and Luzin. Other youths who joined Lusitania when they were 18 or younger and who later became notable mathematicians included Lazar Lyusternik, Pavel Uryson, and Pavel Alexandrov.
In the seminar, Luzin was a showman who knew how to enthrall his class members. He would enter the room of expectant students, take off his coat, and speak to them in his academic gown. People often remarked that he had a “mysterious view of the universe,” He would make statements like “before our intellectual gaze there opens a vision of extraordinary beauty.” And then he would speak of transfinite numbers and of sets possessing subsets each of which was somehow equal to the whole. (For example, there are as many points in a segment of a line as there are in the larger line of which it is a segment.) One of his students observed, “Other professors show mathematics as a beautiful completed structure, and we can only admire it. Luzin shows it in its incomplete form, he awakens a desire to take part in its development.”
Luzin’s approach to lectures was radically different from that of other Moscow University professors. Many f his colleagues simply read to the students, staring down at pages often yellowed with age, and hardly acknowledge the presence of an audience. (In the Russian language one does not usually speak of”giving a lecture”, but rather of “reading” it, chitaet lektsiiu.) The boring character of most university lectures was so well known that some students never attended class, appointing a fellow student to take notes to be shared or obtaining written copies of the lectures from the university porter.
However, if we are to believe the accounts left us by Luzin’s former students, they were eager to attend his classes. And Luzin made sure that they felt involved. He would begin a proof at the blackboard, pause, and then say, “I cannot recall the proof; perhaps one of my colleagues could remind me.” This was a challenge that the class felt obligated to meet: One student would jump up, go to the blackboard, attempt the proof, fail, and then sit down with a red face. Another would get up, perhaps a 17-year-old, successfully write the proof on the blackboard while the whole class stared enviously, and then sit down. Professor Luzin would turn to that student, bow slightly, and say “Thank you, my colleague.” Luzin treated the students as intellectual equals, and his teaching led them to prepare for and anticipate coming lectures. One of them later asked, “Had Luzin [really] forgotten the proof, or was it a well-constructed game, a method of arousing activity and independence? They never knew.
Luzin overcame the traditional chasm between professors and students at Moscow University. When he finished a lecture, it often did not actually end. The students would surround him, asking questions and making suggestions; follow him down the large entry stairway; and then walk with him down Mokhovaia and Argbat streets to his appartment at the corner of Arbat and Afanas’evsky Bouleard. There Luzin’s wife Nadezhda would be waiting with tea (and pastries, if she could buy the ingredients in those hard times), and the conversations would continue far into the night.
Luzin’s approach was wonderful, and it energized a generation of Russian mathematicians. Lusitania was probably the most creative and fascinating chapter in the entire history of Russian mathematics (and there are other glorious chapters).
/////// End of quote from “Naming Infinity”