Lev Arkad'evich Kaluznin was a Russian mathematician who worked in three countries to get a math degree, but was never able to complete his formal education. Other transliterations of his name used by himself include Kalužnin, Kaluzhnin and, notably, Léo Kaloujnine, predominantly used in publications pertaining to his time spent in France.
Biography and education
Kaluznin was raised by his mother as his parents divorced after his birth. His father, Arkadii Rubin, moved to England and was not a part of his life. His mother, Maria Pavlovna Kaluznina, came from nobility and Russian culture, especially for music and literature would become a big part of her influence. She would remain an important part of his life. They lived in St. Petersburg until they moved to Germany in 1923. The mother worked as a governess, while Kaluznin joined a secondary school in 1925, then to be graduated in 1933. He was fortunate that the high school had a very high academic basis. Kaluznin caught his love for mathematics in the school. In 1933, he entered the Humboldt University of Berlin, then left the university in 1936. The university had an important lecturer named Issai Schur who influenced Kaluznin's future interest in algebra. After this, he moved to study at the University of Hamburg, where famous mathematicians such as Emil Artin, Erich Hecke and Hans Zassenhaus lectured. Kaluznin was able to do some research and then was able to complete a theorem of Kurosh on the classification of abelian groups. Moving around again in 1938, Kaluznin and his mother moved to Paris, where Kaluznin started to study at the Sorbonne.World war II made it difficult for him to complete his studies. So he went to a vocational school to try to become an electrician. On June 22, 1941, Soviet citizens living in France were interned at a camp near Paris. This started out pretty easy and Kaluznin could still listen to lectures from other mathematicians in this camp. He even researched Galois theory, which is used to determine if certain equation solutions can be written with rational functions. Unfortunately, in March 1942, Kaluznin was moved to a concentration camp in Wahlsburg. The concentration camp was much more difficult than the internment camp back in France. Somehow his mother was able to send him food while he was at the concentration camp, otherwise he might not have survived. After the war, Kaluznin returned to Paris. He got some work translating for the Soviet Embassy in Paris but was finally able to return yet again to his mathematical studies. In 1948, he completed his thesis on Sylowp-subgroups of symmetric groups. This was probably one of his most productive period in life. He finished many papers collaborating with him, Krasner, and for even presenting at seminars. Around 1951, Kaluznin and his mother wanted to go back to USSR. The Soviet bureaucracy instead insisted that he go work inEast Germany due to the shortage of technical specialist. So Kaluznin went back to Humboldt University in Berlin and did yet another thesis on Stable automorphism groups to become a full professor.
Return to USSR
Finally, in 1955, Kaluznin was able to return to the USSR. Various mathematicians worked on his behalf to get them a professorship at Kiev State University which he would continue until 1985. In 1957 he had to defend a third thesis related to ‘Sylow p-subgroups of symmetric groups. Complete products of groups. Generalizations of Galois theory'. He created a department of mathematical linguistics at the state university maybe due to his marriage in 1962 to linguist, Zoya Mikhailovna Volotskaya. They lived separate most of their life but did have two children. Due to his time abroad in Germany and in France, he was seen as a foreigner. In the 1970s, he had to leave a couple of the positions he had. This prevented him from going conferences abroad and had to try to do his work by mail. He focused on his students, various research projects and the new area of computer algebra. His students very much enjoyed his lectures. His son Mikhail came under government scrutiny due to Mikhail's interest in religion. This did not make things easier for his father. Kaluznin's health deteriorated and he died as a result of burns from an accident. Outside of mathematics, Kaluznin had many interests. He loved classical music, philosophy and western literature. Until 1970, he was a very heavy smoker, sometimes smoking as many as 60 cigarettes a day. Finally, on January 1, 1970, he stopped and never smoked again. He was a good dresser and enjoyed red wine and beer.
Works
Kaluznin's research spread wide most notably in group theory and abstract groups. He worked on the Sylow p-subgroups of symmetric groups and even mathematical linguistics. Despite not being able to go to many conferences he contributed to the application of computers in algebra. The universal embedding theorem is sometimes called the "Krasner-Kaloujnine universal embedding theorem" due to his joint proof of the theorem with Marc Krasner.
