Lev Arkadyevich Kaluzhnin

Lev Arkad'evich Kaluznin (31 January 1914 – 6 December 1990) was a Russian mathematician. Other transliterations of his name used by himself include Kalužnin and Kaluzhnin, while he used the transliteration Léo Kaloujnine in publications while he lived in France.

Biography and education Kaluznin was born in Moscow. His parents divorced not long after his birth, and his father, Arkadii Rubin, moved to England and was not part of Kaluznin's life. His mother, Maria Pavlovna Kaluznina, moved with the young Kaluznin to Petrograd (present-day Saint Petersburg), where she brought him up. She shared her love for Russian culture, including music and literature, with her son, and she would remain an important part of his life. In 1923, Kaluznin and his mother moved to Germany. She worked as a governess, while Kaluznin was enrolled at a Realgymnasium (secondary school), graduating in 1933. His school offered a thorough education in mathematics, and upon graduating, he entered the Humboldt University of Berlin, where he attended lectures taught by the algebraist Issai Schur. He left the university in 1936 and enrolled at the University of Hamburg. Here, he was taught by Emil Artin, Erich Hecke and Hans Zassenhaus. In 1938 he published his first paper, in which he completed a theorem of Kurosh on the classification of abelian groups.

In 1938, Kaluznin and his mother moved to Paris, where Kaluznin became a student at the Sorbonne. World War II and in particular the German occupation of Paris in June 1940 made it necessary for him to halt his studies. To make a living, he trained as an electrician. On 22 June 1941, Soviet citizens living in France were interned at a camp in Compiègne near Paris. Here, Kaluznin was initially able to continue studying mathematics, carrying out research on Galois theory, which determines if certain equation solutions can be written with rational functions. He also attended lectures on a variety of topics given by other prisoners. The universal embedding theorem is sometimes called the "Krasner-Kaloujnine universal embedding theorem" due to his joint proof of the theorem with Marc Krasner.