My encounters with martingales

Abstract

Studying at the University of Berlin right after the war. The University of Berlin had been founded in 1810 during the Napoleonic wars, based on the two ideas of the unity of teaching and research and of classical education for all students. When it reopened in January 1946 after another, and by far more devastating war, most of its buildings lied in ruins but much of the old spirit was alive. In 1949 it was renamed “Humboldt-Universitat”. In late summer of 1946 I applied for admission as a student of physics. I was only 17 years old and my chances were slim because there were many older applicants who had lost years of their life through the war, and they naturally enjoyed priority. Moreover, since the University was situated in East-Berlin and depended on the Soviet and nascent East-German administration, there existed already some kind of an “affirmative action” in favour of descendants of workers and peasants whereas my father was a physician. Nevertheless I was admitted, perhaps because I had obtained my “Abitur” (high-school leaving certificate) in June with the best grade possible. The material conditions were of course difficult, the worst being hunger. In winter, the temperature inside the large physics auditorium descended sometimes to –10° (centigrade). However, there was an enormous enthusiasm for studying as I have seen it later only once more, namely in Hanoi in 1974. As a student of physics I had to follow the normal basic mathematics curriculum. The analysis (calculus) course was taught by Erhard Schmidt (Gram-Schmidt orthogonalization, Hilbert-Schmidt integral equations). He was already over 70 and retired, but had taken up service again because, as a sequel of the Nazi era and the war, there were not enough mathematics professors in Berlin. He was still the dominating figure among the mathematicians at the University. His lectures were marvellous. He used to prepare them on his way from home to the lecture rooms, never used any notes, and often said in the middle of a proof: “Oh, I think I can prove this in a much better way”, and then he started all over again. He also smuggled in little mistakes to test our attention. After the first semester, in spring 1947, I decided that mathematics was really much more fascinating and switched subjects, physics now becoming my minor.