Memories of Vladimir

Dima Arnold in My Life Unfortunately, I have never been Arnold’s student, although as a mathematician, I owe him a lot. He was just two years older than I, and according to the University records, the time distance between us was still less: when I was admitted to the Moscow State university as a freshman, he was a sophomore. We knew each other but did not communicate much. Once, I invited him to participate in a ski hiking trip (we used to travel during the winter breaks in the almost unpopulated northern Russia), but he said that Kolmogorov wanted him to stay in Moscow during the break: they were going to work together. I decided that he was arrogant and never repeated the invitation. Then he became very famous. Kolmogorov announced that his nineteen year-old student Dima Arnold had completed the solution of Hilbert’s 13th problem: every continuous function of three or more variables is a superposition of continuous