Memories of Vladimir Arnold

1. Dima Arnold in my life, by Dmitry Fuchs 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 19 years old student Dima Arnold had completed the solution of Hilbert’s 13-th problem: every continuous function of three or more variables is a superposition of continuous functions of two variables. Dima presented a two-hour talk at a weekly meeting of the Moscow Mathematical Society; it was very uncommon for the Society to have such a young speaker. Everybody admired him, and he certainly deserved that. Still there was something that kept me at a distance from him. I belonged to a tiny group of students, led by Sergei Novikov, which studied algebraic topology. Just a decade before, Pontryagin’s seminar in Moscow V. Arnold, drawing, 1968