My first published result was completeness and some other properties of Medvedev Intuitionistic Logic. I was 16 and learned this logic at Kolmogorov's lectures as a student of Physics/Math Boarding High School at Moscow University. I stopped working on logic after one more paper in this area. However, foundations of Computer Science, Mathematics, Probability and Information theories remained my main interest. Then I started working in a new area of Kolmogorov (or Kolmogorov-Solomonoff) Complexity and obtained its first technically involved results. After that Kolmogorov agreed to supervise my work. I was under great influence of his courses even earlier, but getting his personal supervision at the age of 18 had an overwhelming effect on my mathematical development. Click the links below for a brief descriptions of some areas of my research.