To the Memory of R. Freivalds

The paper contains author’s memories of his mentor and teacher R. M. Freivalds. I met Rūsiņš Freivalds for the first time in September of 1970, and this meeting defined my life in many different ways. At that time I was a fifth year student in the mathematics division of the University of Latvia and was looking for a topic and an advisor for my diploma thesis. My original idea was to write a thesis in the field of Lie Algebras, where I had been doing some research under the guidance of one of the faculty. However, algebraists, led by an outstanding mathematician B. I. Plotkin, were gradually forced out of the University, after one of the star students in his group, I. Rips, attempted a public self-immolation, protesting Soviet invasion to Czechoslovakia in 1968, and, thus, I had to change direction, and did not know what I would do. However, in the first days of September, I was summoned to a meeting by the Dean of the Faculty of Physics and Mathematics A. Liepa. This meeting decided my fate. Prof. Liepa told me that Jānis Bārzdiņš, his former classmate, returned from Moscow (where he was working on his doctoral dissertation under the guidance of A. N. Kolmogorov) and would be forming a new division in the University Computing Center. Prof. Liepa suggested that he could recommend me to J. Bārzdiņš to join his group. Frankly, I was scared – I knew nothing about computer science at the time, except for having taken a couple of courses in programming. But Prof. Liepa told me: “Trust me: computer science is the future, and J. Bārzdiņš is one of not so many people in this whole country (he meant the Soviet Union) who can guide you into this new exciting field”, and that was it. He arranged my meeting with J. Bārzdiņš, but there was another man present at the meeting, Rūsiņš Freivalds. J. Bārzdiņš told me that he himself was too busy at the moment to guide my diploma thesis, and suggested working with Rūsiņš, who just returned from Novosibirsk, where he was completing his Candidate of Science dissertation (Ph.D.) under the guidance of B. A. Trakhtenbrot. Then J. Bārzdiņš left, and we started our very first long conversation with Rūsiņš. In about three hours, he taught me the basics of Turing machines, computability, Church-Turing thesis, introduced me to the concept of so-called (m,n)-computation, and explained to me the results recently