Jacques Tits

Armand Borel As I Knew Him. I do not remember exactly when I first met Armand Borel. It may have been in Paris in 1949 or in Zürich in 1950. After that we often met, and we soon became good friends. He liked to recall jokingly that he was the one from whom I learned that there existed five exceptional simple Lie groups, the study of which became for a while, shortly afterward, my special trade. According to accepted French usage between students and young scholars at the time, we always called each other by our family names, and I shall continue doing so here. A few years later, our friendship was extended to our wives, Gaby Borel and Marie–Jeanne Tits. Almost immediately, the four of us used the second person (“tu”) to address each other, a quite unusual familiarity at the time between two French people of opposite sexes; there is no mystery, however: the Borels were Swiss and the Titses were still Belgian. In the course of years, I came to know Borel very well and to appreciate his great qualities even more. All who have been in contact with him will agree, I believe, that among these qualities the dominant one was his exceptional earnestness, or maybe I should rather say conscientiousness. In German I would perhaps use the word “Gründlichkeit“. This trait was always prominent when one worked with him; I shall give examples shortly when going over our joint work, but I had many other occasions to observe it: here are a few instances of diverse nature: • when opinions were solicited for an appointment or an award, his reports were always highly appreciated for being the most informative and reliable, while being at the same time clear and concise; • participants to meetings that were organized by him knew how seriously they were meant to work, but also how great was the reward; and, by the way, I suppose they had the same experience that I did, namely, that the proceedings were always published rapidly; • in a completely different register (not totally disconnected from the previous one though), hiking was a serious matter for Borel; at the Oberwolfach meetings, he always belonged, of course, to the group of those who made the long walk (at high speed); I believe he felt that strong physical exertion was necessary to his intellectual activity; • I believe that his knowledge of jazz and of a certain variety of Indian music happened at a professional level; I was unable to follow him there, but concerning classical music, my wife and I had with him very enriching discussions about the quality of performances we had heard together; he also introduced us to the art of his friend, the pianist Friedrich Gulda. The term “professional” used here could certainly be applied to most activities of Borel in any domain. The tension that normally goes together with the extreme seriousness I have been talking about was probably responsible for a certain gruffness that some people