大卫 • 卡兹丹自传 (只提供英文版)
I was born in Moscow immediately after World War II, the only son of young academic parents. During the fifth grade of my local elementary school, I became interested in mathematics, and together with my grandfather, who had no high school education, I spent that year making my way quickly through algebra, geometry and trigonometry. I do not recall how much time, if any, was spent in regular classes that year, but that first experience showed me, and I still believe, that many mathematical subjects relegated to high school can be learned much earlier. The young mind can absorb mathematical concepts, like chess skills, at an early age.
By the beginning of the following year, I joined a math club organized by two students from Moscow University. This was a great experience. It opened my eyes ― and my heart ― to the beauty of mathematics, the field that ties together ostensibly unrelated concepts.
At that time, I often shopped for mathematical texts in used bookstores and frequently met Naum Vilenkin on my wanderings. He was an excellent mathematician who attended the seminar led by Israel Gelfand. Gelfand, by then a 45-year-old outstanding scientist in many areas of mathematics (and later of biology), had begun instructing his son, Sergei, who hoped to follow in his father’s mathematical footsteps. They were looking for a partner and I surmise that Vilenkin told Gelfand about meeting me on those shopping expeditions. In any case, Vilenkin gave me Gelfand’s phone number and I eagerly called my future mentor. After a cursory interview, Gelfand invited me to his home and for many years thereafter I would go to his house on a weekly basis. Those meetings opened the world of mathematics to me. The fundamental lesson Gelfand imparted was the feeling that mathematics constitutes a unity, that even if in the apparent diversity of subjects falling within the discipline, such divisions should not be taken too seriously.
I enjoyed participating in various math circles throughout my school years, and later at Moscow University I met a number of excellent mathematicians ― young, committed, and focused partners. We often became friends and shared mutual feelings about the beauty of mathematics. We went together to numerous seminars, living and breathing mathematics, and constantly discussing our ideas and sharing our findings and quandaries. For our group, the Moscow International Congress of 1966 provided the unique opportunity of meeting world-famous mathematicians: Michael Atiyah, a British-Lebanese mathematician specializing in geometry; Harish-Chandra, an Indian mathematician and physicist who did fundamental work in representation theory; and a little later, Pierre Deligne, a Belgian colleague of similar age who began to visit Moscow frequently. Despite the hermetically closed borders of the communist state, for young Soviet students such interactions offered access to cutting edge developments in the various realms of mathematics on an international scale.
In 1968, I married Helena Slobodkin, a fellow mathematics student ― and later computer programmer. Our first three children ― Eli, Dina and Misha ― were born over the next five years in Moscow. Daniel, the youngest, was born in Boston in the early 1980s after our immigration in 1975. Helena and I took advantage of the brief détente in the mid-1970s between Moscow and Washington. As a young, religious Jewish family, the rigidity of the Soviet Union, and specifically the restrictions against any forms of organized religion, did not offer much hope of raising our family as we wished.
Upon arrival in the United States, I was offered a position in the Harvard Mathematics Department where I had the privilege of spending the next 27 years. Harvard was a remarkably friendly and stimulating place. The Department integrated many different mathematical minds and offered a unique platform for interactions and collaborations between the faculty and the graduate student community. And more broadly, the world of Boston academia provided an auspicious environment for my work. I collaborated with various colleagues at Harvard and was exceptionally lucky to become a friend and collaborator of Romanian-born George Lusztig. And beyond the academic satisfactions of my tenure at Harvard, my family quickly made Boston our “home”. Relationships were built and long-lasting friendships forged.
In 2002, Helena and I moved to Jerusalem where I joined the Department of Mathematics at The Hebrew University and where I found a number of excellent mathematicians with whom I worked. Two of our four children were already living in Israel and our first grandchild had recently been born there. Although our family had previously spent two sabbaticals in Jerusalem, moving, yet again, to a new country and burdened with a new language (this time at the age of 55) was not trivial. And yet, I found the environment, the city, and especially my colleagues to be most welcoming. The Department allowed me to structure my teaching with allowances for my less than fluent Hebrew language skills and recognizing my strengths and weaknesses. They created the atmosphere that ensured my productivity by supporting me each step of the way and facilitating interactions with people in a variety of unfamiliar areas. Even now, after my retirement, I enjoy leading three to four seminars each semester.
Throughout my career, in all three countries where I have lived, I have been extremely fortunate ― and continue to be fortunate ― to have worked with many highly talented people. The inherently pure beauty that we see in mathematics is the glue that continues to bring us together. Even if it is via ZOOM conferences in the time of COVID, the world of mathematics, perhaps even more than in other domains of science, allows for professional relationships and cooperation between people in different parts of the globe, who have no shared language, come from diverse backgrounds, and live by dissimilar political orientations. This global community is what makes mathematics special ― at least for me.
20 May 2021 Hong Kong