by Anatoly Konechny
Albert was my advisor at UC Davis where I studied for my PhD in the late nineties. I really enjoyed my studies there and learned a lot from the courses and seminars but the main thing was working with Albert. I would say that the best word that characterises what that time meant for me is apprenticeship. Through Albert’s initiative we embarked on a number of projects on diverse topics in mathematical physics related to string theory, conformal field theory, supergeometry and noncommutative geometry. To me it was quite a roller coaster ride through so many things I had not known (and often had no idea what they were) but had to learn quickly. It was an exciting time in mathematical physics with many breakthroughs in string theory related to dualities, D-branes and M-theory. Albert was on top of all of these developments, constantly trying new ideas, rethinking them in his own way. The work we did together resulted in several publications, but also there were a few projects which were after some time abandoned (or perhaps put on a back burner) but from which I learned a great deal nonetheless. I was learning how to work by observing a great master and by helping him pursue specific trains of thought.
I think Albert has a very peculiar style of thinking and working and I was privileged to have a great deal of exposure to it. I spent a lot of time in his house, often on weekends, discussing the projects. He liked to think out loud and write things while having me by his side. Often I played the role of devil’s advocate asking lots of questions, often naive ones, but through answering the questions we made progress. I always found great hospitality at Albert’s house with his wife, Lyubov Matveevna, making sure we had refreshments by our side when working and often treating me to dinner.
Besides playing devil’s advocate during our discussions, I had to figure out many things on my own which included doing calculations. In theoretical physics a lot of work revolves around particular calculations. I observed many times how various physicists tend to first do a calculation and then try to figure out what the result means conceptually. That is definitely not Albert’s style. The centre of his projects were always about conceptual understanding. Calculations were secondary, serving almost a decorative purpose. Before suggesting a calculation he thought a lot about it until he would come up with what he perceived was the most economical way to do it. Somehow his intuition would always be strong enough to capture many features of the answer before computing it. I have also learned one other important tip from Albert regarding calculations: when searching for errors one should never try to repeat the calculation following the same steps but design a different route or preferably several different approaches. Indeed an error often springs from some false assumption or step that we habitually repeat when redoing the calculation while a different approach gets us off the beaten track.
Often, in different projects, our research would arrive at an impasse of a kind. Albert used some rather peculiar phrases to punctuate these impasses. For example, when the overall harmony of our understanding of a constructed mathematical world seemed to be suddenly threatened by some ugly counterexample or some mismatch, Albert would say a phrase in Russian that can be translated more or less as “sharks do not exist”. The phrase itself, as I have learned years later, is borrowed from a book which is a collection of funny stories about small children. In one of the stories a child claims (using a slightly incorrect language) that sharks do not exist in the world. Besides marking the impasse, the phrase conveyed some reassurance that the obstacle would dissolve and harmony be restored.
Another phrase Albert often used is more widespread in vernacular Russian and can be translated as: “Was there a boy?” Wikipedia describes the origin of this expression to be a phrase spoken by a character in one of Gorky’s novels, although another version I heard claims it to be related to the Beilis affair (an infamous anti-semitic trial that took place in Russia).1 Albert would use the phrase when we would be forced to doubt the existence of some mathematical object or construction.
It is not the phrases themselves that I am impressed with, although they sound amusing, but the work of Albert’s intuition: he would sense a particular tension on the boundary of known and unknown, and would then take the decision about which way to change the course of our research. Similar moments constantly arise in my own work and I do say to myself the same phrases, recalling how Albert used to do it.
Anatoly Konechny was born and grew up in Russia. He received his BSc in Mathematical Physics from the Independent University of Moscow in 1995. He got his PhD in Mathematics from UC Davis in 1999. After postdoctoral positions at UC Berkeley, The Hebrew University of Jerusalem and Rutgers, he moved to Edinburgh in 2006 where he is currently an associate professor at Heriot-Watt University.