Vassiliev

Kolya Vassiliev (centre) with his two close colleagues, AB Sossinsky (left) and NN Konstantinov (right) at Sossinsky's Moscow apartment in 1994.

Nikolai Borisovich Vassiliev (1940-1998)

Nikolai Borisovich Vassiliev, Kolya to his numerous friends, died of a brain tumor in a Moscow hospital on May 28, 1998. By profession, Kolya was a research mathematician (he worked practically all his life in I.M. Gelfand's famous biology and mathematics laboratory at Moscow University), but he will be best remembered as one of the best olympiad problem solvers and problem composers of all time.

As a problem solver, he was second to none in his generation. Even when he was in his forties and fifties, the speed, depth and elegance of his solutions placed him at least at an equal level with the best performers in the next generations -- Dima Fomin of Saint Petersburg, Sergei Konyagin and Sasha Razborov of Moscow, Maxim Kontsevich of Moscow and Paris, Andy Liu of Edmonton. Yet, strangely enough, Kolya Vassiliev had no official achievements in math problem solving contests; in fact, he never actually participated in any. His interest in problem solving (and indeed more generally in mathematics) arose rather late and, in a sense, accidentally, when he was about to graduate from high school, a specialized school for future musicians. Until then, his main interest had been music, and his intention was to enter the Moscow Conservatory in order to study the piano and/or the theory of music. However, he had medical problems with the joints of his fingers, which hampered the prospects of a career as a concert pianist. He began to lose interest in the theory of music because of ``the huge amount of boring details'' it involved, and so Kolya finally abandoned the idea of a career in music just before graduation. He then began preparing for the entrance exams to Moscow University, which included written and oral tests in mathematics, a subject that he had previously neglected. It was his good fortune to be advised by an excellent mathematics teacher, I.Kh. Sivashinski, who discerned Kolya's exceptional mathematical talent and convinced him to apply for the Mechanics and Mathematics Faculty of Moscow University, where his talent blossomed.

Kolya's love of music was never suppressed by his mathematical activities: he was an excellent amateur pianist, an assiduous concert goer, and, most important, the artistic and aesthetic aspect of his personality permeated his work as a composer, compiler, and style editor of mathematics olympiad problems. There is no doubt that Kvant magazine and the Tournament of Towns were extremely fortunate to profit, for decades, from the fact that their problem sections were headed by a person combining the depth of a high class research mathematician with the brilliant aesthetic character of a composer of music. For Kolya himself, the most rewarding period of his activity as a chooser and editor of problems was 1967--1979 (which may be called the golden era of Russian olympiads), when he presided the Methodological Commission of the All-Union Olympiad of the USSR, either de jure or de facto.

The choice of problems and of their final formulation, both in Kvant and in the Tournament of Towns, was always the result of considerable (sometimes heated) discussion. We feel that Nikolai Vassiliev's credo in these matters was best expressed in one of these discussions: when one of us asked him why he was so vehemently against the inclusion of a certain problem, Kolya answered: "How does a composer decide whether to make a new melody available to the public or to throw it into the waste basket? He assesses if the melody will be true gift, if it will give joy to the listener. If not, it is best to forget about it. I choose mathematics problems in the same way."

Kolya Vassiliev was always a mild, soft-spoken, unassuming person, never raising his voice in anger or irritation, never complaining about the vicissitudes of the life of an underpaid scientist in Moscow. To be in his company in or around the university, or to visit his large bedroom-living room, crowded with overflowing bookshelves, two pianos and ancient furniture, with its striking view of the Kremlin, was always a pleasure and a meaningful intellectual experience.

On all important issues, he was a person who stood firmly for high ethical principles, whether this was to his personal advantage or not. In his work ethics concerning mathematics problems, he was inflexible, and would not rest until the best problems were chosen and their best formulations and solutions had been worked out. In this activity he in fact created a specific style in contest problem formulation: the problems must be natural and attractive, they should involve a minimum of professional mathematical jargon and logical formalization, and yet be unambiguous and rigorously stated. This style has now become the prevailing tradition in many places, but we should not forget that Nikolai Vassiliev, more than anyone else, was its creator.

Besides the style, there is also the substance, what a person leaves behind after he is gone from this world. In that respect, Nikolai Vassiliev's legacy is exceptional: besides the numerous problems authored and solved personally, there are those that he selected and edited for Kvant magazine (over a thousand!), for the Tournament of Towns, for the Moscow Math Olympiad and for the All-Union Olympiad; he is the co-author of five olympiad problem books. Kolya was the person who convinced us that the Tournament of Towns should become international and played a leading role in implementing this idea, not an easy task when Soviet Russia was still behind the iron curtain. He is also, in a sense, the main author of the subject-matter of the three previous volumes in the Tournament of Towns series, as well as of the present volume.

A.A. Egorov, N.N. Konstantinov, A.B. Sossinsky

Moscow

September 1998

Some further recollections from Peter Taylor

I do not think Kolya Vassiliev travelled often, if at all, to the West. Therefore I felt very fortunate to meet him on two visits to Moscow (1990 and 1994), the first of which was extended by being able to spend several days with him at a Tournament of Towns Summer Conference in Estonia. He was there, with Nikolay Konstantinov, to meet me at Moscow airport when I first arrived, with Warren Atkins, and helped solve our accommodation problem when it emerged that the USSR Academy of Sciences had not booked us a room as promised. We arrived late in the afternoon after a long flight from Australia via Japan. Despite making many calls for us from Konstantinov's flat at 11 o'clock Kolya came to us calmly to say not to worry, ``tonight is a white night'', a reference to the fact that even though it was after 10.30, it would still be broad daylight for some time. Soon after he came back, quite excited, to say ``I have you in the Ukraina, a top tourist hotel, if you can pay in US dollars'', and took us to check in. For the history of the AMT until my retirement, this was to be, at USD 350 per night for Westerners, the most I ever paid for a hotel room.

Next day we visited him at the Kvant office, where he had been problems editor for many years. Nikolay Konstantinov and I discussed for some time how the Tournament of Towns would run in Australia and other western countries. Although Kolya was vitally interested in the success of the Tournament outside the iron curtain, he knew that this was in safe hands with Konstantinov. He withdrew to the back of the room to read his mail. Obviously a ritual to read it, Kolya received it daily in voluminous quantities from mathematicians and teachers, proposing and discussing problems. We were frequently interrupted when he discovered in his mail a new, presumably beautiful idea. On this evidence alone the culture of mathematical problem creation and solution in the USSR was indeed impressive.

Unfortunately Kolya smoked cigarettes. He was the only person for whom I ever bought cigarettes because I felt I was doing him a favour to ensure the cigarettes he smoked were as clean as possible. Whenever I thought I would see Konstantinov, I had a carton of western cigarettes to pass on.

The USSR Academy of Sciences and American Mathematical Society had compiled a Russian English mathematical dictionary. He told me the only version he could get in Moscow was the English to Russian version, which was not so useful or interesting to him. He told me he was only interested in getting the Russian to English version, which he knew was available in the west and asked me if I could help get him a copy. To his obvious delight I had the pleasure of being able to produce my own, which I had with me at the time, and give it to him.

The above are only a few anecdotes I recall from personal meeting the man. What really stood out were three things:

• Kolya's readiness to help anyone at any time, epitomised by his love for teaching, as I saw at the Tournament Summer Conference,
• the beauty of the mathematics he created and propogated, and
• above all his strong principles. As I understand it Kolya was one of those scientists who was prepared to sacrifice his career and prosperity in difficult times and under intense pressure in order that every citizen, irrespective of race or religion, had access to the excellent teachers who lived in his country.

Clearly Kolya has left behind a rich legacy. The vast collection of problems and solutions of the Tournament, Kvant and elsewhere (he also co-authored the definitive book in Russian of the All Union Olympiad) will ensure that he is well and truly remembered. He was without a doubt the pre-eminent problem creator and editor in Russia for a period lasting decades.