St Petersburg — the heart of Russian mathematics through the years

21 May, 14:00

Russian mathematics appeared in the 18th century. When the greatest mathematician of the time — Leonhard Euler — arrived in St. Petersburg, it almost immediately became one of the world's recognized mathematical capitals. Later on, several top-tier mathematicians worked there. But the phenomenon known as the St. Petersburg Mathematical School is definitely connected with the transfer of Pafnuty Chebyshev from Moscow to St. Petersburg in 1847. These days we celebrate his 200th anniversary.

Among his direct students are such different and outstanding mathematicians as Alexander Korkin, Andrey Markov, Alexander Lyapunov, and others. Almost all mathematicians working in St. Petersburg today are their academic descendants. However, many of the best and most active mathematical schools in Moscow and other Russian cities, neighboring countries, and now worldwide go back to the scientific descendants of Chebyshev.

The second half of the 19th century and the beginning of the 20th century were undoubtedly one of the best periods in the history of St. Petersburg mathematics when several at once brilliant schools suddenly appeared in new directions for that time. Later on, mathematics — like the city and the whole country-went through different periods, but St. Petersburg always remained one of the leading centers of mathematical thought. In the 1920s, many of the older and middle-generation mathematicians emigrated for political and economic reasons. In the mid-1930s, with the relocation of the Academy of Sciences and its Mathematical Institute to Moscow, many leading Leningrad mathematicians also moved there. Many remarkable Leningrad scientists, especially young ones, died in the war and during the siege.

Another great epoch in the history of St. Petersburg mathematics was the 1950s and 1960s when St. Petersburg — then Leningrad — was one of the 5-6 leading mathematical centers of the world. However, in the future, it began to lose these positions. A terrible blow to the mathematical life of the city was the partly relocation of the university to Peterhof in the late 1970s. That included both the mathematics and physics departments. In the following years, especially beginning in the late 1980s, the situation worsened by the mass departure of many of the most qualified and successful mathematicians and talented young people abroad.

The following years were very challenging both for St. Petersburg mathematics and for Russian science at large. The lack of funding and the loss of public interest entailed personnel losses at about the same level as in the 1920s and 1940s. Despite this, by the beginning of the 2010s, we still had world-class research mathematics and maintained a tradition of teaching real mathematics at a high level. The St. Petersburg Branch of the Mathematical Institute of the Russian Academy of Sciences and the dedication of the university mathematicians of the older generation played a big part in that.

However, about ten years ago, everything began to change rapidly again. The downtrend switched back to an uptrend. In December 2010, as part of the first wave of mega-grants, with the support of the Government of the Russian Federation, St. Petersburg University established P. L. Chebyshev Interdisciplinary Research Laboratory. A huge role in the creation and maintenance of the laboratory was played by its heads — Stanislav Smirnov, Dmitry Chelkak, Pyotr Zograf, and Anton Baranov — and the support of many mathematicians of the St. Petersburg Department of the Steklov Mathematical Institute of RAS and the University, the enthusiasm of youth.

The idea to name the laboratory after Chebyshev was born spontaneously, but it immediately became clear that the name was perfect. P. L. Chebyshev was interested in many areas of both pure and applied mathematics kept in touch with scientists from many countries. It significantly raised the level of mathematics in St. Petersburg and expanded its range – his high standards and aspirations are supported by the laboratory named after him.

From the very beginning, the main mission of the laboratory was to restore the highest level of mathematical education that is traditional for our city, to attract talented young mathematicians and create conditions for their implementation within the profession, to revive mathematical life in St. Petersburg and its full integration into world science. There is no doubt that, on the whole, it succeeded much better than could have been expected initially.

The unwavering support of the university administration was vital for the development of the laboratory. Namely, the laboratory got located on the 14th line of Vasilyevsky Island, where mathematics was born in St. Petersburg. Just a few blocks away from where Euler, Chebyshev, Markov, and other remarkable specialists lived and worked, where the founder of the theory of sets, Georg Kantor, was born — a couple of blocks from the Mathematics and Mechanics Faculty on the 10th line, which was the center of mathematical life in the city in the 1950s and 1970s.

Later on, there were other sources of support One cannot omit the long-term assistance of Gazprom-Neft, particularly under the “Native Cities” program, and grants from the Russian Science Foundation. There were others whose support and assistance proved extremely important during this period.

The significance of the past decade for the revival of mathematics in St. Petersburg is enormous. First of all, about 200 young mathematicians got the opportunity to do what they love in their hometown, in a lively and active environment and relatively comfortable conditions, without thinking about additional earnings. Without this, many of them would not have become mathematicians of such a high level, would not be engaged in mathematics now — or were engaged in it abroad.

It is impossible to list them all. But one of the most outstanding examples is Alexander Logunov, an employee of the laboratory since 2011. During this time, he performed research for which he received numerous prestigious awards – Clay Research Award, The Salem Prize, EMS-Prize, and the New Horizons in Mathematics Prize — the youth version of the Mathematics Breakthrough prize.

Initially, the key research field of the laboratory was modern mathematical physics, primarily statistical physics and related sections of analysis and probability theory. However, very soon the range of research was significantly expanded and included other areas of mathematical analysis, algebra, geometry, topology, the theory of dynamical systems, and the branches of theoretical physics close to mathematics.

Another significant purpose of the lab was to activate cooperation with mathematicians from other cities of Russia and abroad. Over the years, more than 300 mathematicians from all over the world visited the laboratory for reports, lectures, and joint scientific work. Again, it is impossible to list them all, but among the most outstanding guests of the laboratory are the Abel Prize Yakov Sinai, Grigory Margulis, and Endre Szemerédi, Fields laureates Cédric Villani, Andrei Okounkov, Martin Hairer, Director of the Max Planck Institute for Mathematics Yuri Manin and many others.

One of the most remarkable projects in this direction, which is completely new for our country, was the creation in 2014 of a special Russian-French professorial position in the laboratory, the Gabriel Lamet Chair (jointly with the Saint Petersburg University and the French Embassy in Russia). In 2014-2019, this department was occupied by eight outstanding mathematicians from the leading universities of Paris, Strasbourg, Marseille, and Bordeaux. Again, it is impossible to list them all. We will only mention that one of the winners of 2014 was Harald Andrés Helfgott, whose research is very closely related to the great epochs of St. Petersburg mathematics. In 2013-2014, he proved the odd Goldbach conjecture asserting that Every odd integer greater than 7 can be written as the sum of three odd primes. The conjecture was proposed in 1742 in the correspondence of St. Petersburg academicians Christian Goldbach and Leonhard Euler. A significant contribution to its solution was made by St. Petersburg mathematicians Ivan Vinogradov, Nikolai Chudakov, and Yuri Linnik.

The laboratory immediately became one of the centers of mathematical life in St. Petersburg, withal in several directions at once. With its creation, many city seminars and advanced courses returned to the university. Moreover, the very spirit of mathematics as a unified science has returned. Before that, for many years, specialists in different fields sat in their separate apartments. The audience overlap even in the close fields seminars on analysis or mathematical physics, was no more than 2 persons. The seminars and colloquiums of the laboratory were inherently interdisciplinary and immediately began to gather dozens of students.

All these years, the laboratory organized or co-organized dozens of international conferences and schools held at St. Petersburg State University, PDMI, Leonhard Euler International Mathematical Institute, and the Higher School of Economics. Hundreds of guests from different countries and cities attended these events.

From the very beginning, the laboratory, in close cooperation with the recently established Club of Physics and Mathematics and Computer Science Club, took over the organization of topical courses in a wide range of mathematics, mathematical physics, and computer science. In other words, it has adopted an educational mission similar to that of the Independent University of Moscow, the Center for Continuing Mathematical Education, and other centers in Moscow.

Cooperation with the educational portal “Lectorium” has become unique for our country. Lectures of foreign guests, courses of different levels for students, special courses in modern areas, and later many general mathematical courses were professionally recorded on video, edited, and posted online on the laboratory's website and the “Lectorium” website. To represent the scope, we are talking here about several hundred courses and many thousands of lectures. It is no great exaggeration to say that these courses played a decisive role in the formation of the entire young mathematics of Russia.

But the most important thing, perhaps, was that the laboratory managed to largely revive the general mathematical environment within the city, the spirit of the old Mathematics and Mechanics Faculty, a lively, enthusiastic communication. The coffeeshop on the 14th line has become a place where mathematicians of all ages discuss mathematical problems on an equal footing, where a student or graduate student can ask any question not only to St. Petersburg professors and associate professors but also to colleagues from other countries. This is exactly what has been missing in St. Petersburg for many years.

The numerous talented young people and an active international scientific environment of the highest level immediately led to outstanding results. Over the past decade, the laboratory staff has published more than 500 scientific articles, most of them in high-level international journals. The laboratory researchers delivered talks at hundreds of international conferences, including invited papers at the most prestigious international forums, such as the International and European Mathematical Congresses.

The laboratory became a starting point and led to the creation of the most powerful world-class scientific and educational center in St. Petersburg State University. Here is just a cursory list of several other areas of our work that are largely new to St. Petersburg, at least in these forms.

In 2013, in the same coffee shop on the 14th line, a group of enthusiasts from the university and PDMI began discussing a project to radically update mathematics education. In 2014, this project proceeded to implementation. The first enrollment took place in September 2015 for the Mathematics program, and then for Modern Programming and Data Science. These programs immediately became extremely popular with applicants. From year to year, we recruit more winners and prize-winners of All-Russian and international Olympiads in mathematics and programming than any other university in Russia.

Later, the undergraduate program developed into the English-taught master's and postgraduate programs “Modern Mathematics”. In June 2019, the institutionalization of these programs culminated in the creation of a new mathematical faculty at St. Petersburg State University — the Faculty of Mathematics and Computer Science — which is located on Vasilievsky Island. Many eminent mathematicians who had previously worked abroad for many years have returned or moved there.

The laboratory did the same not only for education but also for scientific and applied projects. The talent and energy of researchers Roman Mikhailov and Yuri Belov allowed us to make successful entries for two more government mega-grants in mathematics: alongside the Chebyshev laboratory, two new laboratories were created at St. Petersburg State University under the guidance of foreign scientists. Laboratory of Modern Algebra and Applications under the direction of Dipendra Prasad started working in 2018, Laboratory of Probabilistic Methods in Analysis under the direction of Hakan Hedenmalm opened in 2020.

Another unusual area of work for pure mathematicians was participation in industrial projects. Suddenly, it turned out that for many real projects the fields in demand are not applied mathematics and numerical methods, but various sections of fundamental mathematics and advanced computer technologies. Sergey Tikhomirov created a strong group at the laboratory to research for Gazprom Neft. In 2020, this process continued with the creation of the Huawei research mathematical laboratory at St. Petersburg State University, and there are further plans.

Another work direction of the laboratory, and now the faculty of Mathematics and Computer Sciences— is working with schoolchildren, not only from St. Petersburg but also, for example, organizing thematic projects in mathematics and computer science at the Sirius educational center in Sochi.

Such a rapid revival of fundamental mathematics in St. Petersburg was immediately recognized in our country and abroad. Mathematical Petersburg has never completely lost its importance, but in recent years its status as one of the best and leading world mathematical centers has been receiving new confirmation. Here are just two of them.

In 2018, at the General Assembly of the International Mathematical Union, the world mathematical community chose St. Petersburg over Paris as the venue for the next International Congress of Mathematicians, ICM-2022. This is the most prestigious mathematical forum, which is held every four years and is traditionally attended by thousands of mathematicians from all over the world. In our country, the congress will be held only for the second time — the first was in 1966 in Moscow.

In 2019, the Government funded the creation of four international mathematical centers in Russia. One of them, Euler International Mathematical Institute based on a consortium of St. Petersburg State University and PDMI. Two other centers have been established in Moscow one more in Novosibirsk. The Euler Institute has already received dozens of applications from young Russian and foreign mathematicians who dream of working in St. Petersburg.

In conclusion, I would like to specifically note one more point. Mathematics in Russia originated on Vasilievsky Island. All the further development of mathematics in St. Petersburg in its best epochs — not only in the 18th century but also in the 19th and 20th centuries — is inseparably linked with Vasilievsky Island. Euler, Ostrogradsky, Chebyshev, Lyapunov, Markov, Steklov, and many other remarkable mathematicians lived and worked here.

The current building on the 14th line is obviously not enough for Chebyshev's laboratory, for the new faculty, and for everything that has arisen around them. We look forward to the end of construction work in the building on the Kadetskaya Line so that mathematics in St. Petersburg can once again find a residence corresponding to its status. So that students, postgraduates, St. Petersburg scientists, and guests can once again gather for live communication in the center of our great city.

Professor of the Faculty of Mathematics and Computer Science

Nikolai Vavilov