Fields Prize laureate - why all science depends on modern mathematicians

In the partner special project with Gazprom Neft about scientists , Paper publishes an interview with mathematician Stanislav Smirnov, a winner of the Field Prize and a professor of Geneva University.

A few years ago, the scientist received a megagant to create a mathematical laboratory at St. Petersburg State University. During this time, more than a hundred young researchers and graduate students passed through it, and one of them in April received a prestigious prize of the Clay Institute.

Why, in order to prepare good engineers, you need a new generation of mathematicians, which is why the competence of Russian scientists fell at the world level and what prevents modern science in universities from teaching? Smirnov told Paper what is happening today with mathematics and how it affects other scientific fields.

How and why Russian science lagged behind the world

Due to the lack of funding and the “outflow of brain”, Russian science is less integrated into international than even during the Iron Curtain. Then, of course, it was difficult to go abroad, but people read articles, followed the relevant. We had a critical mass of scientists so that we ourselves, without trips, could be close to this front edge. Now we were a little conflicting, because people have no money to ride a conference or invite someone, as well as conduct experimental research at the world level. This is annoying, because a person can be very smart and capable, but at the same time often cannot work at the front edge of science.

Initially, the problem arose due to the fact that many people left or left science and had a qualification. Then the level of teaching decreased. There are specialties where our competence has fallen so much that it will be difficult to restore. This is a question not only to invest in money, to ensure working conditions: you still need to explain to the young generation, which is interesting that it is not interesting than you need to do - and this is not easy. Because if you have no competence in some area, how will you receive it?

In mathematics, the situation is a little better now, because we are less tied to experiments and we do not need modern and expensive laboratories. On the other hand, it is sometimes easier to catch up in a single experimental area, because it is enough to bring one professor and buy one installation - this is the standard structure of the laboratory abroad. In mathematics, one professor will not be enough for you - you need a group for communication, a cultural environment.

From the positive: we have a lot of talented youth at our universities . And in some specialties we still have a critical mass, and in all one cannot be leading. Only a very large and rich country like America is capable of this. In order to cover all specialties, now only the United States, France and the UK are actually fighting. China is trying, but they have not yet increased the level, although they invest a lot of money into science. Other countries - the same Germany - cannot cover everything. In the best years, the Soviet Union is not all, but many specialties were covered.

Why modern science theoretical research

There is an eternal discussion about whether the theoretical research is necessary or only applied . But we never know in advance what will come in handy in the future. Take the same digital photographs: the algorithms used were invented purely for fundamental studies regardless of the photograph, but then, when the technology was needed, it turned out that theoretical studies have already been conducted.

In the Soviet Union, the interaction of fundamental science with applied research was established . In some areas more efficiently, in some-less. In large projects such as a space program or nuclear bombs and energy, it worked quite efficiently. There, the problem was divided into small units, distributed by hundreds of institutions that solved it.

The modern industry is rather not such a megaproble, but of some urgent issues that also need to be resolved. In mathematics, we traditionally had good scientists, and most of the Russian scientific successes were based on this mathematics. We had a sufficient level of fundamental mathematical knowledge to promote other areas. In recent years, the significance of mathematics has only increased. Information technologies, work with large amounts of data, biology, decoding of the genome - all this is largely mathematics.

How the Laboratory for the Government Megagran was opened at St. Petersburg State University

We created the Chebyshev laboratory in 2010 for the government megagagant . This was the first wave of megagrators. 40 laboratories are created in each wave from scratch, which are given a grant for two and a half years, then it may be extended for another two years. Then the laboratory should find some other financing, which, by the way, is non-trivial, because we have very few ways of grant support. In our case, Gazprom Neft helped a lot, giving charitable help, and then we found a grant of the RNF.

Most megagrators are designed mainly for experimental laboratories : biological, chemical, physical. And the structure of the experimental team is one senior professor; Two or three more younger professors; several young researchers; many laboratory assistants who screw the screws, wipe the lenses, support vivaria; as well as students around. This is a hierarchical structure aimed at a certain experiment, in modern science, often associated with any expensive attitude. Mathematicians, of course, have no installations. Therefore, my colleagues and I seriously discussed in which form the laboratory needed to create.

Basically, the Chebyshev laboratory consists of youth and is aimed at theoretical research . It so happened because I created a laboratory for those things that I myself was engaged at that time. The core is a mathematical physics, but with all the surrounding areas. If we talk about practical benefits, the main benefit of this is to raise our competencies to the desired level of mathematics. Recently, several children began to engage in more applied things and have been conducting a dialogue with the same Gazprom Neft, because oil companies always have strong research departments in which mathematicians and physicists also work.

How a mathematical laboratory works

The mathematical laboratory is arranged differently : usually more the older generation, there are no laboratory assistants, but there are much more post-house or graduate students. Having talked with our colleagues, we realized that we wanted to concentrate on the young generation, that is, to include the elders, only to somehow administratively support all this. The average age of our employees is less than 30 years.

Two things were important to us: support for graduate students and support for young candidates of sciences , or, as it is called in the West, postdroks-people who have just received a doctor’s degree and have a temporary position for two to three years. We had local doctors, and those who came from the outside. They are paid a reasonable salary, money is given for participation in conferences and cooperation. This is important, because over the past 25 years, we have fallen a lot to finance science - in particular, there were low salaries. The standard graduate student in Russia works a lot, and this distracts from science. Usually, by the end of graduate school, he simply leaves science, especially if there is a family, children. Therefore, the first part is to provide people. The second is to give them an interesting work, organize some seminars, schools, courses in modern mathematics.

In the golden years of Soviet mathematics, the faculty should have existed as a club , where people communicate a lot with each other, sit at seminars. On the other hand, at St. Petersburg State University ruined the move to Peterhof a lot, where the Faculty of Mathematics and Mechanical was one of the first. This killed seminar activity, because in Peterhof no one will stay until midnight: it is dark, cold, the electric trains go rarely. This activity was never revived, even when it became more equipped there: many mathematical seminars simply died out, at best moved to other institutions.

On the other hand, we decided to introduce a little Western traditions . In Russia, it was accepted that a graduate student was writing a dissertation for three years, once a week he goes to seminars in his specialty, and the rest of the time sits at home in the attic, because there are no offices, and only occasionally communicates with a narrow group of colleagues, and is not much interested in other areas. We tried to change habits so that there were special courses for graduate students, so that they would go not only to their seminars, but also to others. Such a system has successfully taken root.

Why make mathematicians an internship abroad

We tried to ensure that all young people have been trained for a year or two abroad . It is clear that the question arises: will return or will not return? But it seems to me that this is a slightly wrong question: we must do not only return, but some foreigners come to us for such conditions. It must be understood that it is often more profitable to send three people, from whom one will return than to keep them here. Because at another university, having gained experience, they will expand their horizons and bring something else. I believe that it works quite successfully if you look at achievements at the international level.

Students and graduate students from 30 countries and hundreds of universities came to us , if we consider conferences and schools that we organized. For a short time they come very often, they came to longer several times. There are good ties with universities that occupy advanced positions. We often cooperate on the geographical principle - for example, with a technological school in Stockholm or the University of Helsinki. We have quite a few joint articles, but there are also results that are difficult to measure: someone came, gave a lecture, and then some kind of work was born from this.

How St. Petersburg scientists received a prestigious Kleya Prize

For a laboratory that has existed for only six years, we have a very big return . And in the sense of scientific research, and in the sense of integration into world science. For example, Dmitry Chelkak is one of the organizers of the laboratory, who has invested in it a lot of time in the first three years, in 2014 received the Rafael Salem award-this is the most prominent international award in mathematical analysis. Now he is in a very prestigious five -year position in Paris.

The remarkable news came on April 11 . There is a Clay Institute, which is known for announcing a prize of $ 1 million for solving seven specific problems. Of these at this moment, only one was resolved - the Poincare hypothesis - Grigory Yakovlevich Perelman. But the institute also gives from two to five prizes every year for the best, in their opinion, the achievements of recent years. In fact, this is one of the most prestigious mathematical awards. This year, one of the prizes went to Evgenia Malinnikova and Alexander Logunov. Malinnikova is a graduate of St. Petersburg State University, and now - a professor in Norway. And Logunov is a postcard in the laboratory of Chebyshev.

Alexander Logunov is the first of those who received a prize who has affiliation with Russia who works here. At the same time, the Clay Institute presents these prizes every year for 19 years - probably, they were given already for 50 different discoveries. This is just evidence that we had few noticeable discoveries made in 20 years. And if we talk about physics, chemistry, biology, then the situation is also critical: there is no Nobel level of discoveries. But since young colleagues begin to receive such awards, there is hope.

How effective was the system of megagrators

I believe that megagrators are a useful program , but it is necessary that there be many other things in the complex. Of course, everything can be improved - for example, I would create more long -term grants. Now it makes sense if a person does something applied, but then the question arises: why do something that pays off at the university, if you can simply organize your company, not necessarily at the university? Then, perhaps, it would be necessary to make a special system for organizing companies at the university. And for fundamental science, this is too short.

In my opinion, approximately half of the first two wave laboratories were successful and survived . This is a lot according to international standards, this is a large percentage, because when you start some kind of scientific research, you don’t know in advance whether it will go or not. But still, some laboratories died due to the fact that there was no funding, or due to the fact that the manager had to spend part of the time not on science, but on his search.

Why are universities taught outdated mathematics and what can this lead

To have good applied research in any field, we must have a good mathematical base . Now nothing happens without mathematics. If we want the engineers to have a good mathematical base, we need professors of engineering universities to know modern mathematics well. But usually there are graduates of leading mathematical faculties, including St. Petersburg State University. So, you must first raise a generation of mathematicians in order to make up for the hole that we have formed recently. Before you seriously take up applied things, we need to raise even scientific, but educational potential.

We have hundreds of universities, where outdated things are taught by outdated abstracts , which the modern graduate does not need. They are taught not the science that is needed today, but some of the day before yesterday. For example, for the last ten years, machine learning specialists have been in demand, and they are almost not prepared in the country. And the reason is simple: we lack highly qualified associate professors and professors in universities. Apparently, the only way to update is to grow a new generation. But then it is necessary to make sure that, firstly, teaching is at a good level, that is, people are taught something modern, and we will not be able to provide this at once throughout the country. Secondly, it is necessary that graduates are later in demand and go to regional universities where mathematics is needed.

This is an urgent question, because most of the engineers do not know the mathematics that they need . They are taught from textbooks what the engineer needed 40 years ago, but since then everything has changed a lot: other areas, another application. This is a difficult task of the country's scale, and we just took on an important piece that should pull it all up.

What is happening with the teaching of mathematics in schools

We are good with physical and mathematical schools , for leading universities we have a sufficient number of strong applicants. They are well prepared and motivated - this is valuable capital, which in many other countries is not. We work with them, but in St. Petersburg and without us it is good: there are mathematical circles, and in this sense we just add a little to what is.

For the third year in a row, more winners of the All -Russian Olympiads of schoolchildren have been entering the program “Mathematical Progress” than any other mathematical program in Russia. Initially, the laboratory supported graduate students and young scientists, and then Gazprom Neft suggested that we support students with emphasis on the regions. At about the same moment, we rebooted the teaching of mathematics for students, so this initiative coincided with our work. Now we have the 1st and 2nd year, in September the 3rd will appear, and it is already noticeable that we managed to collect a lot of good guys, including from the regions. But the first real results will be when they finish.