1986 and 1987
2001 ).
With 2003
2002 ) and son Nicholas ( 2006 ).
↓Graduated from school number 239 with in-depth study mathematics and physics. From the fifth grade he studied mathematics in the circle of the Palace of Pioneers under the guidance of Sergei Evgenievich Rukshin. At the same time, in the same circle, but 4 years older, he was engaged. AT 1986 and 1987 years member of the USSR national team at the International Mathematics Olympiad among schoolchildren. At both Olympiads, having solved all the proposed problems and showing a 100% result, he twice became the owner of a gold medal.
Later he became a professor at the Royal Institute of Technology in Stockholm and a researcher at the Royal Swedish Academy of Sciences ( 2001 ).
With 2003 years at the University of Geneva.
Smirnov's works are best known in the field of the limiting behavior of two-dimensional lattice models: percolations and the Ising model. In particular, the proof of Cardi's formula for percolations on a triangular lattice, the proof of conformal invariance for various two-dimensional models, a recently appeared preprint containing the proof of the connection constant conjecture for a hexagonal lattice.
Wife Tatyana Smirnova-Nagnibeda, whom he met back in mat. mug, also a mathematician, professor at the University of Geneva. He is raising a daughter Alexandra ( 2002 ) and son Nicholas ( 2006 ).
Stanislav Konstantinovich Smirnov — Russian mathematician, winner of the Fields Prize (2010), professor at the University of Geneva, scientific director of the Chebyshev Laboratory of St. Petersburg State University, member of the Board of Trustees of the Skolkovo Institute of Science and Technology (Skoltech). Graduated from the Faculty of Mathematics and Mechanics of St. Petersburg State University (1992) and postgraduate studies at the California Institute of Technology (USA). Worked at Princeton (Institute for Advanced Study), Bonn (Max Planck Institute for Mathematics), in Yale University and the Royal Institute of Technology in Stockholm. Since 2012, he has been a member of the Public Council under the Ministry of Education and Science of the Russian Federation.
About criteria
Do prizes make sense in mathematics?
- This is complex issue. I think they make some sense for the popularization of mathematics. The same Nobel Prize, it shows people - even those who are not very interested in science - that something is happening in physics and biology. It may also be important for scientists themselves to be somehow noted outside their narrow field. I think there are researchers for whom important role formal recognition of colleagues plays, although for the majority informal recognition is more important. But popularizing the fact that something interesting is constantly happening in science is important. And with psychological point vision received by some scientists award may be more interested in the results of his scientific work than a popular science program or article.
- It's true. But, say, in biology, the Nobel Prize, in my opinion, does not make sense. Because there is no discovery that one or three people would make. There is always a group of people from which the winner is chosen quite randomly. Isn't that right in math?
- WITH Nobel Prize everything is a little more complicated. First, a direction is chosen: for example, if we are talking about physics - astrophysics. Then a specific sub-direction is selected, for example, exoplanets or background radiation. After that, a specific discovery is selected, and then there is a choice of whom to give. This, of course, is difficult, because there is a limit: a maximum of three people.
In mathematics, I don't think this is a problem, because theorems are usually proved by one person. Even 60 years ago, most of the articles were written by one author. There were articles for two, very rarely - for more co-authors. There are famous theorems: Paley-Wiener, Littlewood-Hardy or Phragmen-Lindelöf. But still, most of the theorems were proved by one researcher, and not by a scientific group. Now this is changing.
Thirty years ago articles often began to be written by two authors; now there are many articles for three people. This is due to the fact that science has “spread”, and different competencies converge among different people; and partly, maybe because people have become more social, they enjoy discussing science. But anyway, in mathematics, if there is any worthwhile concrete theorem, then usually a small group of people worked on its proof. It’s another matter if we are talking about extensive breakthrough areas, for example, about integrable systems, where several researchers received awards, but it is clear that this whole area is work. a large number of people.
In general, I have an ambivalent attitude towards awards. It is good to have some markers, they say, look, everything is fine in our science, we are proving new theorems and this is somehow noted. But it is clear that there are many wonderful people who did not receive awards simply because it happened, and this is a shame.
— How are the mechanisms of informal recognition among colleagues arranged in mathematics?
Whether a person proved a good theorem or did not prove it. I respect people who proved what I could not prove. There are informal aesthetic criteria. I remember one of the first theorems I proved. Once my supervisor Victor Petrovich Khavin told about it at a seminar in Paris. A very famous American mathematician Dennis Sullivan came to this seminar by chance, he really liked my work, he said: “A beautiful theorem. I must steal it." I later asked him what he had in mind, and he said that for him this was the highest mark: it happens when you regret that you yourself did not prove it - not in the sense of black envy, of course, but you can imagine what harmony a person had in soul, when he understood how everything falls into place, the world suddenly becomes more beautiful, and you understand how it works.
This assessment of Sullivan was very important for me, then a not very self-confident student, especially since he has several fantastic theorems that I myself would like to “steal”. For example, he applied quasi-conformal deformations to prove the impossibility of wandering Fatou components, and this unexpected and beautiful move immediately allowed him to solve the problem.
Aesthetic criteria - what you like, what you don't like - of course, subjective, they depend on the taste, how you were brought up. But some of them become objective. There are tasks about which it is clear that their solution will lead to great progress. For example, if you ask mathematicians what is the most important task in our field of science, I think a lot of people will say that this is the Riemann hypothesis, because it is clear that many things are tied to it. If you ask people to name the second most important task, I think there will already be at least two dozen options.
- What criteria are there in mathematics besides aesthetic ones?
— There is a criterion of usefulness in other problems of mathematics. If you take the Riemann Hypothesis, there are so many theorems that suggest that it, or rather its generalizations, are true. Therefore, its usefulness increases. There is utility in other areas of science. Mathematicians came up with functional analysis, to solve the partial differential equations that came
from the problems of physics. And then it turned out that this is necessary for quantum mechanics. There are, of course, practical applications - wavelets were invented to solve theoretical problems of harmonic analysis (and before that they appeared in the theory of renormalization among physicists), but their value increased when they found practical applications in data processing. And interesting theorems more about them too.
About mathematics and knowledge of the world
— You said that in addition to aesthetic criteria, there is something else that the result can make it clear how the world works. Does mathematics really help to understand how the world works, or does it create something separate?
- That's a very difficult question.
All my questions are difficult.
- This is interest Ask, not mathematical, but philosophical. There are two points of view. The first is that mathematicians discover something that exists in our world, and then mathematics natural Science. The second is that mathematicians come up with something from scratch, and then, along with philosophy, mathematics is a formal science. The second point of view seems to me more exciting. Then one can go even further and assume that the person who first came up with the theorem can prove that this theorem is true or that it is false. It will be enshrined in stone for centuries, and the next people will no longer be able to prove it the other way - that would be really funny!
But if we return to a more realistic plane and divide the sciences into the humanities and natural sciences, it would be more correct to say that mathematics is a natural science, but it still keeps a little apart. Even if we do something abstract, which is completely different from the world, strangely enough, this is very evident in the natural sciences. But this is a separate topic discussed by many philosophers, such as Wittgenstein and Popper. From the popular - the famous essay by Eugene Wigner "The inconceivable effectiveness of mathematics in the natural sciences". In a good way, people do not understand well why mathematics is so successfully applied in the natural sciences.
— In what sciences besides physics?
- Now in biology, for example.
- Never used successfully.
- You are exaggerating: non-trivial combinatorics was used in bioinformatics. And now mathematics will be applied in biology even more.
- I think no.
— The last article I wrote with my colleagues is on biology. We study the coloring of a particular family of lizards and show that the Turing reaction-diffusion equations relating chromatophore concentrations, with variable coefficients…
“It's old science. There is a wonderful book about coloring shells, which is more than ten years old.
— It’s easier in shells, there is a one-dimensional thing, because it is layered along the border. Turing's article is, of course, an old one, but the experimental study of this in biology began not so long ago. And we have a more complicated picture than, say, Kondo fish - uneven scales lead to variable coefficients in the equations, which, because of this, are reduced to a discrete analogue and, as a result, to a cellular automaton describing the coloring of scales.
- Amazing. Nevertheless, this is both relatively simple mathematics and relatively simple biology.
“I wouldn't say so. Especially after hearing only what the article is about, and not getting to the bottom of it. Biologists-specialists just liked it. Do you know an example of a cellular automaton in biology?
I think I know, I'll have to look.
“Here, look.
— The effectiveness of mathematics in physics is still much deeper than the effectiveness of mathematics in biology.
- This is because physicists had earlier good experiments. The effectiveness of mathematics in physics began with the fact that Kepler had very good astronomical observations (Tycho Brahe. - Red.), processing which he noticed a beautiful regularity - that the planets fly in elliptical orbits with specific speeds. And Newton was able to deduce these beautiful, but incomprehensible laws from the simplest formula, and this was the beginning of a revolution in physics. But it all started with a large amount of very accurate data. Biologists didn't have anything like that, and long time It was common sense say that nothing like that will happen. But I think it will still appear. But it's hard for me to talk about it with you, because you're like a biologist, and I'm like a mathematician. Let's take better others applied examples. For example, information Technology, economy.
- Number theory ... We all know this, credit cards ...
— The theory of numbers there is just an important, but it plays a temporary role.
- BUT? Now you will kill my favorite example. I tell everyone how Hardy said in the twenties that number theory is the most useless science, and now all protected messages are based on it.
- Insofar as there is no quantum computer, and it will appear in ten years.
“And the effectiveness of number theory will end?”
- In fact, they will come up with other algorithms. Many say that there are no others, but they will certainly be found when the need arises. By at least, say the experts.
As for other examples, it's very fashionable to work with big data now, and there are very nice things there. At least it already looks like biological things.
A canonical example: there is a famous Netflix challenge for which the company was offered a millionth prize. Netflix is a video rental service. They have a task, when someone buys something, to advise him on other films that he should like. If they advise correctly, a person buys more and more each time. So does Ozon or Amazon.
And what is the algorithm to do it? What information does the network have? There are, for example, a million users and a hundred thousand movies. Ideally, everyone would watch each film, rate it on a ten-point scale - and we have a complete matrix. And if it appears new buyer, you can tell him about films by comparing him with other people.
But we have something completely different. We have a matrix: each person watched a maximum of 100 films - we know that there are 100 elements in each line, and we want to restore it completely. Of course, there are no clear laws here, people are mistaken. Someone came up with the principle in due time that, although this multidimensional problem, in fact, it does not have a million dimensions, but much less - roughly speaking, 50. There are 50 ideal types of people: say, an ideal person who loves science fiction; the perfect person who understands action movies, and so on. And there are 50 characteristic films: the perfect romantic comedy, the perfect detective, etc. In a sense, this is like expanding the matrix into eigenvectors- rows (people) or columns (movies). If we believe in this hypothesis, we just need to find these 50 people and 50 films, then expand any film into a basis for these films (say, 50% action movie, 35% comedy, 15% romance), and any person into a basis for people .
- Your "man" is still a construct.
- Yes, for the time of solving the problem, this is a construct, this is not a specific person. It's like calculating in quantum mechanics - the particle is replaced by the construct of a square-integrable function. It's strange, but the result of the calculations makes sense.
— Dimension reduction for a highly sparse matrix.
- Yes. You're making the assumption that a matrix—a collection of points in a million-dimensional space—matches very well with a space of much smaller dimensions. If you make this assumption, you get good method, which predicts pretty well.
- What is the depth here? Downsizing is a very good thing, but...
“The assumption that the world is simpler than we think is not mathematics. Then comes the math: how to find the structure, believing in this assumption. Anything is intertwined here: from statistics (you need to average errors) to some kind of analysis. There are algorithms in analysis how to search for a low-dimensional structure. When I was a postdoc at Yale, one of my mentors was Peter Jones, who once solved an analogue of the famous traveling salesman problem. You have cities and distances between them: how to find the minimum length of the path that will cover all the cities?
But is it NP-complete?
- Yes. On the other hand, there are fast algorithms that, with a probability of 99%, give a solution that is less than 5% different from the ideal one. Peter Jones once solved the continuum version of this problem: when you have some set drawn in space and you need to determine when you can draw a finite length curve through it. It was purely a decision theoretical task(and I would also not mind “stealing it”), but an algorithm followed from it, how to draw this curve even if you allow errors in the set. That is, you are allowed to erase 1% of the set, and draw a curve through the remainder. Then this algorithm was generalized; it, for example, allows you to pass low-dimensional surfaces through a multidimensional data set, if this, of course, is possible. There is very beautiful, deep mathematics, and I think that it will work both in biology and in data analysis: in fact, the world is arranged in such a way that almost all the things that we see are simpler and more beautiful than they seem at first glance.
This is a good prediction because it can be tested.
In fact, the world is arranged in such a way that almost all the things that we see are simpler and more beautiful than they seem at first glance.
About the structure of mathematics
— Returning to philosophy. It seems to me that there are people who enter mathematics from the side of physics; in your terminology, this mathematics is a natural science. And there are people who enter mathematics, roughly speaking, from the side of logic. According to your terminology, this is philosophy, but Mikhail Tsfasman told me in general that this is theology.
— Many mathematicians love esotericism. And I like to amuse myself with the semi-serious thought that this is theology. In principle, of course, there is such a beautiful theological element in what you see in mathematics: complex things that have a simple explanation. And vice versa, when a simple mechanism creates complex structures.
Speaking specifically about the theorems to which I had a hand ... For example, you paint a hexagonal honeycomb in two colors. You toss a coin for each hexagon, color it yellow or blue. Then you look at clusters (connected areas) of blue color. It is (almost certainly) 91/48. That is, in an NxN box, the largest cluster will, on average, have N to the power of 91/48 hexagons. Like simple thing, the student understands. And for the first time this problem appeared in a magazine for schoolchildren in 1891 in the first issue American Mathematical Monthly — American counterpart"Quantum". And they solved it only after 110 years ... By the way, the number 91/48 does not just appear, behind it are both beautiful abstruse physics and several areas of mathematics.
In principle, I agree, people come from there and from there. It is very valuable that in mathematics there is an interweaving of these two lines. I once discussed with Moscow colleagues from the HSE Mathematics Faculty how to teach the Stokes formula, and it is interesting that both teachers and students were divided into two camps. For some, it was easier to start with Ostrogradsky's theorem for vector fields, which has a simple meaning: if there are no sources inside the region, then with a steady flow of fluid, the same amount of fluid flows into it as it flows out. And then you can move on to multidimensional generalizations. Others, on the contrary, said that they did not understand physical analogies and it was easier for them to start with differential forms of arbitrary degree and external derivatives.
In fact, of course, a good mathematician should know both and be able to intertwine it: what is an abstract thing, and what is a geometric one. Often quoted, but a little taken out of context: one famous mathematician said that behind every mathematician is an angel of geometric intuition and a demon of algebraic abstraction. Specifically, this statement was about the development of algebraic topology - that it can be considered as an algebraic subject, but can be considered as part of topology. But such interweaving exists in all areas.
- You said that there are several authors in articles, because different authors have different competencies.
- Someone understands about watermelon, and someone - about pork cartilage.
- At this level, I understand. Are there areas of mathematics at all? Or is mathematics really continual, and what we call areas of mathematics is a habit, because departments are called that?
Both answers are correct. I think it's actually continual. It just grew, like all science. Of what's called polymath's English language, universal scientists, there are no more in the world. We were arguing with a friend about who was the last mathematician and physicist at the same time. I named some people of the 20th century, Richard Feynman, for example. The friend says, “No, Feynman was a physicist. Of course, he could do mathematics, but he didn’t want to.” Then I say: "Paul Dirac!" He says: "No, James Maxwell - last man who studied both mathematics and physics.
Mathematics has grown, now they write 100 thousand articles a year. One person cannot read 100,000 articles a year: that's 300 articles a day, you need to read an article in six minutes and not sleep. Certainly, good articles smaller. But we cannot say in advance which of them are good and interesting. It's just that the volume is such that there is some kind of classification, specialization.
- It turns out like in a joke about two policemen.
- One can read, the other can write ... In addition, the area can be determined by the fact that such and such a method is applied or we ask questions of such and such a type. For example, probability theory is a part of measure theory: the measure of the entire space is 1. Because Kolmogorov decided that we model probability by measure theory - it was not obvious - and that we always have at least one event happening, therefore total amount equals 1.
This is not so much a part of analysis, where we study spaces with measure 1, as some special view of these spaces, where we introduce specialized terminology. When you get used to it, you have a new intuition. In this sense, there are areas of mathematics: if I say that I look from such and such a side, I have a special intuition - for a while I forget about the other one, which interferes with it. Usually in mathematics
determine what he did in graduate school, precisely by the way he looks at tasks.
“Mathematicians are really defined by the way they think.
- Yes. Again, in any science there are periods when everything spreads, differentiates, new things are invented. Now is the era of synthesis. The most interesting thing that's happened in the last two decades is when people combine ideas from two fields and it works really well. And then the cooperation of people who think differently is useful.
- You said that 100 thousand articles are published and it is not known in advance which of them are good. Is it really unknown or does the author's reputation filter this?
- Of course, the reputation of the author, and fashion is in any science, including mathematics. It is clear that the articles of people who have already proved something are taken more seriously than the articles of others. And more credibility that the proof will be true, although everyone is wrong. Naturally, among the 100,000 there are a certain number of articles about which it is clear in advance that this is nonsense.
- Nonsense or uninteresting?
“It’s not interesting, because this is a version of an already proven theorem, a copy of something. But what can I say for sure: there are quite a few subjects about which everyone thought that it was not interesting, and then, after 10 or 50 years, it turned out that it was important. It was the same with applications. For example, with the mentioned wavelets, which have found application in image processing. Many worthy analysts were involved in them, but as soon as it became practically applicable, this area rapidly grew and became more interesting.
Again, the mentioned bioinformatics - de Bruijn graphs are used to assemble the genome - this is a small area of graph theory and combinatorics, which seemed to many to be esoteric and unnecessary. But when they were needed in biology, most of the theory had already been built.
It happens that someone came up with some concept in pure mathematics and did not pay attention to it, and then it turned out that in another area you can build a castle on it. And therefore it is very difficult to say with certainty that such and such a result is obviously uninteresting, because there were many examples when people were wrong. If we brush aside repetitions and technical advances, out of 100,000 articles, there will be no less than a dozen or two thousand articles of varying degrees of interest. But what exactly will be important in a generation is difficult to predict.
It happens that someone came up with some concept in pure mathematics and did not pay attention to it, and then it turned out that in another area you can build a castle on it. And therefore it is very difficult to say with certainty that such and such a result is obviously uninteresting.
There are quite a few interesting articles. One of my colleagues said that mathematics is the most democratic of all sciences. When compared, for example, with experimental physics or biology, then a mathematician is less dependent on bosses, on funding, one can prove theorems without a scientific group, many more researchers bring something useful and interesting to the general building of science that we are building. At first I wanted to object, and he suggested counting how many people proved interesting theorems that I liked or I used them in a narrow area that I have been working on for the past few years. We immediately counted 80 people. And this is a really narrow area. In this sense, there are quite a lot of interesting articles among 100 thousand.
- What area is this?
- I was engaged in two-dimensional statistical physics - the theory of two-dimensional random processes. There is a very interesting convergence and complex analysis, and algebra, and combinatorics, and probability theory. Over the past twenty years, there have been several breakthroughs, and we have become much better at understanding what is happening. It turned out that in 10 years more than a hundred interesting theorems have been proved there. And this is a small piece of mathematical physics and probability theory. I think that in mathematics as a whole, several thousand obviously interesting papers are written every year. Naturally, one person cannot read 1000 articles, hence specializations arise.
About schools
— It seems to be generally accepted that there are scientific schools in mathematics. Again: is this some kind of convention that assigns people to their supervisors, or does it really leave a mark? Is it possible to find out by style who was the first teacher?
- Both here and abroad 50 years ago, people defended themselves with Professor X, then they worked in the same city and went to the same seminar, and really was large group like-minded people who discussed something. Now there is globalization, people began to travel more. And now there are two types of scientific school. In the first, scientists go to the same seminar for years and work on the same topic. Due to the increased mobility of researchers, there are now almost no such scientific schools left. Scientists work more remotely, they move from one place to another, fly more often, so you can work remotely with someone and see him once every two months.
But, of course, a person remains the way he was taught to think. Almost any mathematician shows what his original specialization is, even if he changed the area. One of my colleagues said: “Whatever you do, you always need to be the best specialist in some narrow area, for example, it is best to know the application of such and such a method. At the same time, you can be engaged in another area, but someday it will help you. As Richard Feynman said: “To solve any problem, you need to have two cards up your sleeve.” When I was a graduate student, I had five people big influence, and you can see that I think something similar to them.
- What school do you belong to?
- First, of course, to the St. Petersburg school of analysis. Viktor Petrovich Khavin is the head of my thesis at St. Petersburg State University, an absolutely remarkable mathematician. Unfortunately, he died this September (2015. — Red.), he was 82 years old. Together with his colleagues and students, primarily with N. K. Nikolsky, he created an absolutely remarkable school of mathematical analysis in St. Petersburg. And in graduate school, although I was in the USA, but with a bright representative of the same Petersburg school, Nikolai Georgievich Makarov. Second, to a couple American schools because, as a graduate student and postdoc, I learned a lot from (already mentioned) Dennis Sullivan and Peter Jones. And then I went to Stockholm and learned a lot from Lennart Carleson, one of the best analysts of the 20th century, so I also belong to the Swedish school of analysis. True, it differs little from St. Petersburg - after all, neighbors.
- That's about five and counted.
I said "five" mathematical physicist. It's not approximate, it was an accurate estimate.
- Do schools have an international impact?
- Some yes. There is famous story about Bourbaki (Nikola Bourbaki is the collective pseudonym of the group French mathematicians. — Red.), who really wanted to formalize mathematics, and they really had a very big influence with their philosophy.
- V. I. Arnold was already shaking when he heard this word.
- When I was given Bourbaki's books to read as a child, they told me: "Know your enemy." In many ways, their approach, based on abstract formalization, was the opposite of ours, based on the generalization of examples and physical intuition. At the same time, from there you can isolate a completely different point of view, which I partially like, partially not. For example, they wanted to bring it to absolutism, but they could not formalize the theory of probability, because the formalization that they liked included very narrow circle tasks; say, the Wiener measure was not included. Because of this, in France the theory of probability was driven into a corner for a long time and the probability theorists there were a little isolated from mainstream mathematics, although there were absolutely great scientists among them. This is about schools. If schools have an ideological influence, it is detrimental. Although Bourbaki ideologically did a lot of useful things, they also did something harmful.
About politics
- You said that it is more interesting to talk about mathematics than about intrigues. At the same time, you spend a significant part of your time not on mathematics, but on intrigues.
Because you ask such questions.
- Not the time of the interview, but the time allotted from above. You received a mega grant and for some reason started some kind of activity in St. Petersburg, although it was quite possible not to do this, you had something to do. Then he was co-chairman of the Public Council under the Ministry of Education and Science, until you were removed and replaced with Alferov.
- I was not removed, rather, I asked for my resignation, because I decided that two years in this capacity was enough. And Zhores Ivanovich had just returned to the Council. And in many ways he is a more worthy and experienced candidate than I am. Either way, someone has to do it.
"Why does that someone have to be you?"
Some kind of social responsibility. The future of mathematics in St. Petersburg worries me a lot, because I love this city, I grew up there and it was good for me when I was growing up, although these were not best years mathematics, it was on the decline. I want the best years to return again; I can for some reason, in particular thanks to the Fields Medal, work more effectively on this front than others, try to explain what needs to be done.
The future of mathematics in St. Petersburg worries me a lot, because I love this city, I grew up there and it was good for me when I was growing up.
"Does the Fields Medal work with those explanations?"
- Yes. You see, there is some benefit from it. But there is no need to write about it, because then it will be worse to act.
- It's not clear.
- Depends on how you write.
- What are you talking about. We will write it as it is, then you will cross it out, and I will see what you have crossed out. I am ready to understand why you are trying to recreate or revive the Petersburg mathematical school.
Fyodor Kondrashov, for similar reasons, makes summer schools in biology for high school students.
- It more or less succeeds. It's actually going really well.
- And Fedya is doing very well.
- I know. Schoolchildren and students come excellent. This, of course, takes a lot of energy, but for them it is not at all a pity.
— When the mega-grant ended, did you manage to find funding?
- Half of the money goes to the laboratory from the RSF grant (which is now ending, and it is not known whether it will be extended), and half is given to us by Gazpromneft for purely charitable reasons. They are great fellows that think about the future of science and education. So far, there are no applied works, although our guys went to the seminar of the scientific department of Gazpromneft and saw that qualified mathematicians work there, who have interesting mathematical problems.
- All living beings want to multiply, and mathematicians reproduce in this way - they make their own kind. And why the Public Council and some kind of scientific policy that takes a lot of energy?
- This is also important. It is necessary that scientists participate in social and scientific policy. I got into the Public Council unexpectedly for myself.
So he didn't refuse.
- It was interesting to see. And something useful there still happened to be done.
- Still, the folklore idea is that mathematicians are not involved in politics.
- There are different ones. Some scientists should be involved in science policy, otherwise non-scientific politicians will be involved in it, and then science will be bad. Naturally, it is necessary that the scientific community delegate someone. Not everyone loves it, and not everyone can.
- Do you love and can?
— I don't know if I can, the efficiency is not 100%. Whether I love you is a difficult question. I do not feel sorry for the time that I have for life in St. Petersburg.
— What about the time spent in Moscow?
— I still don't give a damn about Russian science in general. I am interested in the future being good, and, of course, time for this must be seized. Of course, I refuse many things. I was offered to lead the direction of mathematics in the Russian Science Foundation, but I refused, because physically there is no time, although this is a very important matter.
- How do you prioritize? There are 24 hours in a day - how do you decide how much time will be spent on mathematics, how much - on the creation of the St. Petersburg school, how much - on Moscow intrigues?
What's with the intrigue? I was a member of the Public Council, chaired the group on educational standards in mathematics, etc. This is normal work that someone has to do. Here is my late colleague Jean-Christophe Yoccoz who chaired the same commission in France, and I would be very surprised if the French would ask him why he is doing this.
“Again: why is that someone you?
- I was asked to. About the programs - if not me, then Viktor Vasiliev. And he has already invested more time in it than me. Perhaps the main trouble is that many good people have either left science in general, or remained in science, but went abroad. The most active people left and left first of all. There must be a certain percentage of people who are ready to organize science, and we do not have enough of them. As a result, those that are are overloaded.
If you look at the standard American faculty, the administrative burden is distributed there: someone is responsible for the library, someone is responsible for admitting graduate students. No one particularly complains, everyone understands that this is an important burden. There is a third or half of people who are not responsible for anything, because they are not professionally qualified. And someone says that he does not want at all, and they leave him alone. But there are enough people who are ready to do something to cover everything without overexertion. We have a problem that many active people gone or gone.
- You say "with us", meaning - in Russia. How much time a year do you spend here?
- A lot, comparable to Geneva. But it is difficult to calculate exactly - like many colleagues, I spend significant time at conferences and traveling in some third places.
— Do you rather associate yourself with Russian mathematics or is this a meaningless question? Or with Russia, just like the sickest child is loved?
— No, it's not. There is different levels identification. Naturally, I associate myself with St. Petersburg and Vasilyevsky Island and with Russia in general. In a sense, and with gone into oblivion Soviet Union: this is the country where I was born and raised; I really love the places closest to St. Petersburg, and Ukraine, and Estonia, and Armenia, and everything. I worked in Sweden for a long time, studied in the USA - naturally, these countries are also close to me, but in a slightly different way. Russian culture is more European and I associate myself with Europe. Then, there world civilization, from which all this is made, and this is perhaps the most important, especially since now is the period of globalization.
By the way, Swiss science is very closely connected with Russian. Our first scientists were Swiss: both the Bernoulli brothers and Euler. And the famous shape of the loopholes of the Kremlin walls was also invented by the Swiss. By the way, in the 19th century, a lot of students of Swiss universities were from Russia. Because in our country women could not go to university, they went there - it was both cheaper and a good education. Again, Jews, and for political reasons too.
Vladimir Ilyich...
If I understand correctly, he didn't finish anything there. By the way, I was told that in 1917 he was put into a sealed wagon by a convoy under the command of Michel Plancherel, a famous mathematician, but I could not verify this. But, let's say, my scientific ancestor Shatunovsky (through the chain of scientific supervisors Fikhtengolts - Kantorovich - Khavin - Nikolsky - Makarov) studied in Switzerland. At some point, I accidentally stumbled upon the complete lists of students of the University of Geneva of past years and tried to find him there. I didn’t find it - apparently, he was at another university where complete lists were not published. But then I was just struck by the fact that these lists contain a huge number of Russian names, especially female ones. Why Sofya Kovalevskaya had to leave - because in Russia she could not study or work at the university. That is, about Switzerland and Swiss science, I also use the word “ours”. About the USA and Sweden, when he lived there, he did the same.
- I asked everything.
“We didn’t talk much about science, you all wanted to gossip, but you scolded my science.
“Gossip, by the way, has created altruism in human society. Because altruistic behavior can only exist in a society where there is an institution of reputation. And it is supported exclusively by gossip.
Stanislav Smirnov
Interviewed by Mikhail Gelfand
Photo by Evgeny Gurko
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Stanislav Konstantinovich Smirnov(genus. September 3 , Leningrad , the USSR) - Russian mathematician, Fields Medal winner(2010) , is a member of the Public Council under the Ministry of Education and Science (2012) . With 2003 Professor University of Geneva.
Biography
Like a winner international olympiad enrolled without exams Faculty of Mathematics and Mechanics, St. Petersburg State University, who graduated in 1992 (supervisor - Viktor Petrovich Khavin).
After graduating from St. Petersburg State University, he was invited Nikolai Georgievich Makarov(whose course he listened to) to graduate school at, where in 1996 he defended doctoral dissertation. Trained in Yale University, worked for some time Princeton() and in Bonn ( ( German )).
In 2010, he won a mega-grant from Ministry of Education and Science, within which St. Petersburg State University allocated 95 million rubles for the creation of a laboratory.
His wife Tatyana Smirnova-Nagnibeda, whom he met back in a mathematical circle, is also a mathematician, a professor at the University of Geneva. He is raising his daughter Alexandra (2002) and son Nikolai (2006).
Scientific contribution
The most famous works of Smirnov are in the field of limiting behavior of two-dimensional lattice models: percolations and Ising models. In particular, proof Cardi's formulas for percolations on a triangular lattice, proof of conformal invariance for various two-dimensional models, proof of the connection constant conjecture for a hexagonal lattice.
Prizes and awards
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Notes
- . Polit.RU (August 19, 2010). Retrieved August 19, 2010. .
- (English) . International Congress of Mathematicians 2010. Retrieved August 19, 2010.
- . Retrieved August 7, 2012. .
- (English) . International Mathematical Olympiad. Retrieved August 19, 2010. .
- Smirnov, Stanislav K. (1996) Dissertation (Ph.D.), California Institute of Technology.
- . lenta.ru. Retrieved May 29, 2012. .
- . fontanka.ru. Retrieved May 29, 2012. .
- (English) . Retrieved August 19, 2010. .
- Hugo Duminil-Copin, Stanislav Smirnov. The connective constant of the honeycomb lattice equals Unable to parse expression (executable file
texvcnot found; See math/README for setup help.): \sqrt(2+\sqrt2)// Annals of Mathematics. - 2012. - Vol. 175, no. 3. - P. 1653-1665. - arXiv :1007.0575 . - DOI :. . - Harry Kesten.(eng.) (pdf). ICM. Retrieved 22 August 2010. .
- Julie Rehmeyer.(eng.) (pdf). ICM. Retrieved 22 August 2010. .
- . Polit.RU (August 19, 2010). Retrieved May 19, 2012. .
Links
- . "Our newspaper" (Switzerland). Retrieved 24 September 2013.
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About roots
I have a quite typical Leningrad, Petersburg family. I grew up with my mother and her parents. Grandfather was a professor at the Military Mechanical Institute and a very good design scientist. I think he instilled in me a craving for science and engineering. Grandma was a paramedic besieged Leningrad, most carried out blockades in the city. The second grandfather worked in the criminal investigation department, during the war he commanded a police company that fought on the Nevsky Piglet, where many people died. My father's mother is a military doctor, major, surgeon, she went through Khalkhin Gol, the Finnish campaign, and the Great Patriotic War.
Stanislav Konstantinovich Smirnov
Officially
Mathematician, Fields Medal winner. Born on September 3, 1970 in Leningrad. Twice - in 1986 and 1987 - he became the winner of the International Mathematical Olympiad. In 1992, Smirnov graduated from the Faculty of Mathematics and Mechanics of St. Petersburg State University, then - postgraduate studies at the California Institute of Technology, where he received doctoral degree. He completed an internship at Yale University, worked for some time at the Institute for Advanced Study (Princeton) and the Max Planck Institute for Mathematics (Bonn). In 2001, Smirnov was appointed professor at the Royal Institute of Technology in Stockholm, doing research at the Royal Swedish Academy of Sciences. Since 2003 he has been a professor at the University of Geneva.
In 2010, Stanislav Smirnov was awarded one of the most prestigious mathematical awards - the Fields Prize. In the same year, he won a mega-grant from the Ministry of Education and Science of the Russian Federation: 95 million rubles were allocated for the creation of a laboratory under the leadership of Smirnov at St. Petersburg State University. Among his awards: Prize of the St. Petersburg Mathematical Society (1997), Prize Mathematical Institute Clay Prize (2001), Salem Prize (2001), Gran Gustafson Prize (2001), Rollo Davidson Prize (2002), European Mathematical Society Prize (2004). Smirnov is co-chairman of the Public Council under the Russian Ministry of Education and Science.
Married, has two children.
Mom was an engineer, then worked as a programmer. Dad was an experimental physicist. Both had mathematical ability, and in this sense, I think I took a lot from my parents. Psychologically, emotionally, of course, I am my mother's son, my character is all in her - serious and a little stubborn.
About childhood
I don’t really remember myself at an early age - I have a pretty bad memory. Leo Tolstoy wrote that he remembers how he was swaddled, but I hardly remember primary school. Maybe that's why I became a mathematician: in mathematics, you can not remember a lot - everything is derived from primary principles, if you think about it, of course. Unlike, say, chemistry or medicine, where you have to memorize a lot.
I was not brought up strictly, although I was rather hooligan and, perhaps, capricious. Sometimes such ... jokes were joking. Once, before classes, I changed the material for my grandfather - instead of one lecture, I put another one. I was scolded, although I probably should have been punished. But in the family everyone was very kind, they did not punish.
About teaching
Today they often say that we have a collapse, horror, horror with education. But this is a global problem, primarily because children have changed. For example, concentration of attention has decreased, children cannot focus on one subject for a long time, they are distracted. Previously, they were asked to read and retell a seven-page story - and it was easy for the child, but now he cannot sit through the end of the story. On the other hand, modern children switch faster, can do several things at the same time: write a text message, talk to a friend, and listen to music with the other ear. Children have not become worse or better, they are just for recent decades changed more than in previous centuries.
There is another side. Society is changing, its educational needs are changing. Now everyone has calculators, and the question arises: should children be taught to count? Yes, because mental counting is still useful, and it lays down the skills for further study of algebra. And most importantly, this is gymnastics for the mind - squats while exercising are useful, including for those who do not have to squat at work.
So the difficulty with school education exists in most countries. For example, on the one hand, all more people receives higher education On the other hand, more and more students are coming to the end of school without having mastered the program. We teach them logarithms, but they have not learned how to add fractions in a good way. Of course, they are trying to solve these problems, but this is not a matter of one year. In Russia, I was a member of the working group on new concept mathematics education. Why did you decide to start discussing changes in the educational system with mathematics? Even the ancient Greeks believed that the art of thinking and reasoning is best trained in mathematics, since it has black or white, proven or not proven - the correctness of reasoning can always be verified. That is why mathematics runs through all school curriculum as a carrier, along with the native language and literature. And the goal of mathematics as a school subject has not changed in 2,000 years. What they do in the classroom and how they do it should change. I would say that the main thing in this process is the solution of problems, the development creativity and, of course, the individualization of education. In Russia, by the way, there is a good start - our system of out-of-school work with gifted children is unique in many respects, there was no such experience of circle work anywhere in the world. So this tradition exists.
If we talk about Russian schools in general, then, in my opinion, we have a percentage good schools no less than in other countries. But yes, there are many bad ones, and we need to work with them. I would say that the main problem of our education is with universities. The university system over the past 25 years has lagged behind in many respects, many scientists have left or gone into business, and a generational gap has formed. But, working at St Petersburg University, I am quite optimistic. Current students- more active and so ... looking ahead. I think in 10 years the situation will improve. It is only necessary to restore the prestige of science in society, create competitive conditions for scientists and teachers, a long-term perspective.
About friendship
I think most of my friends are from my school and student years. New ones, of course, appear, but most are from those times. I graduated from the university in 1992 and went to graduate school at the California Institute of Technology. I didn’t intend to leave for good, they offered it unexpectedly, but here there were problems with places, and I decided to go, for three years. And when he graduated, no one needed scientists in Russia at all. So my generation fell into an interesting, but such... turbulent time. Classmates and classmates swept away. Some of my good friends are in St. Petersburg, some are scattered from Canada to Great Britain. What unites them? They are smart for the most part. It is interesting with them, you learn something new from them, they have a sense of humor. But life is twitchy, leaving little time for communication, so we see each other less often than we would like. Skype? No, I do not like Skype, there is something fake in it.
About love
Pros and cons
Most of the 40 people who received government mega-grants are world-famous scientists... For example, Fields Prize winner mathematician Stanislav Smirnov... According to the program, a person must create a world-class scientific unit. Learn our young specialists, publish the required number of articles in reputable journals. Then this scientist can leave, and his "apprentices" will continue to work, start their projects. The main thing is that they will have the same positive model, an example to follow.
Konstantin Severinov, biologist, runs laboratories in the US and Russia, December 2010
Talented students go abroad very often. My second Fields winner, Stas Smirnov, works in Switzerland. He comes here for four months a year, distributes the money to his laboratory in Russia. But he cannot create educational system, a scientific school for the country ... I have no moral right to reproach, you can only teach more people. Because at least the middle peasants will stay here.
Sergei Rukshin, mathematician, among his students - Stanislav Smirnov and Grigory Perelman, November 2013
Tatyana and I studied in the same group, but she was in graduate school in Geneva, and I was in Pasadena, California. Then both I and she found work in Europe. We both do math, but a little different areas. In principle, they intersect: Tatyana laughs that we should write some scientific article together. Of course, the fact that we both work at the university has positive sides. A similar mode of life, such as a big vacation. A similar approach to life is curiosity, all that. In general, Tatyana wonderful person. I think more wonderful than me. She treats other people better, she is much more open man, Well beautiful person and I love her very much. But in general, better love do not analyze, otherwise it will be too mathematical.
About success
When they gave me the award, at home, of course, everyone was happy, especially the children - they even boasted at school. I can’t say that it was a big surprise, I was told about such a possibility. But they could not give - there are many good mathematicians who deserve it no less. And this is probably unfair to someone, because the award greatly changes life. Maybe she would have been better off changing someone else's life. How does it change? Not money, of course, 15 thousand Canadian dollars is not an astronomical amount. It changes that you are listened to more, there are more responsibilities in relation to your community. I became more involved in many near-scientific and administrative things. It's hard to say if it's a success or not. There are two aspects to my work that I like. The first is teaching: it's nice to teach and it's nice when your students achieve more than you yourself. Second - scientific work: the satisfaction of curiosity when trying to solve a problem that no one has yet solved. And it’s an absolutely wonderful feeling when you thought and thought, worked for three years, and suddenly you realize that all the components are there, you just need to insert one piece of the puzzle and everything adds up in an instant! Of course, then it often takes months to write down the proof on many pages. But this moment of insight is very pleasant when you find hidden harmony. And it's nice to discuss it with others later, not just to brag, but simply: "Look, how interesting everything is arranged." That's how I see success: making discoveries, proving theorems, teaching well. A bonus is an external sign, a formal one. I love science even without it.
About freedom
I was born and raised in St. Petersburg-Leningrad, I feel Russian, even Soviet man. And I think that, by and large, I'm free. Although I often do not use this freedom - I do what is expected of me, what I must, and not what I could. But with the concept of "freedom" now all over the world there are some problems, take at least the cartoons in the French weekly "Charlie" or demonstrations against the Islamization of Germany. It seems to me that there is a crisis with the understanding of freedom. On the one hand, it is necessary to have absolute freedom On the other hand, people do not always use it wisely. Even look at Switzerland, which is rightly proud of its traditions of freedom and direct democracy: it doesn't always work there either. A year ago, an ultra-right party put to a referendum the issue of limiting the influx of foreigners from the EU countries. They did not even expect to win - they just wanted to raise their popularity with xenophobic advertising, but they accidentally won. So what? The country has great economic and political difficulties with all its neighbors just because 50.5 percent voted for some nonsense. That is, freedom and democracy are also the ability to make a choice, having understood the situation. So if there are problems in countries with centuries-old traditions, then it is difficult to expect that everything will work here soon. But you need to strive for it.
I don't really believe in organized religion - I think it should be personal and not public question. And here I am very scared that we have in recent times identify spirituality with religiosity, and religion breaks through into public life. As a scientist, I see that there is a lot of order in the world, it is interesting, complex and beautiful. Does it follow from this that there is some higher authority? Not necessary. And, perhaps, we will never know, although it would, of course, be very interesting. In mathematics, too, there are insanely beautiful structures that, as many philosophers believe, exist independently of us - we simply describe them, and do not invent them ourselves. But this is not an argument that there is something from above—beautiful and complex things often spring from very simple principles.
About fear
Most of all, of course, I'm afraid that something will happen to the children, pah-pah. As for the rest, thank God, I have such a profession that I don’t have any special fears. Well, what can happen? What did I teach the students wrong, but they noticed it? Or did he publish something wrong in a magazine and disgrace himself? Well, it happens eventually. "Have I forgotten the flash drive with the report at home?" It happens, but it's not fear. And the fear of not proving the theorem that you have taken on, no one will know about it. The question here is how high you set the bar. You can set it so that you will always jump over: write an article once a week, but the articles will be simple and not very interesting. And you can put it in such a way that you will jump over only in one case out of two. I worked for a year - it didn’t work out, in the second year - it worked out. I spent a third of my time on one task for 10 years - and did not solve it. But my friend says he did not "spend" time, but "invested" - suddenly it will come in handy. So it's not scary either. Of course, there are several questions in mathematics and in science in general, to which it would be very interesting to know the answer, and sometimes it is scary that neither we nor the next generations of scientists will ever know this answer. Was it all in vain?
About money
What is money to me? I don't think the thing paramount importance, although, of course, I wanted them to be enough. Today I like most of all, probably, to spend on books. What would I buy if I suddenly had a lot of money? I don't know... for example, a dacha on the shore of the Gulf of Finland, I spent a lot of time there as a child. Yes, on any scale you can think of how interesting to spend. If there are millions, let's say, I would buy Bosch or Brueghel Sr. in the Hermitage. Your home? No, it’s somehow uninteresting to go home, it’s better to go to a museum. Although, if there is twice as much money, you can have a second home. If there were a billion, I would organize an expedition to Mars. No, a billion is not enough, you probably need ten. We stopped in space exploration, and this important thing You can't live on the same Earth for millions of years. In general, there are many important scientific projects that have no immediate practical benefit and therefore do not find state funding. Some are lucky: the recent mission of the Rosetta apparatus to a comet is an amazing achievement of scientists and engineers. But there are many other projects in space exploration, physics and biology. For example, how our brain works - I would like to understand. On the curiosity of money is not a pity.
About children
Alexandra is 12, Nikolai is 8. Alexandra was born in St. Petersburg, on Vasilyevsky Island, and Nikolai was born in Geneva. For the last 5 years they have been living roughly halfway between Switzerland and Russia. Both there and there they go to school, they speak Russian quite normally, French, maybe a little worse. They associate themselves very much with both St. Petersburg and Geneva. Their generation already perceives the world globally and can say: I like Russia, but I can go to work in London or Rio. I want them to have an interesting life, but how exactly it will turn out is unknown, a lot of accidents affect our fate ... And an interesting life can be lived by the most different ways. The main thing is that they are very joyful and happy, I hope they will remain so.
Three words about myself
I am a rather talkative person, I talk a lot and loudly. You know, Norbert Wiener was once asked who a professor is, and he said that he is a person who can speak without preparation on any topic for exactly 45 minutes. I still can’t say that I’m conflicted, but sometimes I want to bang my fist on the table. I am irritable, sometimes I argue in vain - I am dissatisfied with this, but I do not control it well. I'm also smart, I guess. Not stupid, so to speak. Talented? This is from a slightly different area. You can be smart in one sense and stupid in another. I hope I'm not stupid in most ways.
