JOST A MON

The third meeting

Venue – Independent University of Moscow. November 2002.

There were three of us in the meeting with Laurent Lafforgue, with the interpreter Darya Sisoeva helping out.

OO: Monsieur Lafforgue, you are well-known as a patriot of French culture and language. You know several languages, including Russian, and have always defended the right of mathematicians to communicate in scientific circles in their native tongues. This position – is it the result of reflection, or a fruit of family upbringing?

LL: Since childhood, books have been the most important part of my life. From early on, I began to read not only French but also Russian literature. In fact, till I was about twenty years old, my main occupation was literature. I was also interested in history, which kindled in me an interest in other cultures. I didn’t plan on taking up mathematics as a career. I had a very good education, and I had a wide ranges of choices on what to do next. But I’m Parisian, and I wanted to remain in Paris, and so at the age of 19, I joined the École Normale Supérieure– the best school for mathematics and physics, completely unaware of my future career as a researcher. Only in the second year did I realise that I was attracted so much to mathematics. I began to read the works of Grothendieck – he is a French mathematician, and founder of algebraic geometry. That’s when I began my interest in algebraic geometry, because I found in it the sort of beauty that had always appealed to me in literature. I have always thought that in mathematics there’s a deep link to literature, just as with history. After all, mathematics is a collective endeavour. And if I count for something in mathematics, then surely I count for something in the historical process as well.

OO: Is there anyone you would like to share your success with?

LL: Certainly. There are people who supported me in my most difficult moments. In addition, having spent six years at University and in graduate school, when I was unable to write my thesis, I was admitted into a research group with some fellow investigators. Still, for two years I had no serious results to show. I was getting paid, but I just couldn’t complete my dissertation. This wasn’t the best time of my life. But the head of my group, Luc Illusie, not only believed in me but also took charge of my situation, and offered to change my supervisor. Now I understand that I just wasn’t interested in working on old themes. If you don’t like what you are doing, you can’t come up with any beauty in your work. Thus I got a new supervisor, Gerard Laumon,  who then took charge of my fate.

He gave me a new topic, and things improved – I began to get good results. My supervisor, despite being a famous mathematician, took a lot of interest in me, uncaring of his own time. I owe him personally no less than I do professionally.  And the next topic, the one for which I won the prize, was one he founded. But even here, things were not simple. I worked on the subject for six years, and as my research concluded and I began to present expository lectures on my work, I realised that I had somewhere along the line committed an error.

This was a deeply tragic moment in my work, because the error cast doubt on my entire research. I have to say that at that time not only my supervisor, but also all my colleagues at University understood the gravity of the situation that I found myself in, and all of them supported me. All of them.

OO: Are you from an academic family?

LL: My grandparents were uneducated, and my parents are physicists. I have two younger brothers, both of whom are mathematicians. One is a researcher, and the other a teacher.

OO: In earlier times, during the USSR, there were widely distributed scientific family dynasties. Following a career in science didn’t bring much by way of material gain, but much honour and respect. But in the last fifteen years, the situation has changed dramatically. How does a mathematician feel about himself in France? Is there a problem of ‘brain drain’ in your country?

LL: French scientists receive good money, albeit less than in the US, but overall they do lead good lives. Importantly, in France we have very strong mathematical schools and many famous universities. There isn’t much of a brain drain because the majority of French mathematicians want to work in their own country. Nor is there much unemployment because there are lots of places open to researchers. So we have not only Russian mathematicians visiting us, but also Americans. They are happy to lose monetarily because they are attracted by the high scientific level.

Undoubtedly, France has not been unaffected by the changes that have occurred throughout the world: the undervaluing of intellectual capability. Our youth prefers to entertain itself. They prefer sport or show-business, anything other than science. And that’s a pity. Young people do not want to occupy themselves with anything intellectual because there are no guarantees of any material fortune. But I have always sought beauty. In the beginning, in literature and poetry, then in history. I realised very late that in mathematics too there is an equal beauty. If you work in the fields of scientific discovery, this is always interesting. I felt this most keenly in the university when all around me were so many bright people, all of whom were inventing, discovering something new.

OO: In Russia, we have a joke: “An American university is where Russian instructors teach mathematics to Chinese students.” Don’t you think that in coming years, Russia might stop supplying mathematical brainpower, and the arena will be left open to that other scientific superpower, namely China?

LL: Of course, having been in Beijing, I am able to assess the level of state support for science. But I think such pessimistic forecasts are premature. In Russia, despite the poor funding for science, mathematics cannot really die out – after all, for seventy years, the Russian school has been the strongest. And other countries, too, won’t let Russian mathematics die out. For example, the Independent Mathematical Institute where we are now has been financed by the US.

OO: Our interview with Vladimir Voevodsky ended with his apocalyptic predictions about the future of mathematics in general as a fundamental science. In this regard, are you an optimist or a pessimist?

LL: As you prefer… Voevodsky is a representative of the American mathematical scholarship. That is a completely different world; true, they are paid a lot, but intellect in the US has never been particularly valued. My prognosis is more optimistic. Science with such a long history cannot die, and people will continue their researches. On my own part, I have two themes that will over the next thirty years interest a lot of people.

OO: Are you ready to return to this debate in thirty years?

LL: If we live that long.

[I translated loosely from Olga Orlova's piece on Polit.Ru. It appears that in 2002, when she first wrote it up to link with the International Congress of Mathematicians at Beijing, the journal that had commissioned it, 'New Model', went out of business without publishing it. She and her editors decided that the content was still relevant in 2006, when the Perelman story was appearing in the world's press in the run-up to the ICM in Madrid. The previous parts are here and here.]

The second meeting

Venue – A Moscow Kitchen. October 2002.

Vladimir Voevodsky came to the interview not alone, announcing from the entrance that his prize should be shared with three people, of whom he couldn’t bring along the first and the third, but he had managed to snare the second.

VV: Let me introduce you: this is Yuri Shabat, Professor at the Moscow State University. If I make a mistake in something, he’ll correct me.

OO: And who is the first person?

VV: Well, actually even before him were the dinosaurs. When I was really little, I loved dinosaurs. And then books on chemistry began to fall into my hands; my mum brought them, she was a chemist. From theory I soon moved onto practice, and there were explosions in the bathroom, after which there were experiments with electricity, and then, going backwards, theoretical physics, which my father, a physicist, introduced me to. When I was seriously ill with pneumonia, my father’s friend Oleg Sheremetyev brought me a Rubik’s cube to distract me. There were no published solutions to the puzzle at the time, and I killed two days to crack it on my own. And then Oleg and I went on to solve more complicated mathematical puzzles. Oleg used to spend much time those days teaching mathematics to kids at the Pioneers Palace. He was the first to show me that mathematics could be interesting of itself, in a very pure sense.

OO: Volodya, you finished high school but you do not have a degree. Does that mean, by Russian standards, that you are under-educated?

VV: I was rusticated from Moscow University for academic failure. I was already interested in algebraic geometry, but attending classes seemed like such a waste of time. I took a break from academics, and began an apprenticeship at a vocational school where kids were being taught programming. One day, I found some scrap paper on a table with formulae scribbled over it – and immediately realised that there was someone around who thought just like me. I was overjoyed and went in search of the owner of that paper. And that’s how I found Yura Shabat. He didn’t deny it. “Yes,” he said, “These are my papers. So what?” Well, I said, I have also been thinking along those lines. It was very important to me that I had found him.

YS: Yes, and after that, we worked for a long time together.

OO: So what attracted you to algebraic geometry?

VV: Purely subjective factors, I have to say. At the time, algebraic geometry was being done by interesting people, such as Shafarevich.

OO: And how did the move to America come about?

VV: Even after returning to academics, I still wouldn’t attend classes. In 1989, then, obviously, everything collapsed, and such formalities as degrees seemed quite useless. After Yura Shabat, I began to work with Misha Kapranov, and we published several papers. Then he went off to graduate school in the States, talked about our work, and thanks to him, I became a graduate student at Harvard.

OO: Your relationship with America, it appears, was not entirely idyllic?

VV: To be honest, America impressed me at once. On the very first day I arrived at Harvard, I was handed keys to an apartment, to an office, and a cheque for a thousand dollars. And I was a mere graduate student! At the time, there were many Russian mathematicians on the faculty. Dmitri Kazhdan was Dean. I need to share my prize with him as well.  He and his colleagues supported me at a period when I could no longer live in Russia, and I was still new to America. I remember, during my first Christmas in Boston, I got drunk and wandered into a black ghetto. There I was robbed, beaten and hurled into the snow. This, of course, added to my discomfort; but I was deeply anguished, missing Moscow, and thinking how much I hated their Christmas. I wanted my New Year [My note: Russians celebrate New Year rather than Christmas], with a fir tree and my mum and presents. I went to Professor Joseph Bernstein, and said to him – I can’t stay here. He answered me in one sentence, “Well, if it’s so bad for you here, then go home.” I am eternally grateful to him for this. I went to Moscow for four months, and he covered up for me, saved my fellowship and stipend. Then I returned and lived for a few months in my office, writing up my dissertation quickly. When I went in the mornings to brush my teeth in my sweat-pants, students would be coming into the department and looking askance at me. But Dean Kazhdan gave me the possibility to complete my work in peace. So I got my doctorate, but without any college degree either from Russia or America.

OO: Was such an option open to you in Russia?

VV: Formally, it wasn’t prohibited, but it is clear that the entire procedure would have been much harder, and taken much longer. There have been earlier precedents, but in my opinion, perhaps more often in the pre-war days than today.

OO: Setting aside material comforts, what distinguishes a scientist’s life in Russia from that in America?

VV: Everything. It’s a different professional environment. In my own field, there are ten times as many people working in America. There is the corresponding level of competition. In Russia there is no direct relationship between a scientist’s academic success and financial situation. If a person is comes up with an extraordinary idea, then everybody says, ‘Praise God, we are happy,’ but his salary is not going to go up from tomorrow. In America, it is likely to increase; but if you prove something interesting with your colleagues, at once the question arises – who did what first? Because the prizes have to be divided. In Russia, when people think up the same idea simultaneously, it is rather nice. There’s a professional collegiality. But in the US, this would decrease the material consequences of a scientific achievement. Although I have to say that in mathematics this is not as strongly felt as in biology, chemistry or medicine.

OO: Besides science, you have always had a wide range of interests. You have travelled the world, kept up your interest in history, followed politics. You live in the US, your wife is Egyptian, and you have friends of various religious persuasions. You have, perhaps, a nuanced view of events in the world.

VV: Undoubtedly, I have a cosmopolitan regard of current events as I do constantly listen to views of people from different sides of the barricades. And it is not difficult for me to note that not all of them are true. No less, it is evident nuclear weapons that used to be so difficult to obtain, will become quite common. And I don’t see any reasons that can stop those people who want to use them. Clearly, nuclear war awaits us in the coming decades. On the other hand, in American scientific journals, such as Science, I regularly read that its consequences are not as scary as we might imagine.

OO: Well, thanks for the consoling thought… And what will happen to mathematics in these projections?

VV: Nothing good is going to happen to mathematics, even if there’s no nuclear war in the near future. Mathematics has developed over a long time with lots of intensive research. But today’s mathematics requires immensely larger resources: of people, time, and money. You understand, in modern science we have a situation where the amount of time a person has to spend just to bring himself up to speed with an open problem is unacceptably long. I cannot explain - even to a very good student in his final year at University – the details of my work! Today, new people find it harder and harder to engage in the scientific process. I think it’s a bad sign. If mathematics does not turn to the practical needs of mankind, in fifty years it will no longer be in any form we can recognise.

YS: Well, here I’d like to object. I am well acquainted with the history of mathematics, and can say that apocalyptic predictions of its demise are not new. But mathematics, paradoxically, has always evolved in an irrational fashion. Its history is very similar to that of poetry. In some periods there is a crisis, and then there’s a period of barely discernible development in new directions, and then there’s a powerful creative explosion. Forecasting this systematically is impossible. I think than in fifty years mathematics will still exist as a fully-fledged science.

VV: Shall we bet on it? Let’s meet in thirty years, say, and examine the situation. We won’t wait fifty years – who knows if we’ll live that long?

Vladimir and Yuri made the wager, I excused myself. Time passed.

[To be continued.]

[I translated loosely from Olga Orlova's piece on Polit.Ru. It appears that in 2002, when she first wrote it up to link with the International Congress of Mathematicians at Beijing, the journal that had commissioned it, 'New Model', went out of business without publishing it. She and her editors decided that the content was still relevant in 2006, when the Perelman story was appearing in the world's press in the run-up to the ICM in Madrid. The first part is here.]