To begin in the beginning, you were born in a difficult time and place.

Can you tell me a little bit about the circumstances of your family when you were a child? I was born in the summer of 1978. That was just before the revolution, the Iranian revolution. So even before the revolution, the situation was not very peaceful.

It was not very stable, a bit chaotic. So I was born in a village, the village name is Ne, just N-E, which is not very far away from the local town, which is called Meriwan. At that time, the town was actually pretty small, but later got much bigger.

So where I lived in the village, life was basically very traditional. And the main means of people living was agriculture, basically. And that's what my parents, my ancestors, had been doing for a very long time.

Their own land? Their own land. So we have different plots of land in different areas. Basically all close to the village. And we used to go to work on this plots of land every day. So we used to go to different plots, just depending on what we had to do.

And my grandfather, he could read and write. And my uncle, I think, maybe was the first person who entered school. More than any sort? School in a modern sense. I mean, there was traditional school, which was more like attached to the religious institutions.

Yes. But I think my uncle was the first person in the family who entered modern style school. And after that... So not long after I was born, just a couple of years later, there was the Iran-Iraq war. And that lasted for eight years, which basically covered all my primary school education.

And even at a certain point, we had to leave the village and immigrate to some other places. So my hometown was right on the border of Iran and Iraq. And that meant that we were an easy target for especially aerial threats.

Because of the mountains, land invasion was very difficult from a military point of view. But aerial threats like airplanes or shelling and all kind of aerial bombs was really very easy for them. Because the town was so close to the border. Even you can walk to the border just like one hour, basically.

Were there Kurdish people and you were one? Kurdish assumed to be particularly loyal to one side or the other? No, in a way that was also a painful aspect of the war. Because it wasn't really our war. It had absolutely nothing to do with the Kurdish issue.

The Kurdish issue has a long history, especially in the last 100 years. It's a very complicated thing in the region. But that Iran-Iraq war didn't have anything to do with the Kurdish issue. So we were just being killed basically for reasons. Yes, but not active participants.

No, I mean the thing is that parallel to that also there was more or less another war. Which was between the Kurdish forces, outlawed forces and the Iranian government. And on the other side of the border also between the Kurdish forces and the Iraqi government.

So it was a quite complicated thing. And that one had to do more with the Kurdish issue. In your family, just to place you, how many children are you? Which order? Where do you come in the family? The children? Are you the first child? Are you the third child?

No, we are six children. I have four brothers and one sister and I am the third child. And a third brother? I have one older brother, I have an older sister, so I am the second boy. What are the conditions of the possibility of an education in a time of war?

There are schools, so all the time. I think maybe just except the time when we had to just leave the village and go away. Otherwise there always was school. But the thing is that in that kind of situation you just can't get a proper education.

It's just very hard. So I remember so many times that we were sitting in the classroom and then suddenly the airplane would come and just we had to run out for our lives. Run to the mountain basically. And then the schools were, there weren't much in the school really.

Just was the building and the blackboard and the teacher and the student. That's basically it. Even didn't have adequate heating. In the sense of equipment there are almost nothing really. There are so little. And the teachers, I should say that I am grateful to all the teachers in my whole life

who did their best to educate, especially in such a difficult situation. But at the end of the day, the truth is that compared to what you get a reasonable education in the West, what I got was really very inadequate, you know.

The child, as he's growing up, let's put you at eight, shows a talent in something, shows curiosity, shows an inclination in some way or the other. Are they seeing that they have a clever young fellow in the family?

How is your mind beginning to develop and your curiosity? So in my case it really had a lot more to do with the family, especially my older brother, than with the school itself. As I said, the school wasn't really, the whole system was under such difficult circumstances, it wasn't really just good enough to induce that kind of idea in children.

Especially I should also mention that, for example, beating was very common at the time. So until I was 14, I had been beaten, I don't know, maybe, at the time. It was completely illegal to beat, the teachers could beat children physically, I mean with a stick.

For behavior, for getting an answer wrong. Both, both are both, yes. And then of course it's difficult to motivate people. Another thing is that before I entered school, like almost everyone else,

we had absolutely no preparation, there was no even no nursery, so I never attended a nursery. And then once I entered school, I had to study in a different language. It's of course Persian is related to Kurdish, which as like Italian is related to French. So the school was in Farsi.

School was in Farsi, but for us it was just a little different. That was not a problem at least. It was a problem, we had no idea. In my time, before I entered school, I think I didn't know maybe one single word in Farsi, except the common word between Farsi and Kurdish. So it's difficult for children in that kind of circumstances to just start education.

So I'm not seeing a future Cambridge dawn yet. What did your brother do to stimulate your mind in the face of this difficult political situation, difficult schooling framework?

Where does your mind begin to take off? So my brother in a way was really very unique, and I'm extremely lucky to have a person like that around me. He was just so different from everyone else. He was extremely creative. He would do things at that time of war and chaos that no one else was even thinking about.

He just loved building things, making things, designing new things, and he just had this passion for doing, inventing things. That was just somehow out of the place.

For example, I remember once he built a projector, this old-style projector that was in cinema a long time ago. He built a projector himself. He even did an animation, and then he gathered a bunch of children in a basement and he showed us this movie that he made.

You don't have to be a genius to do that, but just to think of doing it, that was the key, I think. He did a lot of this sort of thing, and not surprisingly, later on he became an engineer. So I think that was, in a way, as far as my education is concerned, that's the genesis.

That's the guy who pushed me toward. Was it math in particular that was beginning to emerge as an interest, or he was educating you at home and almost everything? It wasn't like a formal education. He was doing something and I was just curious and I was interested in the things that he was doing.

It wasn't so much about mathematics, at least in the beginning. But later on, after primary school, then it became more mathematical and physical. I remember he used to try to teach me when I was maybe 11, 12.

I like calculus, some primitive, easy kind of elementary physics. So that was more, a little bit more formal. But still, there was no pressure or push. He didn't tell me, you have to sit down and do this and that. He just tried to make it interesting, to tell me that this is something actually interesting.

And you responded? I responded. We'll call him your first teacher, your first real teacher. Who is your second? Is there a time as school progresses where you find the beginning of a mentor,

or somebody else who then takes you to the next level, at secondary school perhaps? No, unfortunately, I probably have to wait another, until I started to do PhD. Really? I met a lot of interesting people. Yes, of course. We have nice teachers and so on. But in the sense of influence, I think there wasn't really much.

Especially in high school, I was, you could say, completely isolated from the rest of the world. But you don't get to a PhD without stages before. There has to be some point where preparation happens, where at least you prepare yourself.

How does that happen? I think in my whole education, my high school is probably the most important, in a way it sticks out. So after my brother tried to teach me things, then he entered university and I entered high school. In a way, we kind of got separated. By that time, I already had developed a passion for physics and mathematics.

First, I liked physics more, but then when I studied more and more, I realized that I actually like physics mainly just because of the mathematics. It's just because mathematics is the language. And then I tried to follow mathematics more seriously.

And there are people there to help you? I mean, really? Absolutely not. Absolutely not. I was completely isolated. So books, are there books you pull from the library? Yes. How do you educate yourself? Exactly, the books. The only thing really I had to rely on was the book.

So there are the local library, not even the school library. For some reason, for some strange reason, there were really, really many nice books about mathematics. And not surprisingly, for many of them, I was maybe the only or the first person who actually picked them up from the library.

Especially, there was a book about the lives of mathematicians. This is also actually quite famous in the West. It's called Men of Mathematics. It's a big book about the lives of all the generation of mathematicians, like 16, 17, up to first half of 20th century mathematicians.

And I read the biography of these people and I just got so much more interested in mathematics. I thought that these people spending time discovering things, creating things, it's just so interesting in a way. It's just more interesting than a completely ordinary life.

And were you optimistic about the possibility that you might join them? I mean, from your circumstance, where you were, the life you were living, you were not pessimistic about the future? You know, I was optimistic when I was young, energetic.

In fact, in high school, I already decided to become a professional mathematician. So that was when I was maybe around 16 years old. And now the thing is that I told you high school is maybe the most important stage in my education. Not only reading mathematics, so I read a lot of books in that stage.

But I also got this idea that just reading is not enough for me. It just doesn't satisfy me. I have to create also new mathematics. It's not just learning, it's being a participant in the...

Exactly. I think maybe this has to do also with my personality. I don't like so much to be a spectator. I like to also participate. So let's say when I go to a music concert, after a few minutes, I have the feeling I want to go on the stage, get a violin from the guy and say that, okay, let me play.

I don't know how to play violin, but you get that. I think I have the same exact idea for mathematics. Just to learn, just to watch what they do is not enough for me. I want to do my own mathematics. And I try to do it, in fact.

But I didn't do anything significant, but just the idea is what is really important. Now there are economics involved in education. I mean the economics of paying for a school, going on to university. I know you do go on to university, you go to Tehran University, but how is that possible?

What is the economic basis for doing so? Well, in Iran, education was free, at least at the time. It was free, so you didn't have to pay to enter university. Otherwise, I would just have not really the economic means to go to university.

As I said, my parents were farmers. In fact, in that period of, I don't know, maybe when I was ten until I left the country, I, in fact, spent a huge amount of time doing farming. Yes.

So in that high school period, especially when I was trying to read books and so on. So quite often when we had the exam tomorrow, the day before, I actually had to go and work on the farm. So we produced almost everything that we needed, but it didn't generate money. We didn't have very much cash.

But also the opportunity to go to university, even though it was free, represented you're leaving the family's place, leaving your labor, taking your labor, and going somewhere else. So this is a serious decision for the family, for you to leave to go to Tehran.

No, not really. By that time already, there were a huge number of people entering university, so it was highly encouraged to go to university. It was encouraged, and your family was behind it. Yes, of course. There was no... Anyways, from the beginning, my parents were very much trying to get us an education,

so there was no resistance at all. So they were encouraging. Okay, you go to the university. I know you passed the exams, and I know you were welcome there, because you demonstrated talent. How do you make the intellectual decisions within university?

Maybe you're already a committed mathematician, and you take the mathematics course, or do you begin with physics? So I entered pure mathematics. Pure, from the beginning. So in Iran, when you take the exam for university, you can choose many different subjects.

So in my case, I only picked pure mathematics, and nothing else. I'm going to ask you to define pure mathematics in terms of the options that were there. I mean, applied mathematics would be for engineers, something like that? So I could pick applied mathematics, pure mathematics, engineering of all kinds. I could pick all the other sciences, physics, chemistry.

So there were so many options, and people would choose maybe many different subjects, especially if they weren't sure what to do. But in my case, because I was completely sure what I wanted to do. So I picked, I had like 100 choices to make. I did pick, I think, like six, seven pure mathematics in different universities.

Maybe I'm wrong to say this, but for somebody from a poor family, it's a rather bold decision, rather than to go into one of the fields that would lead to a kind of dependable income and so forth. Yes, in fact, that's the only thing maybe that was under discussion when I entered university, before I entered.

So my family tried to say, well, if you do pure mathematics, you maybe end up with no job. Why not go to engineering? I was extremely stubborn, but in the end, my father also said, okay, no one is allowed to put him under pressure.

Just let him do whatever he likes. You were lucky in your family, very lucky, your brother, your father, your mother probably supporting you in this almost unimaginable career choice.

So there you are in Tehran at the university, you've chosen pure mathematics. Are you finding an exciting mentor there, somebody who begins to direct you in your career? Well, there were a lot more interesting courses compared to high school. There were more advanced teachers also.

There were basically professional mathematicians. That was for the first time in my life that I actually met and saw professional mathematicians. In a way, it was more interesting. I wasn't as isolated as before in high school. I was completely isolated, but not at the university.

The truth is that that experience in high school, just to read on my own and also try to do research, I just continued that into undergraduate also. So I just picked up books, I mean, beyond the lectures. For example, the first year I entered university, I just picked a book in algebraic topology and I tried to read the subject.

I could have attended a course maybe a few years later, but I just didn't want to wait for courses and so on. I just followed my interests, algebraic topology, then mathematical logic, then commutative algebra, then later on algebraic geometry.

So I talked to the professors time to time, but I think I was really very independent. Especially the third year and fourth year, I attended very little lectures. I just read my own, took the exams, and that was it.

Was this considered a problem from a traditional academic perspective, or were you encouraged, allowed, even celebrated for your independent mind? I think it wasn't allowed normally and not encouraged. But in my case, I think the professors were more relaxed.

So I remember that once one of the professors said that, okay, if this guy even doesn't attend the exam, I'm going to just give him the marks. At the end, in fact, I did not attend the exam. And he gave me not full marks, but he gave me enough to pass.

Now, the next thing that comes to mind because I've talked to a number of mathematicians in this series. Some of them were Jews in the Soviet Union. And I bring this up only because they literally found barriers to their intellectual progression simply by being Jewish in that system at that time.

Was there an ethnic problem of being Kurdish at the university, even a very intelligent young mathematician? Or was that absolutely not a factor in how you were going to progress? Well, just to enter university and get a degree, no.

That was not a factor. In fact, in a way, the system, especially the entrance examination was in a way which was very much in favor of people like me. Because it was completely computerized. So that means that there was essentially no person directly involved to have any bias.

But the thing is that indirectly, of course, there is discrimination. When you don't get a proper education in primary school or high school and so on, of course, you don't have a good chance compared to others to enter university and continue to be good. So there is indirect discrimination when there is an economic problem, when there is a political problem.

It gets much, much deeper in a sense. It's psychological. When, for example, in school, there was very, very little about Kurdish history. So naturally, we would just think that we don't have anything in our history.

In fact, only after I left Iran and came to the UK, I got more books to read and I realized how rich the Kurdish history is. But when people don't tell you that, then you just feel kind of you are maybe less than others. But that still is, I'm not minimizing it, it's tragic, still it's indirect discrimination.

But there was never a sense that it has occurred that you could not progress in the academic system if you stayed in Iran. The thing is that after you get a job and you continue, I don't know because I didn't do. But just to study, if you don't talk about politics, if you just keep quiet, then there is no problem to enter university and get a degree.

So what did you decide to, just broadly, to leave? You got your degree from Tehran University, yes? You completed the program. May I ask before we take you away from the university what the direction of your thesis was?

Or did you not have a thesis? We didn't have a thesis. So UK is going to be the next stop. You make this decision on your own to go? How do you wind up there? Just an academic aspiration?

Yes and no. You know, I had the feeling that maybe there isn't much future in the country. I mean, even if I got a degree, even if I did PhD, then, I mean, you could say that the education was good up to maybe masters, but starting from PhD then is much behind compared to the Western countries.

Right. So it was natural for a mathematician who wanted to participate in the wider world to get an education. That's why most, let's say, bright students would do, but of course there were other reasons for ending up here.

So in terms of the history of your mind, where do you wind up going for your next stage of your education? So I came to the UK. The first year in the UK I was a refugee, so basically I didn't even, I could not even choose where to live.

You couldn't choose? No. So I happened to live in Nottingham, the city of Nottingham, just because the government sent me to live in Nottingham. What happens is that they send you to a place, wait for a decision of the government to whether to give you a refugee status or not.

So in my case, you know, unfortunately that took only one year, but in fact, I know a lot of people who have been waiting for 10 years or more at the end, they even get a no. At the end of 10 years, you know, their lives are almost completely wasted.

So we count this lucky that it was just a year for you. I think it was kind of lucky, but it was also a difficult year just to wait and completely answer. I don't underestimate it. I can imagine. I can barely imagine, actually. Now, this is the right point to stop before we develop your career, your remarkable career.

If I've gotten this right, the name you use now is a translation of migrant mathematician. Is that true? Yes, basically. So after I got the refugee status in the UK, then I decided to change my name to something that really reflects me, my personality as a person.

And kochar means both, it means a migrant, but also can means like explorers, people who don't stop in one place. They go from one place to another place. And berkhara just means mathematician. So in a way, you could say it means a migrant mathematician or an explorer of the world of mathematics.

So it's kind of a dumb meaning. To me, it's a remarkable decision to change your name. Absolutely. Was your family surprised? Yeah, more or less.

Maybe they didn't like the idea, at least first, but I just thought that I should call myself something that is... That reflected who you were. Yes, not just the name someone picked for me. Okay, with the new name and the new status, you go to the next stage of university.

You already have a bachelor's. Are you admitted then into the graduate program? So during that one year that I waited for the refugee status, I talked to the mathematicians, the mathematics department in Nottingham, just informally. Even attended maybe some lectures. So there was communication with them and then they

already knew my level, how much I know and my interest and so on. But during that year, they couldn't give me a scholarship just for formal reasons. But after I got the refugee status, then they did it immediately. They already knew about me and so I just started immediately a PhD in Nottingham.

Did they respect the education you had gotten? I mean, sometimes they're snobbery, sometimes there's a sense to go back to square one and build within our system. But it was not a problem for you. No, I think, I mean, they didn't rely just on the fact that I had a bachelor degree.

But they just relied on the conversation that we had on, for example, they gave me a book to read, I read it and then it came back to them. We talked and so they had a sense of how much I'm interested in mathematics and how much I know about mathematics.

So they appreciated that. Is there a direction to the mathematics department in Nottingham, something that they favored as a community of mathematicians that may have influenced you one way or the other? So they had a relatively large group of arithmetic geometers, which is a bit close to algebraic geometry.

That was the most natural for me, the closest, because I already was interested in algebraic geometry from undergraduate days. I had decided to do algebraic geometry. So it was natural for me to go to these people. So there was a good fit, really? In a way, not exactly, because my interests were a little bit different.

Okay, explain that. I was essentially a number theorist, but I was more like trying to be a pure algebraic geometer. But they knew some algebraic geometry, especially Ivan Fesenko, who became my PhD advisor. He's a number theorist, but he in fact knows a lot about algebraic geometry.

So it was not difficult for him to at least give me some direction. But in fact, I spent a lot of time outside Nottingham during my high PhD. So I stayed in Warwick and Cambridge for six months in the first year.

I stayed five months in John Hopkins in the US. In the third year, I spent a couple of months in law school. So I was all over the place. So you were a migrant mathematician in a literal sense at this point? In a way, yeah. You're choosing places to go, presumably because of their competence in algebraic geometry.

How are you picking those times in Cambridge? Why are you going to Johns Hopkins? What are you seeking? What community of mathematicians are you in search of? So in the first year, Ivan knew what I wanted to be, an algebraic geometer.

Then he suggested that I go to a workshop in Warwick, which was for basically introducing young people, PhD students, to some part of algebraic geometry, which happened to be bi-rational geometry in my field now. And then there was a follow-up, a much longer program in Cambridge at the Newton Institute.

Ivan again suggested that I come there. In fact, they didn't even accept me to participate in the program. But finally he put a lot of pressure on me and accepted me. I just came here, rented a room, so I had no office or anything.

I just followed this program and at the end I met Shakur, my second PhD advisor. Much of this program in Cambridge that I attended was about a paper that he had written recently. And it was a very long and complicated paper.

People were trying just to understand what he was trying to do. And that paper also reads, and I tried just to make sense of it as much as I could. And then it was very natural for me to follow Shakur, which I did at the end. So I'm also very interested in the process of picking the problem, if you will,

that would define your thesis, your dissertation. So is that happening through his suggestions? Are you just exploring and do you come up with the problem that will be at the core of the dissertation? How did that work for you? So the first and second year I did it basically just on my own.

I picked the problems and I tried hard to solve them and I couldn't. Maybe not very surprisingly because the same problems are still open until now. But in the third year when I went to Hopkins I talked to Shakur and then I felt that I just didn't have enough time.

Because just one year left and then I asked him for a problem. He suggested a problem to me and then I wrote my thesis in the third year basically. Can you explain to a layman the elements of the problem and what attracted you to it? The core problem was about final varieties.

In fact, the conjecture that I solved just a couple of years ago was in a way one of the main reasons for the Fields Medal. So he told me to look at this problem. That problem itself was already known in Dimension 2. And he tried to do it in a completely different way, reprove it.

He just asked me to reprove that statement which had been proved by Alexeyev in a different language. In a way different techniques using his theory of complements. And the thing I really liked about the problem was that it was related to many other problems.

Not just one isolated thing. I think in a way that became probably one of the things that defines my work in a way. It's not just about one problem, it's about a web of problems. And just to understand how these problems are related, how they are connected, is also in a way part of the whole process.

So for the following years, for many years, I on and off worked on these problems. Not only in Dimension 2 but also in higher dimensions. In a way the notion which is central to the PhD thesis and so on is about Fano varieties.

The Fano varieties are algebraic varieties. They are algebraic geometric spaces defined by polynomial equations which have positive curvature. So for example a sphere is an example of a Fano variety. But when you go to higher dimensions they become much more complicated.

And then the problem is just to understand these varieties in higher dimensions. And the fascinating thing is that it's related, this understanding is related to so many other problems. Like termination of flips, it's related to singularities, it's related to flips and so many central notions.

Is it fair to say you're still working on some of the problems that were framed by your dissertation or have you since gone into another direction? I worked on many other problems but they are all somehow related.

Just to understand how they are connected in a way is part of the problem. I want to advance your career now, you've gotten your dissertation. Have you published before that or do you publish that dissertation?

I published on archive but I actually never published it in journal which was kind of very risky. I think I just had the feeling I wanted to do more because to publish a paper even after writing it, it actually takes a lot of time. Just to publish it and then submit a journal, you often get rejected, submitted again, it takes time.

It's not a big risk, somehow I didn't do that, instead I tried to do new things, to prove new results. You need an academic birth, you need recognition, you need a place that will accept you after your dissertation. How does that happen?

When I was a PhD, before I finished, I applied for a postdoctoral research fellowship by EPSRC, similar to NSF in the US. I got one of the fellowships for three years, so that means I could work for another three years and then after that I would worry about a child.

But in a way it was kind of a risky thing, I just didn't pay so much attention to the distant future. So you have three years before you have to worry about the distant future. What kind of inquiry happens in those three years, so to speak, when you can really just explore what you want to?

I'm always interested in the choice of the problems, the direction of the mind in this case. In a way, the problem was somehow natural for me, because as I said there is a web of problems, and then it's just a matter of which one to work on.

So even before I finished the PhD, I worked on this termination of flips, conjecture, and then the minimal model of conjecture. So much of the post-life years I spent on this kind of thing, but also again on singularities, on final varieties, and so on.

So it wasn't very hard to pick a problem, it was just whether one can solve it or not. I'm very interested, for the sake of those who are watching this, to ask, and maybe it's not answerable, your process.

How do you think? It's not just the direction you're going in terms of your interest, but are you a brooder, are you always thinking, are you isolating yourself? What's the process of research for you?

So in practice, when I pick a problem, let's say focus on a problem, usually not just one problem, but some related problem, and then maybe at each given time I pick focus on one of them. And just learn about it as much as I can. Although unfortunately in my case, the problems that were working, actually there wasn't so much

to read in the literature, that doesn't mean we have to come up with new things. Yes. So that means much of the time I spend on thinking about just maybe getting a new idea somehow, do something new.

That means of course a huge amount of time just to think, but when you focus on some problem for weeks and months, and then somehow you get into a state where then you feel maybe there is some ideas coming out. A kind of recognition that you're going in the right direction.

Well, you have to decide, but not always. Sometimes you have to, I don't know, six months and then you realize that it's just not working. Then you have to maybe go back to the beginning and take a different strategy, apply different ideas.

Again, it may be romantic of me to ask, but is there a moment, let's say in the perspective that led to your field, where you feel that yes, it can be called the eureka moment, it can be called

anything, but is there a moment or is it just the constant process and the feeling that you're in the right direction? I think there are that kind of moments, but not one or two. It just happens many times. So because that's the kind of guidance, and I suppose since you're not a student

at this point, you're a full practicing mathematician, those moments are ones you have to determine. That's your instinct that tells you that you're going in the right direction or not. So again, I can only marvel at that from outside, but I'm sure there's a guidance that your mind and gut gives you as you proceed.

But what was the basic insight and maybe complex web of insights that led to the field medal, which you only just received?

The field medal was two separate works. They were done at different times. One of them was back in 2006, jointly with Paolo Cassini, Christopher Haykin, and James McKenna.

That was about me, all models, finite generation, flips, and many things. And then the other work was about final variety, which was more related to my PhD thesis. That was done much later, in 2016. They were separated by 10 years, basically.

It's true that you need some intuition to progress. In a way, you have a feeling that maybe you are going in the right direction, and then of course you have to prove that you are going in the right direction. So you spend months, but if you don't get anywhere, then maybe it is a sign that you are not going in

the right direction. Maybe you have to go back, or at some point in the process you have to change your direction, maybe. This, in a way, is a part of the whole game, and it's not actually so easy just to decide where to give up.

I'm not remotely suspecting that it's easy. I'm assuming quite the opposite, that it's very difficult. In a way, it is part of the learning. You just need to learn this part of the profession, when you should say that it's enough. You have to go back and take a different strategy.

You said that the field was in response to two, if you will, two pockets of insights. So 2006 was the first, you are saying? And the second? So, two years ago? Two years ago, yes. At first it was before that, but it appeared in 2016.

And what was that, again, I spoke into a language, what was that insight? So this was about fun or variety. In a way, in the center of the whole thing was fun or variety. And the main problem was about showing that if you put some conditions on these

varieties, especially about their singularities, then you can prove that they form a bounded family. And that basically means that you can somehow parametrize them, you can index them just by using finitely many parameters.

I understand, yes. In a way, sometimes if you have a group of varieties and they are bounded, that means that they share many properties. Many of their environments, of their numerical data attached to them somehow are in a finite set. So it can tell you a lot about the whole family.

But as I said, it's also related to many other things. For example, related to understanding singularities, related to the so-called termination conjecture and the minimal model conjecture, related to stability of fun varieties. I think that's what I like about the problem that I work.

It's just somehow related to so many different things that I don't feel like I'm working in just one isolated problem. Right. I'm going to end with, again, an outsider's look at this question, which I've asked others, about the assumptions about youth and mathematical creativity.

I'm very struck. I don't know of any other award, there may be many, that restricts, has an age restriction. I mean, the field of metal may even be said to be the highest honor in mathematics, and the cutoff point is 40, I think.

Yes, 40. What do you think about this assumption, particularly as, I don't know what age you are now, you gave me the proof. I'm 40. Just snuck in. So that being said, I mean, do you look forward, and I say this really very lightheartedly because I know it's not true, to a life of decline, of mathematical innovation?

What is this assumption that the young are particularly prone to mathematical insight, genius? Yeah, well, of course, I can answer from my own experience because I'm just 40. I can answer 20 years later.

But I know many other mathematicians in their 50s, 60s, would do a great thing. For example, Shakurov, I think he did his best work after 40. So this is a superstition? The thing is, in a way, younger people are more energetic. It's not only mathematics, in sports, in arts, in everything.

So they're just more energetic, and maybe also when they don't have family, they have more time to do whatever they like. For example, I have my son, he was born in 2013, and I just can see how more difficult it is to work after that.

In a way, in fact, in my case, ironically, I was much more productive after he was born for whatever reason. But it's understandable. Then I have to spend also a lot of time playing with him on his development. And when you are 20, maybe you don't worry about this kind of thing.

These days, people, even in their 30s, they don't have children. So there are many practical reasons, but also just age. When you're aged, you get less maybe energetics. I think it's not particularly about mathematics, it's more about just the human life experience.

I think I like ending with your son. Thank you very much. Thank you very much.