 Today, we will be speaking to the 2015 Distinguished Salam Lecture Series speaker, Professor Don Zagir. Professor Zagir, thank you for agreeing for the interview. And my first question to you would be why you chose to speak on modular forms for this series? Well, that's very easy. It's my biggest love in mathematics. It's my own field. So, modular forms are a very special kind of function, like the sine and cosine function, much more complicated, with a huge symmetry group, incredibly beautiful properties. And in recent years, they've become important in more and more fields of mathematics, but also of mathematical physics, for instance, in string theory. And since, as far as I know, the first Salam lecturer was a mathematician rather than a physicist, I also thought it was my job to choose something that could be of interest to both schools. And because the ICTB is more physics-placed, of course, in mathematics, it's only the cousin. And what peaked your interest in mathematics? Well, nothing specific, I think. I love mathematics as a child. When I was eight or nine, I already was thinking about why the squares of odd numbers, if you subtracted one, you could always divide by eight, and I didn't know why that was when I was seven, but I discovered it for myself. But I also liked history at school and French and physics. I liked everything except German, which later I went to Germany and had lived there for most of my life as punishment. So I liked every field. And when I was eleven, I decided I should pick one subject that I liked and convince myself that that was who I was and that's what I would do and do it seriously and not do everything. And I said, well, why not mathematics? It's fun. And I started becoming a mathematician when I was eleven. And a year later, I was a mathematician. I couldn't imagine doing anything else with my life. Of course, I was still just a child, but I told myself that's what I want to do. So it was, in some sense, a conscious decision. Probably mathematicians have maybe favorite equations. Do you have one? Well, certainly not an easy one. My favorite mathematicians, like Euler, is a big hero of mine and several others. And of course, they have equations that I particularly love because it's Euler's discovery. If I said one single equation, but it's a very boring choice because every mathematician and physicist has seen it, it was Euler's great discovery that if you add up one and a quarter and a ninth and a sixteenth, so one over every square, then that infinite sum has a value and it's pi squared divided by six. That's an utterly marvelous formula. And actually, the whole field of multiple forms from some point of view comes out of that formula or is connected with it. So if I had to pick one, I would pick that one. So do you think it's one of the most, do you consider it one of the most beautiful equations? Oh, certainly, yeah. But I think it's not an original choice. It's a very popular choice for one of the most beautiful equations in all of mathematics. Because it puts together, it's completely amazing that you start with just the ordinary numbers, one, two, three, that you can count with your fingers. And then on the other side of the equation, you have pi and it was a complete surprise. Euler discovered it when he was a young man. The problem was very famous. People knew that that sum had a value. But they didn't know what it was. And when he solved it, he became immediately famous. So even at that time, it was a sensation. Because mathematics is sort of abstract, is considered abstract, how would you go about trying to get students more interested in the subject? Well, that's a hard question. I mean, a kind of an unfair answer would be if you're not already interested in mathematics, why are you sitting in a mathematics lecture even listening to it? Basically, you have to love it. Some people do. I did. Some people don't. And if it's not in you, like some people love music and some don't, you can't really talk somebody into it. But of course, if the love is there or some attraction, you can make it, I hope, much more attractive or much less attractive by bringing out the beautiful connections between different things. A little bit the human side. It's, of course, a very abstract field. But it's still what I love about mathematics, what I've always loved about it. You do it with only one piece of equipment. That's that one. You don't need machines. You don't need computers. You may need a computer to check something. You don't need a laboratory. You don't need accelerators. All you need is your head and maybe other people to talk to and share. So it's a very personal activity. Of course, it's abstract, but you're all alone in a room with a mouth problem, and it's you and it, and somebody's going to win. Usually it's the problem that sometimes it's you. And that's somehow very beautiful. And I think if one can convey that in a lecture to students, if it catches their fancy, then they're maybe meant to be mathematicians. And if it leaves them cold and they say, I just want to know what it's going to be on the test, then maybe they aren't going to be mathematicians. It's a question of love. It's not a question of technique, mathematics. You spoke about the human side of mathematics. How would you define that? Well, of course, it's the people who do it. I mean, a mathematical equation itself has no human side. In fact, mathematicians often say, and I agree that it's the most scientific of all sciences, because if you study, for instance, chemistry, well, it's the chemistry of our particular elements, but maybe in some faraway part of the universe, the laws of chemistry are different, or even the laws of physics could be different in a different universe or way back in time. But in biology, if there are other planets with animals and so on, they will be completely different. So mathematics is the only science which is utterly basic. So in that sense, it's not abstract. It's the real world, but it's this very abstract world of thoughts. I think I've wandered away from your question, actually, my enthusiasm. I'm not sure if I'm answering what you asked. But it's a nice concept. My question was the human side of mathematics. Well, that's exactly so. In that sense, mathematics is not at all human. You're studying something which not only is not if you study political science, that's a completely human thing, or economics. Biology already isn't physics much less, and mathematics not at all. But it is very human because to do mathematics, you need other people to talk to. Nobody can do mathematics in a vacuum, maybe for six months, but not permanently. You need people to try your ideas, hear their ideas discussed. You can read, of course, but it's sort of a communal thing. And mathematics has been built up by many people over the centuries by discussion, and you have to build on what other people do. Of course, that's true in every science. But in science, a new discovery may not be made by human. It may be made by an accelerator or a telescope. But in mathematics, every discovery of everything was made by some person who suddenly realized, aha, it's like that. And so in that sense, the same as I was saying before that you're alone with the problem, it's between the human mind and something very abstract. There's nothing in between. So in that sense, it's very direct human activity. For students, especially for students coming from developing countries and who want to pursue mathematics as a career, what kind of advice do you have for them? Well, I mean, one thing is, of course, I already said. I mean, the beauty of mathematics as a special field is that it is something that doesn't require a lot of apparatus. And therefore, one advice as well, you're making a good choice, because mathematics can be pursued in countries that don't have the money to have a laboratory like CERN or a huge spaceship or something. It's something you can do. You do need people, so you have to be able to travel. But you can do a certain amount at home with the internet. You do need human contact. You can't learn it all by yourself. So in that sense, it's a very good choice. It's also, I mean, many people, more in developing countries, but also in other countries, study mathematics and end up not pursuing an academic career, but becoming a work in a computer company or becoming an administrator or working in a big, huge company at a high level or maybe becoming a minister. So they may do something very different. And especially in developing countries, they don't have the luxury of letting many of their best brains be doing something very abstract like number theory. They need to build up the country. Very often people later turn to something else. Then the years studying mathematics are not wasted, because I believe and many people believe that it's one of the best preparations for solving problems in everyday life. So for instance, in Germany, I know that big companies, not just computer companies, but companies doing something completely different, if they're looking for high level people to employ, they'll often take a mathematician above somebody with the training, with the specific training, because they know in two or three years he'll have figured out those things, but he'll have a much more trained approach to how to actually solve problems. And that's something you can only learn in the years as a student and that mathematics really teaches, I mean, studying mathematics teaches you. So in that sense the advice is mostly that it's, I think, a very good choice. And the other general advice for any young person is, maybe in every science, I think one should have a dream. One should have one particular thing that may change. Ten years later you might have another one. But not just I solved this problem because somebody gave it to me, but really a picture. What I want to do is understand this. I've learned about it, I've read it, and I'm really fascinated. That's what I want to understand. So the extreme example I mentioned in my first lecture two days ago was Andrew Wiles, whom I know well, he's a good friend, and he told me that it's been written in many books, interviews. When he was eight years old he learned about Fermat's Laus Theorem, and he became a mathematician because that's what he wanted to do. Well, for the rest of us that wouldn't be a very sensible choice because it's too hard. But to have a goal and to really feel a particular thing is I think even at the beginning of your studies it's very important. Even if it changes later, that's what I want to learn. That's where I'm going because otherwise it's such a big field you get lost easily. Now you have been at ICTP for quite some time and you are also the distinguished staff associate here. How has your experience here been so far? Well, I haven't yet really been here for some time. I've been here many times over the last four or five years as a visitor. And starting last September I now am attached to the institute as a staff associate. It's a so-called distinguished staff associate. I'm very happy about it. But I spent then two months and now I'm here for a week and the idea is I'll spend a considerable portion of each year at least many weeks. And I'm looking forward very, very much to a prolonged association with the institute. It's an utterly marvelous place. I hear that from everybody else who comes here. It's a place one falls in love with both because of the atmosphere. It's very warm, accommodating and also the mission that there is this idea that we're trying to do very good signs but we're also trying to make sure that it's not just for us or for the rich people of the rich countries of the world that it's somehow a global effort and they don't just say it, they really do it here. And you're very aware of it that that's important and it somehow changes everything it makes. You feel that it's a very nice place but it is a very nice place anyway in every respect. And of course Trieste also is a fantastic place. Professor Zagir, thank you very much. Thank you, Nisha.