 My name is Hugo Duminil-Copin and I'm a professor of mathematics at the Institut des Hauts études scientifiques in Paris. My specialty is mathematical physics, which is a study of physical phenomena, but from a mathematical side. And what I do for a living is using probabilistic techniques to study this physical phenomena. I have always been interested in mathematics, but I cannot say that I was raised to become a mathematician. My parents always wanted that I would have a training in very diverse things like sports, music, and science was one of these things. Actually, at the origin I was rather interested in astronomy rather than math. I was part of a club when I was 10 years old and I loved it. But then I realized that maybe this was not exactly the type of science I wanted to do. And I kind of tried to go in the direction of mathematics and physics, which were the two things that I loved. I love physics because it was kind of the study of the world of what is surrounding us. And I love mathematics because there is this kind of beauty when you end, you have the solution to a problem. There is something very pure about it that was very satisfying for me. So I had these two loves when I was younger and it took a very long time before I actually decided to go for mathematics instead of physics. It was not before maybe the second or third year of my university studies that this happened. The reason why I got decided in mathematics was probably that for me the need to have this perfect answer to a problem was stronger in some sense. That's the curiosity for understanding what is around me. I preferred to be focusing on something where I'm really satisfied with the proof rather than being too diverse and maybe have only partial answers. So when I entered Ecole Normale Supérieure in Paris, I had to decide between math and physics and at this point in some sense it was clear to me that I would be needing this math purity in some sense. And I decided to go entirely for math. Interestingly, recently I spoke with my father who explained to me that he never wanted to consider me as a special kid, like a genius or anything like that, but that he loved to train me on something that I remember vividly, which was that he liked to give me mathematical puzzles that we would try to solve together. And I love this kind of shared time with my father. My father is not at all a mathematician, he's a sport teacher, but he loved to have, he had this curiosity for this like solving problem type of reasoning. And he liked to share it with me. So I remember this and probably it had a big impact on my future way of looking at things and looking at science. So I entered Ecole Normale Supérieure, which is a classical school to become a researcher in France. And there I had to choose between math and physics, so I chose math. And when you do this choice, you are facing very general teaching in mathematics, like you still get classes from all sides of it. So why did I choose one area rather than another one? Well, sometimes things are just, you know, getting down to small details. And in this case, it's a fantastic teacher that I had called Jean-François de Gaulle, who gave this absolutely marvelous class on probability. He really felt like the whole theory was like painless, like everything was getting so smooth and so naturally in place, like completely felt in love with this area. So I decided to do a master in probability. And in order to do that, I went to the best place around Paris, which was Orsay, so Paris-Saclay master classes. So I went there and we got these classes in probability with a very big inclination for, very strong inclination for what we call statistical physics. And this was like perfect because this reconciled my will to have this pure solution to problems coming from math with my interest for physics, because this is exactly an area where math and physics talk to each other very intensively. And there, among the different classes that were all super interesting for me, so you already feel that you are in the right place in some sense, there was one class that completely stood out. It was given by Wendel and Werner, and it was a class on percolation and the easing model. And it was really like targeted to give us an idea of how physics intuition can become a mathematical argument. And for me, it exactly matched my way of looking at mathematics, my way of thinking about mathematics. So from day one in this class, I knew that this was what I wanted to do. Funnily enough, the first conjecture that Wendel and Werner mentioned in his class, it was the old conjecture from the 80s. Well, it happened that a few years later, we actually solved this conjecture with my advisor at the time, my PhD advisor. And this was kind of a very cool circle that got closed that this problem that was still open when I was a student became one of my areas of research. And one of my favorite research problem. So after I completed my master, I had to choose where to do my PhD. And the natural thing was to do it with Wendel and Werner. But at the time, he explained to me what would end up being one of the greatest advice that was given to me, that there was this researcher in Geneva called Stanislaw Smirnov, and that he was really the guy moving lines at the time. So he sent me to see him and we immediately loved each other and I did my PhD with him in Geneva. And it was a very successful PhD, so I'm very thankful to Wendel and Werner for this advice that truly changed the course of my career. After being a professor for five years in Geneva, I got a position of permanent professor at the Institute of Institute of Scientific where I arrived basically in 2016. So for me it was a funny story because I was raised in Bure-sur-Vivette. So I from day one knew the area and my mom was living like 200 meters from the Institute and it was kind of coming back home. But at the same time, it was also discovering a new place and kind of intimidating one because there is this whole history of the former professors of the Institute that were really like extremely important members of French mathematics and French history of mathematics in the 20th century. So for me it was intimidating especially that I was coming with a new trend. I was the first professor in probability, so I had to make my probability part of the history of IHES. But it was very exciting for me to try to do that and to kind of bring something new to the Institute. What the Institute brings you as a researcher is very subtle. You see when you are in a standard university, the main core of the university is to teach students. That remains its main duty. So it doesn't necessarily mean that you have a lot of teaching but the whole thing is organized around teaching. At IHES, teaching is subsidiary to research. The Institute is made in such a way that people should do research and should be in the best possible position to do research. And that changes everything because everything is organized around this target which is breaking new grounds in science, in my case in mathematics. And I felt it instantly. I could have full freedom. My days were free to really think. The environment is such that it makes you very creative because it's beautiful, it's peaceful. There is enough activity to still foster your imagination. So this was immediate and the two first years at the Institute were probably the most productive years of my short career. And the other thing which is amazing about the Institute is that it gathers many forces, many brains from all over the world. And for me it was very important because this is exactly the way I'm doing research. I want to be sharing my ideas with people. And here with the research program, the visiting program, which is a very big part of the DNA of the Institute, I could bring many collaborators, new people that I didn't have the occasion to discuss with yet, and to bring all these people together and in some sense to shake everything. I mean not literally obviously, but to shake all of these to create new things with it. And that was a fantastic feeling. And I'm very thankful to the Institute for that and I hope that this part of the Institute will be kept for years and years because in my case it really completely changed the level of energy I had for research. So my area of research is called statistical physics. And the idea of statistical physics is to try to understand the behavior of a huge physical system but only having as an information the interaction between the small constituents of the system. So there are many physical phenomena that falls within the range of statistical physics but the one that I work the most on is called ferromagnetism. The idea is how do you explain why a magnet is actually attracted by a surface or a magnetic field or why it's not. And it's a very difficult question because if you look physically, a magnet in some sense is kind of made of a huge number of small constituents that we call dipoles. And the way these dipoles interact with each other is very complex. But what you can do is you can do a mathematical model. It's kind of a caricature of what is happening. And this caricature in the case of ferromagnetism, it's called the easing model. So what is the underlying idea in the easing model? Well, imagine a huge system of dipoles. It's very difficult to understand exactly the state in which the dipoles are. So instead of trying to do that, you are going to simplify your task by only looking at the probability in some sense you look at what are the typical states of the system. And by looking at probability instead of looking at trying to determine explicitly all the details of your system, you simplify your task as a mathematician greatly. Now, once you have said that, you have done only the first step towards a very long trip. Because it's not that if you just look at probability, things become just trivial. They are still complex. And there are degrees of complexity. So for years and years and years, there have been thousands of papers that were dealing with two-dimensional magnets, if you want, two-dimensional easing models, which is not the dimension of real magnets. Our magnets are three-dimensional. So in recent years, I tried with my co-authors to study three-dimensional magnets. That's where the second area of my research appears into the game, which is percolation. Percolation has nothing to do with ferromagnetism. It's actually a theory of how water flows through porous medium, like imagine a porous stone. And it's a theory, it's a mathematical model again, probabilistic again. This time, you kind of modeled your stone as a random graph. And by using the theory that we developed for percolation, we could prove new things on the easing model. It's a typical example of what you do in mathematics, which is building a bridge between two areas that before that were completely disjoint. The story of blackboards and mathematicians, you know, it's something special. I mean, people try to change blackboards into whiteboards into plastic or glassboards, and nothing works as well as the blackboard. And I think one of the reasons for it is that there is no other thing that you can erase as easily as a blackboard. And I think it's one of the deep and most important things about blackboards is that it's a place of complete freedom of creativity. And to have complete freedom, you should be allowed to make mistakes. And in some sense, you are with everybody. It's a big area, a big surface. So each one has his own space in some sense. You can write, you can come and erase what the other person wrote because you want to interact and change it into something else. It's a beautiful just area of pure freedom. And to my opinion, it was never, I mean, nobody found a better solution than blackboards. And I'm like very fond of all my blackboards. I don't give them names, but I could almost do it. Mathematical education is in some sense completely wrong on one thing, which is that it's teaching us that any tiny mistake is fatal. If you do math, you should have a result which is absolutely perfect, except that indeed the end product should not contain mistakes. But the process that is leading to this product actually is made of many mistakes. If you do not make mistakes, if you do not allow yourself to make mistakes, then you don't take the opportunities in the right way because sometimes it's just by pure luck you have an idea. And at first sight, it's not clear it's going to be the solution to your problem. So if you don't investigate and you don't allow the possibility that this is the wrong direction, you will never actually take the right one at the time where it will occur in front of you. And this is something that I think is not taught enough to youngsters is that, well, you know, try to solve your exercise, make mistakes. Sometimes you will actually find a solution which is not the same as one of your neighbour, and that's fine. And in my case, for instance, I'm a mathematician who makes tons of mistakes in the process of getting to the right solution. I'm not at all this type of person that just sees from miles away exactly the way of going somewhere. I'm kind of not trying all the directions and sorting out what is good from what is not interesting and making my understanding progress that way. So I think people should not be afraid if they are like that because, you know, I mean, it can lead somewhere. And I mean, I feel like I'm a reasonable mathematician. So making mistakes was not something that prevented me from doing what I wanted to do.