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Emmanuel Giroux (Dijon, 1961) is a French mathematician who is an expert in a branch of geometry called contact topology. He suffers from Marfan syndrome , a rare genetic disease that affects the connective tissue. For this reason, he has been blind since he was eleven years old, a condition that has not prevented him from making a name for himself in the exact sciences.

Giroux baffles his colleagues by the way he operates in his field, without writing down equations on paper . "You can write in Braille, but that is much more complicated," he assured this medium in an interview that took place during the holding of a congress at the Institute of Mathematical Sciences of Madrid (ICMAT). His refuge is geometry, which he investigates by drawing the space in his head with a complicated mental scheme.

Giroux co-directs the International Mixed Unit of the National Center for Scientific Research (CNRS) of France and the Center for Mathematical Research of Quebec (Canada).

Why is math so special to you? What I like about this job is that you have great freedom. You can do math with almost nothing. Walking down the street and thinking about your favorite objects. Anywhere. Sitting a coffee. You hardly need anything. It is something that makes you really free. It is very creative work. Sometimes, of course, you need to read books and articles. You have to read what others do because mathematics is a collective task. You add your work to that of others. It is like building something together, with a very specific and personal point of view of things. There are bright, strong people who make you think they are better than you. You have to discover what you can contribute in this construction of mathematics. Therefore, it is something that gives you the possibility to express your own personality, to create something within this collective work. Do the theorems, the formulas, not limit that creativity? Of course, it is not about doing anything and pretending that's math. In mathematics there are very strict rules. And that's what I like: how to see, how to feel, how to inscribe yourself within this process, which is a creative process. You have modified the famous phrase of Antoine de Saint-Exupéry: "In geometry, you only see with the spirit, the essential is invisible to the eyes. " Is this your secret to doing math without seeing them? This is a derivation of Antoine de Saint-Exupéry's phrase he wrote in The Little Prince. The original phrase says: "It is not seen well but with the heart, the essential is invisible to the eyes". It is a play on words that I made to translate into geometry what you can only see with your mind. I use it because many people ask me why I work in geometry and not in other areas of mathematics. I am blind and people think that the fact that I dedicate myself to geometry is a paradox when you cannot see. And the truth is, this is the only kind of math that a blind man can do. Why is geometry feasible for a blind mathematician? There have been several blind mathematicians in history and they all devoted themselves to geometry. In other types of math, like mathematical analysis or algebra, you mostly work with equations that you have to write. You write formulas that go from your mind to paper. You write them, you see what you are writing, you realize something and your mind makes you think how you can transform that equation. The formula manuscripts guide your thinking. You go back and forth between the paper and your mind. And you cannot do this when you are blind. You can write in Braille, but it is much more complicated. When you do geometry, there are also equations, but basically what you do is work with a series of concepts for which you create a mental image. And you can manipulate these objects only in your head. This could be different if it's someone who was born blind or lost their sight afterward, but I don't know. I have not been blind from birth. I lost my sight when I was 11 years old. How do you draw these geometric objects in your mind? You rely on your own intuition. But when you do math you follow very strict rules. I do not know how to say it. This is the most difficult question you could ask me. (Laughs) You solve really complicated problems. I would like to understand the process. How does a blind man see the mathematics in his head and how is the mental effort that you make, without using formulas on a paper? In geometry you try to investigate the shape of objects. What is certain to me is that, when I think about these objects for a time, in the end they become very concrete. Some of these objects are the ones I live with. And this is closely related to what we have come to talk about at this congress. We study objects that we know perfectly locally. If you look at Earth. When we look at it it looks flat and you can determine the position of anything around you using two coordinates. But what happens when you go to infinity? Are you reaching the end of the Earth? How is it? Is there a great cliff that you could fall into empty space on? This is not so because the Earth is round, it is a sphere. I understand that these questions appear when adding dimensions. This is how you consider things when they are not two-dimensional. Now you can imagine a different number of objects and different observers. Each observer can determine the position of anything with a collection of coordinates. But each observer cannot see very far, they have only one domain around which they can see these objects. All observers together do see the whole world. The question is then: what is the shape of that space? These are the kind of questions that are solved in geometry. At the moment, it seems simple. Geometry always starts out simple and has an intriguing ending. When does it get complicated? When the third dimension enters. In the universe you can put someone on a point and if this person looks around they can determine the position of anything with three coordinates. But what is the global shape of the universe? In geometry we try to understand what are the possible forms of this universe. When you consider the third dimension, listing all of these possible shapes has been a success for math. It was the reason why Grigori Perelman was awarded the Fields medal, here in Madrid in 2006. [Perelman rejected this award and never received it]. His research, the contact topology, goes even further. What exactly is it? What I have explained before is based on understanding the possible global forms of objects, considering them as empty. What I do is try to understand the same thing but in species that have matter and how is the distribution of matter, which is given by the laws of physics. These concepts are somewhat abstract. What applications would you say they have? They have no direct applications. Nor is it the goal. Is it useful to know that the Earth is round? For people who do not move from their country, knowing it does not change anything. Was it helpful to know before the planes existed? Still, I think it is important. It is not about studying abstraction as such. Geometric structures are related to physics. In mathematics we produce models that can be useful for physics or for other sciences and we push these concepts to the limit, which in some way helps to understand the world. What is your goal in research? Keep understanding things. Keep learning. I find it difficult to explain my work to a general audience, but there is one thing I really like: explaining things to students and not just those who do math. Tell them something they don't know and help them in their first steps in research. 

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