Until recently, only a small group of people knew who Alessio Figalli was (Rome, 1984). Its trade consists in solving problems of calculating variations and equations in partial derivatives. Today this mathematician, of quiet and close manner, that the mathematical outreach magazine Quanta in an article defined as "tall, fit and stylish"), enjoys an unusual fame among his co-workers.&
In 2018 he was awarded, along with three other mathematicians, the most quoted award in the mathematical world: the Fields Medal, a recognition that the International Mathematical Union confers only once every 4 years from 1936 (with an interruption until 1950) to mathematicians under 40 years old. In total there are only 60 mathematicians who can boast of this recognition, among which only one woman: the Iranian Maryam Mirzakhani.
Figalli, professor at ETH Polytechnic in Zurich, visited Barcelona on the occasion of the ceremony organized by the Polytechnic University of Catalonia (UPC), which has awarded him doctor honoris causa last Thursday. With his usual humility, he said that that day was celebrated, more than himself, "the world of mathematics" and his successes in society.
"There are a lot of stereotypes about mathematicians," he says, "but we're not all the same. The Medal has made me better known, it's true. Not following stereotypes is positive because it helps remove that wrong, harmful image that you can only be a mathematician if you're weird. Many people have the image of mathematicians like Nash from the movie A wonderful mind or R.m.nujan, who with the 5 years solved I do not know what problem. I did a humanistic high school without any special contact with math before college. It is true that great mathematicians such as Terence Tao [Medalla Fields in 2006] or Akshay Venkatesh [also Medalla Fields in 2018] started university very young, but I like to think that you can have a normal life and succeed."
Math of math helps us reason and is an excellent exercise to stimulate creativity and imagination
Question, What should the school teach about math?
Answer. It is clear that mathematics helps us to reason and is an excellent exercise to stimulate creativity and imagination. What often happens is that in school we are not taught to combine different concepts. In addition, the problem is that, if you do not study for one time, it is not easy to follow, while in other subjects you can avoid the gap. Therefore, it is important to repeat the key concepts a lot. On the other hand, we also have to talk about applications. Many school programs make monstrous and complicated calculations on topics that have already become obsolete in mathematical research, when you could invest your time in giving some more interesting advanced math elements. For example, use the concept of congruences to talk about RSA cryptography algorithms. Everyone can understand that multiplying two prime numbers is easy, and factoring is much more complicated, and on this is based cryptography. Or perhaps explain a very simplified version of the Markov chains [a special type of statistical process], which explain Google's mathematics. Or that Whatsapp messages are based on the sound being an overlay of fundamental frequencies that are transformed thanks to Fourier's analysis in digital signal. Mathematicians working in spaces of 100 dimensions are no crazier than anyone who takes a photo with the mobile, which is an overlay of 8 million pixels, each with its value. When we apply a filter to post it to Instagram we work in an 8 million dimension space. So the concept of "many dimensions" is not so abstract! Without going into the details, it is worth teaching that not everything is magical, that although I will not become a scientist, I can understand what is behind things.&
P. Which part of your work do you like best and which less?
Mathematicians don't need tools or a place to work. That's good and bad at the same time: it's hard to get an idea out of your head, our work always accompanies us
R. As an academic, my great privilege is that I have a lot of freedom to work on the problems I love most. And this is critical to research. All great revolutions come from creative thinking with no deadlines. Also, I like the exchange of ideas, and in general working with other people. Perhaps the hardest part of our job is that you can never completely disconnect. Mathematicians don't need tools or a place to work. That's good and bad at the same time: it's hard to get an idea out of your head, our work always accompanies us,
P. How is mathematical research in the world doing right now?
R. In general, research is going very well in many countries. Italy has a long tradition and remains strong. Switzerland, like the US, still imports brains. In Zurich, 70% of teachers are foreigners. Spanish mathematics is growing a lot in recent years. Society is changing and mathematicians are one of the most versatile and sought after professionals. We are few, we know how to think and reason, we know how to face problems creatively and we learn fast. Companies like this. They are realizing the importance of mathematics and that is positive: the more they ask for mathematicians, the more we have to train.
Society is changing and mathematicians are one of the most versatile and sought after professionals. We are few, we know how to think and reason, we know how to face problems creatively and we learn fast
P. Talk about creativity, a term we don't usually associate with mathematicians.
R. When you study a problem, you have to abstract the concepts you know from the formulas that allow you to interpret the world. And sometimes you have to be creative in this abstraction. An example that fascinates me is that of imaginary numbers: i is equal from minus 1. It seems straight out of the joker, and it turns out it's central to math and physics, which are based on these numbers. At one point, someone came up with the case to introduce them to solve polynomials in general. This is also imagination, giving a name to something that appears and then realizing that a world is opening up. Sometimes you have to imagine where you want to go and invent math to get there, as happened with general relativity or quantum mechanics. I like this creativity, and I like to live in a world regulated by formulas. It gives me peace of mind, it amuses me,
P.&What problems would you like to see a solution?
R. Obviously, there are very famous problems such as Riemann's conjecture, Navier-Stokes's and many other "millennium problems". I'm fascinated that they exist, even if I haven't taken care of them. The point is not the result, but what procedure will have to be invented to solve them. As happened with Fermat's famous last theorem: Andrew Wiles developed to demonstrate it a beautiful mathematics, very important to the scientific community. Today, after years of optimal transport, I am especially interested in problems of free borders, such as when the ice melts in the phase transition. In this, great mathematicians such as Xavier Ros-Oton and Joaquím Serra, in Barcelona, have been working in my team for years. These are very rich problems, where there are many mathematics, some of which we are still developing,