The American mathematician Charles Fefferman says that facing a complex problem is like playing chess against the devil. In 1611, the German astronomer Johannes Kepler started one of these devilish games. The challenge was to figure out the best way to stack spheres, whether they were cannonballs or orange ones, in such a way that they took up as little space as possible. For centuries, some of the best mathematicians of humanity were crushed by the devil, until in 1998 it was shown that the ideal was to stack oranges in a pyramid. In 2016, a then 31-year-old Ukrainian woman, Maryna Viazovska, crushed the devil. Outgrown three-dimensional space, she discovered the best way to stack spheres in eight dimensions. And, a few days later, in 24 dimensions. This July 5, Viazovska became the second woman to win the Fields medal, one of the pinnacles of mathematics.
The researcher, born in kyiv 37 years ago, has her parents and grandmother in the Ukrainian capital. When Russian despot Vladimir Putin decided to invade Ukraine in February, Viazovska, a professor at the Federal Polytechnic School in Lausanne, Switzerland, became a person unable to think in numbers. “Was a shock something like that could happen, but now I understand that you don’t get anything by not working, so I’m back to math. In addition, mathematics is a refuge from real life, from the bad things that happen in real life, ”he says by videoconference from the Swiss city.
Ask. How do you stack oranges in the kitchen?
R. I don’t usually have that many oranges, my kids eat them right away. The problem is not to stack them, the problem is to replace them as they run out [risas].
P. It is difficult to imagine a world in eight dimensions or in 24. Can you?
R. I do not try, I think it is very dangerous and bad for health. For mathematicians, the number of dimensions is simply the number of coordinates. Imagine an Excel file with eight cells and you enter eight numbers in them. These coordinates can be represented as a point in eight-dimensional space, but I don’t think of it as a physical space where I can be present. I see it as a row in an excel table, nothing more.
P. When you say that it is dangerous to imagine a world in eight dimensions, is this just a joke or can a person get lost trying to imagine such a multidimensional world?
R. It was a joke, but I wouldn’t try it. I think that, very often, our mental health is more fragile than we think. So I prefer to refrain from doing dangerous experiments.
P. The problem of what is the best way to stack spheres is very simple to formulate and very difficult to solve. Are there more problems like this that you want to face?
R. There are many problems in number theory [la rama de las matemáticas que estudia las propiedades de los números] with a very simple formulation, but I think that solving just one of these problems in a lifetime is something exceptional. Now I am working on problems that are not as well known and attractive to the general public, but are important for the internal structure of number theory. Choosing the problems you want to face is an art. You don’t have to choose them just because they are attractive or look pretty, you also have to take into account if you can contribute special knowledge to solve them.
We are still tapping into the math that was done in the 19th century
P. Solving some mathematical problems requires decades or even centuries.
R. Yes, it happens with many important problems in pure mathematics, but luckily not always.
P. You claimed, after receiving the Fields Medal, that the applications of your work could come within a century.
R. It was a bit of a metaphor, but it is true that we are still taking advantage of the mathematics that were done, for example, in the 19th century.
P. The author of the sphere stacking problem, the astronomer Johannes Kepler, actually published his laws of motion for the planets at the beginning of the 17th century, and almost four centuries later mankind sent spaceships to some of them.
R. This is often how science works.
P. What can be the applications of knowing how to stack spheres in eight dimensions or in 24?
R. What is probably useful are the methods we developed to solve this problem. It’s hard to say what the practical application is of knowing the best way to stack spheres. This problem is very special, very symmetric, very idealized, but the real world is full of other important geometric optimization problems. [procedimientos para minimizar la energía de un sistema, por ejemplo]even if they are uglier. One of the collateral results of my work is the construction of a kind of magic functions, which I hope can be used in signal processing problems. It’s like we have a new medicine. Now you have to find the disease to use it on.
P. What kind of signal processing?
R. For example, this videoconference we are in is the result of image and sound compression. These signals are compressed in the computer, converted into ones and zeros [el código binario utilizado en la informática], are sent down one channel and decoded at the other end. Our results are potentially useful for signal processing in all kinds of communications, but we’ll have to wait for some engineer to read my work, get inspired, and find a real application.
We will have to wait for some engineer to read my work, get inspired and find a real application
P. The Ukrainian mathematician Bogdan Rublyov has suggested that you did not win the Fields medal in the previous edition, in 2018, due to pressure from Russia. Do you believe it too?
R. I don’t know anything about that, I hope not. I hope that the committee chooses the winners with a strictly mathematical criterion. I have no reason not to think so.
P. What would you say to Vladimir Putin if you were in front of him?
R. I don’t want to have it face to face. And I don’t think there’s any point in talking to him. Many European presidents, prime ministers and political leaders have spent hours and hours talking to him and there seems to be no progress. If I had to say something to someone it would be the people of Russia. He would tell them that what Russia is doing to Ukraine is horrible, evil, and that they need to stop it. Saying this to Putin would serve no purpose. Putin already realizes how evil and destructive his actions are.
P. Going back to the math, you are the second woman to win a Fields medal since the inception of these awards in 1936. There have been about 60 male winners and only two females. Why?
R. I don’t know, there are probably many reasons. I hope this changes in the future. There are more and more women in science and mathematics. I hope this trend continues and in the future we will see more women among the Fields Medal winners.
P. Is there machismo in mathematics?
R. Sexism exists in our society, and the mathematical community is part of society. Anything bad that exists in society will exist in the mathematical community, but I don’t think the mathematical community is particularly bad in this regard. There is a will to correct this situation and I hope it will be successful.
Sexism exists in our society, and the mathematical community is part of society
P. You were born shortly after the Chernobyl disaster. And the Soviet Union fell apart when you were six…
R. Yes, the Chernobyl accident had a great impact on everyone in kyiv, because it is less than 100 kilometers from the nuclear power plant. I was a year and a half when it happened, so I don’t remember, but I know what my parents and grandparents have told me. I was taken to Moscow, which was considered a safe place, and we lived there for several months with relatives. My father and grandfather, like almost all the men who lived in kyiv at that time, had to participate as liquidators, those in charge of fighting against the consequences of the explosion. My grandfather had to go to Pripyat [la ciudad fantasma en la zona de exclusión de Chernóbil] to rescue some documents, because the city had emptied of people, but some important papers had remained there. Staying in the city for a while was risky, because people received large doses of radiation, so a lot of people went, but for a short time. They would go for a few hours, collect what they needed and return. The factory where my father worked [una planta de producción de aviones Antonov] also provided liquidators. He had to go to a washing station to clean the cleaning vehicles themselves that got dirty in Chernobyl. My father was very angry that he had to go there, because it seemed like a very dangerous place, full of radioactive vehicles. In the end he only had to clean a few, most of which ended up in another washing station. So my father didn’t get too much exposure to radiation.
P. Do you hope to return to kyiv soon?
R. Yes, of course, it is my city. I have lived in many places in my life, but I always think that kyiv is my home. I would like to go in the summer, but I haven’t planned it yet. Making plans in Ukraine now is not easy.
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