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# Maryna Viazovska, mathematician: Imagining a world in eight dimensions is ‘bad for your health’

## The Ukrainian researcher has won the Fields medal, the pinnacle of mathematics, after demonstrating the best way to stack spheres beyond three-dimensional space

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 in such a way that they took up as little space as possible. For centuries, some of the best mathematicians were crushed by this problem, until, in 1998, it was shown that the ideal way was to stack oranges in a pyramid.

In 2016, a Ukrainian woman, Maryna Viazovska, crushed the devil again. She discovered the best way to stack spheres in eight dimensions and, later, in 24 dimensions. On July 5, 2022, Viazovska became the second woman in history to win the Fields Medal, the most prestigious award in mathematics, which is given out every four years.

The researcher was born in Kiev 37 years ago. Her parents and grandmother still reside in the Ukrainian capital. When Vladimir Putin invaded Ukraine in February, Viazovska, a professor at the Swiss university École Polytechnique Fédérale de Lausanne (EPFL), was suddenly unable to think about numbers.

“It was a shock that something like this could happen. But I understand that you don’t get anywhere 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,” she told EL PAÍS in a video call from Switzerland.

Question. How do you stack oranges in your kitchen?

Answer. I don’t usually have that many oranges – my kids eat them right away. The problem isn’t stacking them; the problem is replacing them as soon as they run out [laughs].

Q. It’s hard to imagine a world in eight dimensions or in 24. Are you able to?

A. I don’t try to… I think it’s very dangerous and bad for your 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 into them. These coordinates can be represented as points in an 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.

Q, When you say that it’s dangerous to imagine a world in eight dimensions, is that just a joke, or can a person get lost trying to imagine such a multidimensional world?

A. 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 dangerous experiments.

Q. The problem regarding what is the best way to stack spheres is very simple to formulate, but very difficult to solve. Are there more problems like this that you want to face?

A. There are many problems in number theory [the branch of mathematics that studies the properties of numbers] with very simple formulations. I think that solving just one of these problems over a lifetime is something exceptional.

I’m now 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 math that was done in the 19th century

Q. Solving some mathematical problems requires decades or even centuries.

A. Yes, it happens with many important problems in pure mathematics, but luckily not always.

Q. You claimed, after receiving the Fields Medal, that real-life applications for your work could come within a century.

A. It was a bit of a metaphor, but it is true that we are still taking advantage of math that was done, for example, in the 19th century.

Q. The author of the sphere-stacking problem – the astronomer Johannes Kepler – actually published his laws of motion of the planets at the beginning of the 17th century. Almost four centuries later, humankind sent spaceships to some of them.

A. This is often how science works.

Q. What can be the applications of knowing how to stack spheres in eight dimensions or in 24?

A. What is probably most 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 idealized, but the real world is full of other important geometric optimization problems [procedures to minimize the energy exerted by a system, for example], even if they are uglier. One of the collateral results of my work is the construction of a kind of magic function, 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.

Q. What type of signal-processing?

A. For example, this videoconference is the result of image and sound compression. These signals are compressed in the computer, converted to 1s and 0s [the binary code used in computing], 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.

Q. The Ukrainian mathematician Bogdan Rublyov has suggested that you did not win the Fields medal in 2018 due to pressure from Russia. Do you believe this to be true?

A. I don’t know anything about that. I hope not. I hope that the committee chooses the winners based strictly on mathematical criteria.

Q. What would you say to Vladimir Putin if you were in front of him?

A. I wouldn’t want to have a face-to-face encounter. And I don’t think there’s any point in talking to him. Many European presidents and prime ministers 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 to the people of Russia. I 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.

Q. Getting back to math: you are the second woman to win a Fields medal since the award’s inception in 1936. There have been about 60 male winners and only two females. Why?

A. 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.

Q. Is there sexism in mathematics?

A. 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.

Q. You have an interesting background. You were born shortly after the Chernobyl disaster. And the Soviet Union fell apart when you were six...

A. Yes, the Chernobyl accident had a big impact for everyone in Kiev, 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 – we lived there for several months with relatives. My father and grandfather, like almost all the men who lived in Kiev at that time, had to participate in the cleanup, in the fight against the consequences of the explosion. My grandfather had to go to Pripyat [the ghost town in the Chernobyl exclusion zone] to retrieve some documents, because the city had been emptied of people, but some important papers had been left behind. Staying in the city for a while was risky, because people received large doses of radiation, so a lot of people went, but only for short periods of time. They would go for a few hours, collect what they needed and return.

The factory where my father worked – an aircraft production plant – also made cleaning vehicles. He had to go to a washing station to clean the cleaning vehicles 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, though, he only had to clean a few, so my father didn’t get too much exposure to radiation.